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PDF Document:Normal distribution,Probability Density Function(PDF),PDF:f(x)=(1/√(2*π*σ^2)*e^(-(x-u)^2/(2*σ^2))


DateFile NameSize(KB)MD5 Hash
2011/09/0120110901-001.pdf599359367ee307e0f31f9b01c8b0d733bc1

Keyword

Normal distribution,Probability Density Function(PDF),PDF:f(x)=(1/√(2*π*σ^2)*e^(-(x-u)^2/(2*σ^2))

Reference

[1]:NIST/SEMATECH e-Handbook of Statistical Methods:1.3.6.6.1. Normal Distribution
[2]:WIKIPEDIA:Normal distribution

Remarks

・PDF:Probability Density Function

PDF Document:Normal distribution,Cumulative Distribution Function(CDF),CDF:F(x)=1/2*[1+erf((x-u)/√(2*σ^2))]


DateFile NameSize(KB)MD5 Hash
2011/09/0120110901-002.pdf628b1f7288703bdaa813c1c79944ed59743

Keyword

Normal distribution,Probability Density Function(PDF),PDF:f(x)=(1/√(2*π*σ^2)*e^(-(x-u)^2/(2*σ^2))

Reference

[1]:NIST/SEMATECH e-Handbook of Statistical Methods:1.3.6.6.1. Normal Distribution
[2]:WIKIPEDIA:Normal distribution

Remarks

・CDF:Cumulative Distribution Function

PDF Document:Normal distribution,Percentage between standard deviation from the mean(u),F(x*σ+u)-F(-x*σ+u)





DateFile NameSize(KB)MD5 Hash
2011/09/0120110901-003.pdf337e7ac6a2825c2eb665ed4e9fbe535110b

Keyword

Normal distribution,Probability Density Function(PDF),PDF:f(x)=(1/√(2*π*σ^2)*e^(-(x-u)^2/(2*σ^2))

Reference

[1]:NIST/SEMATECH e-Handbook of Statistical Methods:1.3.6.6.1. Normal Distribution
[2]:WIKIPEDIA:Normal distribution

Remarks

・PDF:Probability Density Function
・CDF:Cumulative Distribution Function

PDF Document:Normal distribution,Hazard Function,h(x)=f(x)/(1-F(x)),u=0





DateFile NameSize(KB)MD5 Hash
2011/09/0220110902-001.pdf64910792c3c81f13d3f55e439a01f12d4a3

Keyword

Normal distribution,Hazard Function,h(x)=f(x)/(1-F(x)),u=0

Reference

[1]:NIST/SEMATECH e-Handbook of Statistical Methods:1.3.6.6.1. Normal Distribution
[2]:WIKIPEDIA:Normal distribution

Remarks

・PDF:Probability Density Function

PDF Document:Normal distribution,Cumulative Hazard Function,H(x)=-ln(1-F(x)),u=0





DateFile NameSize(KB)MD5 Hash
2011/09/0220110902-002.pdf4691aa9bb9e814dbe6714879a355da3f579

Keyword

Normal distribution,Cumulative Hazard Function,H(x)=-ln(1-F(x)),u=0

Reference

[1]:NIST/SEMATECH e-Handbook of Statistical Methods:1.3.6.6.1. Normal Distribution
[2]:WIKIPEDIA:Normal distribution

Remarks

・CDF:Cumulative Distribution Function

PDF Document:Normal distribution,Survival Function,S(x)=1-F(x),u=0





DateFile NameSize(KB)MD5 Hash
2011/09/0220110902-003.pdf6171cd6dd007554620c69f169112588b87c

Keyword

Normal distribution,Survival Function,S(x)=1-F(x),u=0

Reference

[1]:NIST/SEMATECH e-Handbook of Statistical Methods:1.3.6.6.1. Normal Distribution
[2]:WIKIPEDIA:Normal distribution

Remarks

・PDF:Probability Density Function
・CDF:Cumulative Distribution Function

PDF Document:Cauchy distribution,Probability Density Function(PDF),PDF:f(x)=1/(π*γ*(1+((x-x0)/γ)^2))





DateFile NameSize(KB)MD5 Hash
2011/09/0220110902-004.pdf793d4f3710558bc12045e7dcbc7d18a7b7f

Keyword

Cauchy distribution,Probability Density Function(PDF),PDF:f(x)=1/(π*γ*(1+((x-x0)/γ)^2))

Reference

[1]:NIST/SEMATECH e-Handbook of Statistical Methods:1.3.6.6.3. Cauchy Distribution
[2]:WIKIPEDIA:Cauchy distribution

Remarks

・PDF:Probability Density Function

PDF Document:Cauchy distribution,Cumulative Distribution Function(CDF),CDF:F(x)=1/π*arctan((x-x0)/γ)+1/2





DateFile NameSize(KB)MD5 Hash
2011/09/0220110902-005.pdf8544be6f4a4908648ccaeda0b5da83c764b

Keyword

Cauchy distribution,Cumulative Distribution Function(CDF),CDF:F(x)=1/π*arctan((x-x0)/γ)+1/2

Reference

[1]:NIST/SEMATECH e-Handbook of Statistical Methods:1.3.6.6.3. Cauchy Distribution
[2]:WIKIPEDIA:Cauchy distribution

Remarks

・PDF:Probability Density Function

PDF Document:Cauchy distribution,Percentage between F(x) and F(-x),(F(x)-F(-x))*100





DateFile NameSize(KB)MD5 Hash
2011/09/0220110902-006.pdf38397d1d8e0ed6da57d6b4b8b916b86b265

Keyword

Cauchy distribution,Percentage between F(x) and F(-x),(F(x)-F(-x))*100

Reference

[1]:NIST/SEMATECH e-Handbook of Statistical Methods:1.3.6.6.3. Cauchy Distribution
[2]:WIKIPEDIA:Cauchy distribution

Remarks

・PDF:Probability Density Function

PDF Document:Cauchy distribution,Hazard Function,h(x)=f(x)/(1-F(x))





DateFile NameSize(KB)MD5 Hash
2011/09/0220110902-007.pdf802a0d6ecd49742cd31f1cb8ea41cdbd197

Keyword

Cauchy distribution,Hazard Function,h(x)=f(x)/(1-F(x))

Reference

[1]:NIST/SEMATECH e-Handbook of Statistical Methods:1.3.6.6.3. Cauchy Distribution
[2]:WIKIPEDIA:Cauchy distribution

Remarks

・PDF:Probability Density Function

PDF Document:Cauchy distribution,Cumulative Hazard Function,H(x)=-ln(1-F(x))





DateFile NameSize(KB)MD5 Hash
2011/09/0220110902-008.pdf7460eeb45141da9dd642d07be896250fc43

Keyword

Cauchy distribution,Cumulative Hazard Function,H(x)=-ln(1-F(x))

Reference

[1]:NIST/SEMATECH e-Handbook of Statistical Methods:1.3.6.6.3. Cauchy Distribution
[2]:WIKIPEDIA:Cauchy distribution

Remarks

・PDF:Probability Density Function

PDF Document:Cauchy distribution,Survival Function,S(x)=1-F(x)





DateFile NameSize(KB)MD5 Hash
2011/09/0220110902-009.pdf84556dcfdf808451bb2424a8a0e4a78500d

Keyword

Cauchy distribution,Survival Function,S(x)=1-F(x)

Reference

[1]:NIST/SEMATECH e-Handbook of Statistical Methods:1.3.6.6.3. Cauchy Distribution
[2]:WIKIPEDIA:Cauchy distribution

Remarks

・PDF:Probability Density Function

PDF Document:Student''s t-distribution,Probability Density Function(PDF),PDF:f(x)=(1+x^2/ν)^(-(ν+1)/2)/(B(0.5,0.5*ν)*√ν)


DateFile NameSize(KB)MD5 Hash
2011/09/0520110905-001.pdf769867ba8b8182fa2965a7ab56a29c06545

Keyword

Student''s t-distribution,Probability Density Function(PDF),PDF:f(x)=(1+x^2/ν)^(-(ν+1)/2)/(B(0.5,0.5*ν)*√ν)

Reference

[1]:NIST/SEMATECH e-Handbook of Statistical Methods:1.3.6.6.4. t Distribution
[2]:WIKIPEDIA:Student''s t-distribution

Remarks

・PDF:Probability Density Function
・CDF:Cumulative Distribution Function

PDF Document:Student''s t-distribution,Cumulative Distribution Function(CDF),CDF:F(x)=Ix(ν/2,ν/2)=Bx(ν/2,ν/2)/B(ν/2,ν/2)


DateFile NameSize(KB)MD5 Hash
2011/09/0520110905-002.pdf856540d7dcbf65bcc046ed1ba57b4e2c1b1

Keyword

Student''s t-distribution,Cumulative Distribution Function(CDF),CDF:F(x)=Ix(ν/2,ν/2)=Bx(ν/2,ν/2)/B(ν/2,ν/2)

Reference

[1]:NIST/SEMATECH e-Handbook of Statistical Methods:1.3.6.6.4. t Distribution
[2]:WIKIPEDIA:Student''s t-distribution

Remarks

・PDF:Probability Density Function
・CDF:Cumulative Distribution Function

PDF Document:Student''s t-distribution,Critical t value,Degrees of freedom(ν)=n-1


DateFile NameSize(KB)MD5 Hash
2011/09/07Date20110907-001.pdf3282c8df2a070bc91b9ea2de28ce1f46f40

Keyword

Student''s t-distribution,Critical t value,Degrees of freedom(ν)=n-1

Reference

[1]:NIST/SEMATECH e-Handbook of Statistical Methods:1.3.6.6.4. t Distribution
[2]:WIKIPEDIA:Student''s t-distribution

Remarks

・Example:If population is normally distributed, when sample number(n. x1,x2・・・xn) is 20, unbiased variance(s^2) of sample is 5 and mean of sample(m) is 100, estimated mean of population is no fewer than 98.9535(=100-2.093*(5/20)^0.5), nor more than 101.0465(=100+2.093*(5/20)^0.5) with 95% confidence.・Unbiased variance:s^2=((x1-m)^2+(x2-m)^2・・・(xn-m)^2)/(n-1)・PDF:Probability Density Function
・CDF:Cumulative Distribution Function
・ν:Degrees of freedom
・n:Sample Number

PDF Document:Student''s t-distribution Critical Value Table. ν:Degrees of freedom





DateFile NameSize(KB)MD5 Hash
2011/09/0820110908-001.pdf826057f8d29e2f52ce788ad697fdc098bf

Keyword

Student''s t-distribution Critical Value Table. ν:Degrees of freedom

Reference

[1]:NIST/SEMATECH e-Handbook of Statistical Methods:1.3.6.6.4. t Distribution
[2]:WIKIPEDIA:Student''s t-distribution

Remarks

・Critical t-values in the table are calculated by the function "TINV" of Office Excel 2010.・Example:If population is normally distributed, when sample number(n. x1,x2・・・xn) is 20, unbiased variance(s^2) of sample is 5 and mean of sample(m) is 100, estimated mean of population is no fewer than 98.9535(=100-2.093*(5/20)^0.5), nor more than 101.0465(=100+2.093*(5/20)^0.5) with 95% confidence.・Unbiased variance:s^2=((x1-m)^2+(x2-m)^2・・・(xn-m)^2)/(n-1)・PDF:Probability Density Function
・CDF:Cumulative Distribution Function
・ν:Degrees of freedom
・n:Sample Number

PDF Document:F-distribution,Probability Density Function(PDF):f(x),f(x)=(df1/df2)^(df1/2)*x^(df1/2-1)/(B(df1/2,df2/2)*(1+df1*x/df2)^((df1+df2)/2))


DateFile NameSize(KB)MD5 Hash
2011/09/0820110908-002.pdf6564cedd72220a7c99ceae0897dc5ad7237

Keyword

F-distribution,Probability Density Function(PDF):f(x),f(x)=(df1/df2)^(df1/2)*x^(df1/2-1)/(B(df1/2,df2/2)*(1+df1*x/df2)^((df1+df2)/2))

Reference

[1]:NIST/SEMATECH e-Handbook of Statistical Methods:1.3.6.6.5. F Distribution
[2]:WIKIPEDIA:F-distribution

Remarks

・PDF:Probability Density Function
・CDF:Cumulative Distribution Function
・df1,df2:Degrees of freedom

PDF Document:F-distribution,Cumulative Distribution Function(CDF):F(x),F(x)=1-Ik(df2/2,df1/2). k=df2/(df2+df1*x)


DateFile NameSize(KB)MD5 Hash
2011/09/0920110909-001.pdf416268a7ba67cde458ba9c6b557309af7c0

Keyword

F-distribution,Cumulative Distribution Function(CDF):F(x),F(x)=1-Ik(df2/2,df1/2). k=df2/(df2+df1*x)

Reference

[1]:NIST/SEMATECH e-Handbook of Statistical Methods:1.3.6.6.5. F Distribution
[2]:WIKIPEDIA:F-distribution

Remarks

・PDF:Probability Density Function
・CDF:Cumulative Distribution Function
・df1,df2:Degrees of freedom

PDF Document:F-distribution,Lower Critical Value:F(x)=95%,F(x)=1-Ik(df2/2,df1/2). k=df2/(df2+df1*x)


DateFile NameSize(KB)MD5 Hash
2011/09/0920110909-002.pdf286feeab7f87057afcd32f5dec2e19b0ddb

Keyword

F-distribution,Lower Critical Value:F(x)=95%,F(x)=1-Ik(df2/2,df1/2). k=df2/(df2+df1*x)

Reference

[1]:NIST/SEMATECH e-Handbook of Statistical Methods:1.3.6.6.5. F Distribution
[2]:WIKIPEDIA:F-distribution

Remarks

・F-distribution is calculated by the function "FINV" of Office Excel 2010.
・Example:If there are two populations which are normaly distributed and independent of each other, when numbers of sample from each populations are 10 and 5 respectively,variance ratio of two sample, it is called F-value,is fewer than 4.735,then variances of two sample may be equal with 5% significance level.
・F(4.735)=1-Ik((5-1)/2,(10-1)/2)⋍1-0.05=0.95. k=(5-1)/((5-1)+(10-1)*4.735).
・PDF:Probability Density Function
・CDF:Cumulative Distribution Function
・df1,df2:Degrees of freedom

PDF Document:F-distribution.Upper critical values,Significance Level(α),Upper:0.1%, Middle:1%, Lower:5%,df1:Numerator degrees of freedom,df2:Denominator degrees of freedom





DateFile NameSize(KB)MD5 Hash
2011/09/1220110912-001.pdf3,9199ec3a9de1eff6219a1407fefb411db45

Keyword

F-distribution.Upper critical values,Significance Level(α),Upper:0.1%, Middle:1%, Lower:5%,df1:Numerator degrees of freedom,df2:Denominator degrees of freedom

Reference

[1]:NIST/SEMATECH e-Handbook of Statistical Methods:1.3.6.6.5. F Distribution
[2]:WIKIPEDIA:F-distribution

Remarks

・When both df1 and df2 are ∞, upper critical values is 1regardless of significance level .・F-distribution is calculated by the function "FINV" of Office Excel 2010.
・Example:If there are two populations which are normaly distributed and independent of each other, when numbers of sample from each populations are 10 and 5 respectively,variance ratio of two sample, it is called F-value,is fewer than 4.735,then variances of two sample may be equal with 5% significance level.
・F(4.735)=1-Ik((5-1)/2,(10-1)/2)⋍1-0.05=0.95. k=(5-1)/((5-1)+(10-1)*4.735).
・PDF:Probability Density Function
・CDF:Cumulative Distribution Function
・df1,df2:Degrees of freedom

PDF Document:Chi-Square Distribution,Probability Density Function(PDF),PDF:f(x)=e^(-x/2)*x^(ν/2-1)/(2^(ν/2)*Γ(ν/2))


DateFile NameSize(KB)MD5 Hash
2011/09/1320110913-001.pdf653e11f2212932b88bb627fc45d6641f950

Keyword

Chi-Square Distribution,Probability Density Function(PDF),PDF:f(x)=e^(-x/2)*x^(ν/2-1)/(2^(ν/2)*Γ(ν/2))

Reference

[1]:NIST/SEMATECH e-Handbook of Statistical Methods:1.3.6.6.6. Chi-Square Distribution
[2]:WIKIPEDIA:Chi-square distribution

Remarks

・PDF:Probability Density Function
・CDF:Cumulative Distribution Function
・ν:Degrees of freedom

PDF Document:Chi-Square Distribution,Cumulative Distribution Function(CDF),CDF:F(x)=γ(ν/2,x/2)/Γ(ν/2)


DateFile NameSize(KB)MD5 Hash
2011/09/1320110913-002.pdf736b69b30fc916d68eab5bb6750acf03c14

Keyword

Chi-Square Distribution,Cumulative Distribution Function(CDF),CDF:F(x)=γ(ν/2,x/2)/Γ(ν/2)

Reference

[1]:NIST/SEMATECH e-Handbook of Statistical Methods:1.3.6.6.6. Chi-Square Distribution
[2]:WIKIPEDIA:Chi-square distribution

Remarks

・PDF:Probability Density Function
・CDF:Cumulative Distribution Function
・ν:Degrees of freedom

PDF Document:Upper critical values table of Chi-square distribution





DateFile NameSize(KB)MD5 Hash
2011/09/1520110915-001.pdf99d72b7f8dc63c3b39794b99671d1afb85

Keyword

Upper critical values of Chi-square distribution

Reference

[1]:NIST/SEMATECH e-Handbook of Statistical Methods:1.3.6.6.6. Chi-Square Distribution
[2]:WIKIPEDIA:Chi-square distribution

Remarks

・Example:The following table shows population by age group and age structure of sample group.
AgePopulation(%)Sample(%)
10-98.677
210-199.4310
320-2911.34
430-3914.3620
540-4912.8710
650-5913.236
760-6913.9620
870-799.9811
980-895.157
1090-1.055
Total100100
Then χ^2 is
χ^2=((8.67-7)^2/8.67+(9.43-10)^2/9.43+(11.3-4)^2/11.3+(14.36-20)^2/14.36+(12.87-10)^2/12.87+(13.23-6)^2/13.23+(13.96-20)^2/13.96+(9.98-11)^2/9.98+(5.15-7)^2/5.15+(1.05-5)^2/1.05)=30.12 and upper critical value of Chi-square distribution is 33.7199 with 0.01% critical value and 27.8772 with 0.1% critical value.※Degree of freedom is 9(=10-1).
Therefore, sample group represents entire population by age group with 0.01% critical value but does not with 0.1% critical value.
・Upper critical values of Chi-square distribution in the table are calculated by the function "CHIINV" of Office Excel 2010.
・PDF:Probability Density Function
・CDF:Cumulative Distribution Function
・ν:Degrees of freedom

PDF Document:Cumulative Distribution Function table of the Standard Normal Distribution,From -∞ to x. u=0. σ=1





DateFile NameSize(KB)MD5 Hash
2011/09/1620110916-001.pdf1069b3e9ba754299e28fdca482d537dfae3

Keyword

Cumulative Distribution Function table of the Standard Normal Distribution,From -∞ to x. u=0. σ=1

Reference

[1]:NIST/SEMATECH e-Handbook of Statistical Methods:1.3.6.6.1. Normal Distribution
[2]:WIKIPEDIA:Normal distribution

Remarks

・PDF:Probability Density Function
・CDF:Cumulative Distribution Function

PDF Document:Cumulative Distribution Function of the Standard Cauchy Distribution,From 0 to x. x0=0. γ=1





DateFile NameSize(KB)MD5 Hash
2011/09/1720110917-001.pdf625c8fe5f059d750783c017724262670c7a

Keyword

Cumulative Distribution Function of the Standard Cauchy Distribution,From 0 to x. x0=0. γ=1

Reference

[1]:NIST/SEMATECH e-Handbook of Statistical Methods:1.3.6.6.3. Cauchy Distribution
[2]:WIKIPEDIA:Cauchy distribution

Remarks

・PDF:Probability Density Function
・CDF:Cumulative Distribution Function
・x0:Location parameter
・γ:Scale parameter

PDF Document:Exponential Distribution,Probability Density Function(PDF),PDF:f(x)=λ*e^(-x*λ)


DateFile NameSize(KB)MD5 Hash
2011/09/2420110924-001.pdf5445b190fe6c25c486a0fec549faa20ecda

Keyword

Exponential Distribution,Probability Density Function(PDF),PDF:f(x)=λ*e^(-x*λ)

Reference

[1]:NIST/SEMATECH e-Handbook of Statistical Methods:1.3.6.6.7. Exponential Distribution
[2]:WIKIPEDIA:Exponential distribution

Remarks

・PDF:Probability Density Function
・CDF:Cumulative Distribution Function
・λ:Scale parameter

PDF Document:Exponential Distribution,Cumulative Distribution Function(CDF),CDF:F(x)=1-e^(-x*λ)


DateFile NameSize(KB)MD5 Hash
2011/09/2420110924-002.pdf557a78318ef6ca41dd16d2e0800daa844c4

Keyword

Exponential Distribution,Cumulative Distribution Function(CDF),CDF:F(x)=1-e^(-x*λ)

Reference

[1]:NIST/SEMATECH e-Handbook of Statistical Methods:1.3.6.6.7. Exponential Distribution
[2]:WIKIPEDIA:Exponential distribution

Remarks

・PDF:Probability Density Function
・CDF:Cumulative Distribution Function
・λ:Scale parameter

PDF Document:Exponential Distribution,Survival Function,S(x)=e^(-x*λ)


DateFile NameSize(KB)MD5 Hash
2011/09/2620110926-001.pdf405b079904ff6b3c2af697d3e2e1e8df98a

Keyword

Exponential Distribution,Survival Function,S(x)=e^(-x*λ)

Reference

[1]:NIST/SEMATECH e-Handbook of Statistical Methods:1.3.6.6.7. Exponential Distribution
[2]:WIKIPEDIA:Exponential distribution

Remarks

・PDF:Probability Density Function
・CDF:Cumulative Distribution Function
・S(x):Survival Function
・λ:Scale parameter

PDF Document:Probability Density Function(PDF) of the Exponential Distribution.PDF:f(x)=λ*e^(-x*λ),λ=1


DateFile NameSize(KB)MD5 Hash
2011/09/2620110926-002.pdf183d8a0889692b150cf92b0ab07ad7af4ae

Keyword

Probability Density Function(PDF) of the Exponential Distribution.PDF:f(x)=λ*e^(-x*λ),λ=1

Reference

[1]:NIST/SEMATECH e-Handbook of Statistical Methods:1.3.6.6.7. Exponential Distribution
[2]:WIKIPEDIA:Exponential distribution

Remarks

・PDF:Probability Density Function
・CDF:Cumulative Distribution Function
・S(x):Survival Function
・λ:Scale parameter

PDF Document:Cumulative Distribution Function of the Exponential Distribution.CDF:F(x)=1-e^(-x*λ),From 0 to x. λ=1


DateFile NameSize(KB)MD5 Hash
2011/09/2620110926-003.pdf18486c505eef232de049b64c2c6ec57b627

Keyword

Cumulative Distribution Function of the Exponential Distribution.CDF:F(x)=1-e^(-x*λ),From 0 to x. λ=1

Reference

[1]:NIST/SEMATECH e-Handbook of Statistical Methods:1.3.6.6.7. Exponential Distribution
[2]:WIKIPEDIA:Exponential distribution

Remarks

・PDF:Probability Density Function
・CDF:Cumulative Distribution Function
・S(x):Survival Function
・λ:Scale parameter

PDF Document:Survival Function of the Exponential Distribution.S(x)=e^(-x*λ),λ=1


DateFile NameSize(KB)MD5 Hash
2011/09/2620110926-004.pdf1846c8dbadd05c7b224f069649b80deae19

Keyword

Survival Function of the Exponential Distribution.S(x)=e^(-x*λ),λ=1

Reference

[1]:NIST/SEMATECH e-Handbook of Statistical Methods:1.3.6.6.7. Exponential Distribution
[2]:WIKIPEDIA:Exponential distribution

Remarks

・PDF:Probability Density Function
・CDF:Cumulative Distribution Function
・S(x):Survival Function
・λ:Scale parameter

PDF Document:2-Parameter Weibull Distribution,Probability Density Function(PDF),PDF:f(x)=γ/α*(x/α)^(γ-1)*e^(-(x/α)^γ),α=1


DateFile NameSize(KB)MD5 Hash
2011/09/2820110928-001.pdf4621f3ae64aa52af0039b1e97b8babdae45

Keyword

2-Parameter Weibull Distribution,Probability Density Function(PDF),PDF:f(x)=γ/α*(x/α)^(γ-1)*e^(-(x/α)^γ),α=1

Reference

[1]:NIST/SEMATECH e-Handbook of Statistical Methods:1.3.6.6.8. Weibull Distribution
[2]:WIKIPEDIA:Weibull distribution

Remarks

・PDF:Probability Density Function
・CDF:Cumulative Distribution Function
・γ:Shape parameter
・α:Scale parameter

PDF Document:2-Parameter Weibull Distribution,Cumulative Distribution Function(CDF),CDF:F(x)=1-e^(-(x/α)^γ),α=1


DateFile NameSize(KB)MD5 Hash
2011/09/3020110930-001.pdf350cf1260bc85904b71d2750b2eb0325446

Keyword

2-Parameter Weibull Distribution,Cumulative Distribution Function(CDF),CDF:F(x)=1-e^(-(x/α)^γ),α=1

Reference

[1]:NIST/SEMATECH e-Handbook of Statistical Methods:1.3.6.6.8. Weibull Distribution
[2]:WIKIPEDIA:Weibull distribution

Remarks

・PDF:Probability Density Function
・CDF:Cumulative Distribution Function
・γ:Shape parameter
・α:Scale parameter

PDF Document:2-Parameter Weibull Distribution,Hazard Function:h(x),h(x)=γ/α*(x/α)^(γ-1),α=1


DateFile NameSize(KB)MD5 Hash
2011/10/0420111004-001.pdf6364b49d5d879eab5b01c58222c28b3d01a

Keyword

2-Parameter Weibull Distribution,Hazard Function:h(x),h(x)=γ/α*(x/α)^(γ-1),α=1

Reference

[1]:NIST/SEMATECH e-Handbook of Statistical Methods:1.3.6.6.8. Weibull Distribution
[2]:WIKIPEDIA:Weibull distribution

Remarks

・PDF:Probability Density Function
・CDF:Cumulative Distribution Function
・h(x):Hazard Function
・γ:Shape parameter
・α:Scale parameter

PDF Document:2-Parameter Weibull Distribution,Survival Function:S(x),S(x)=e^(-(x/α)^γ),α=1


DateFile NameSize(KB)MD5 Hash
2011/10/0520111005-001.pdf34949e21363ee562823fa5de318eb0f465b

Keyword

2-Parameter Weibull Distribution,Survival Function:S(x),S(x)=e^(-(x/α)^γ),α=1

Reference

[1]:NIST/SEMATECH e-Handbook of Statistical Methods:1.3.6.6.8. Weibull Distribution
[2]:WIKIPEDIA:Weibull distribution

Remarks

・PDF:Probability Density Function
・CDF:Cumulative Distribution Function
・h(x):Hazard Function
・S(x)Survival Function
・γ:Shape parameter
・α:Scale parameter

PDF Document:Cumulative Distribution Function of the Standard Weibull Distribution,From 0 to x. α=1. γ=1



DateFile NameSize(KB)MD5 Hash
2011/10/1320111013-001.pdf18619fae1ab0900117bf733e22c66d32bdd

Keyword

Cumulative Distribution Function of the Standard Weibull Distribution,From 0 to x. α=1. γ=1

Reference

[1]:NIST/SEMATECH e-Handbook of Statistical Methods:1.3.6.6.8. Weibull Distribution
[2]:WIKIPEDIA:Weibull distribution

Remarks

・PDF:Probability Density Function
・CDF:Cumulative Distribution Function
・γ:Shape parameter
・α:Scale parameter

PDF Document:Standard Lognormal Distribution,Probability Density Function(PDF),PDF:f(x)=e^-((ln(x))^2/(2*σ^2))/(x*σ*(2*π)^0.5)



DateFile NameSize(KB)MD5 Hash
2011/10/1820111018-003.pdf6367afea8b581afa3997509faf9c61a370b

Keyword

Standard Lognormal Distribution,Probability Density Function(PDF),PDF:f(x)=e^-((ln(x))^2/(2*σ^2))/(x*σ*(2*π)^0.5)

Reference

[1]:NIST/SEMATECH e-Handbook of Statistical Methods:1.3.6.6.8. Weibull Distribution
[2]:WIKIPEDIA:Log-normal distribution

Remarks

・PDF:Probability Density Function
・CDF:Cumulative Distribution Function
・σ:Shape parameter

PDF Document:Standard Lognormal Distribution,Cumulative Distribution Function(CDF),CDF:F(x)=Φ(ln(x)/σ),Φ is the cumulative distribution function of the normal distribution



DateFile NameSize(KB)MD5 Hash
2011/10/1920111019-001.pdf60993a234793dae9ac9ad11653debbf3eae

Keyword

Standard Lognormal Distribution,Cumulative Distribution Function(CDF),CDF:F(x)=Φ(ln(x)/σ),Φ is the cumulative distribution function of the normal distribution

Reference

[1]:NIST/SEMATECH e-Handbook of Statistical Methods:1.3.6.6.8. Weibull Distribution
[2]:WIKIPEDIA:Log-normal distribution

Remarks

・PDF:Probability Density Function
・CDF:Cumulative Distribution Function
・σ:Shape parameter(or Standard deviation)

PDF Document:Standard Lognormal Distribution,Hazard Function:h(x),h(x)=f(x)/(1-F(x))=1/(x*σ)*φ(ln(x)/σ)/Φ(-ln(x)/σ),φ and Φ are the PDF and the CDF of the normal distribution,respectively.



DateFile NameSize(KB)MD5 Hash
2011/10/2020111020-001.pdf4507a13bc11a9f474c681f42982adb96a9b

Keyword

Standard Lognormal Distribution,Hazard Function:h(x),h(x)=f(x)/(1-F(x))=1/(x*σ)*φ(ln(x)/σ)/Φ(-ln(x)/σ),φ and Φ are the PDF and the CDF of the normal distribution,respectively.

Reference

[1]:NIST/SEMATECH e-Handbook of Statistical Methods:1.3.6.6.8. Weibull Distribution
[2]:WIKIPEDIA:Log-normal distribution

Remarks

・PDF:Probability Density Function
・CDF:Cumulative Distribution Function
・σ:Shape parameter(or Standard deviation)

PDF Document:Standard Lognormal Distribution,Survival Function:S(x),S(x)=1-F(x)=1-Φ(ln(x)/σ),Φ is the cumulative distribution function of the normal distribution



DateFile NameSize(KB)MD5 Hash
2011/10/2020111020-003.pdf61469fa06e1cc325e5ce2fc2ec9e80b5c06

Keyword

Standard Lognormal Distribution,Survival Function:S(x),S(x)=1-F(x)=1-Φ(ln(x)/σ),Φ is the cumulative distribution function of the normal distribution

Reference

[1]:NIST/SEMATECH e-Handbook of Statistical Methods:1.3.6.6.8. Weibull Distribution
[2]:WIKIPEDIA:Log-normal distribution

Remarks

・PDF:Probability Density Function
・CDF:Cumulative Distribution Function
・σ:Shape parameter(or Standard deviation)

PDF Document:Cumulative Distribution Function of the Standard Lognormal Distribution,From 0 to x. σ=1



DateFile NameSize(KB)MD5 Hash
2011/10/2120111021-001.pdf104c1bbaf513df8168713c7b660bcb7841a

Keyword

Cumulative Distribution Function of the Standard Lognormal Distribution,From 0 to x. σ=1

Reference

[1]:NIST/SEMATECH e-Handbook of Statistical Methods:1.3.6.6.8. Weibull Distribution
[2]:WIKIPEDIA:Log-normal distribution

Remarks

・PDF:Probability Density Function
・CDF:Cumulative Distribution Function
・σ:Shape parameter(or Standard deviation)
・CDF of the Standard Lognormal Distribution in the table are calculated by the function "LogNormDist" of Microsoft Office Excel 2010

PDF Document:Standard Birnbaum-Saunders(Fatigue Life) distribution,Probability Density Function(PDF),PDF:f(x)=(√x+√(1/x))/(2*γ*x)*φ((√x-√(1/x))/γ),φ is the probability density function of the standard normal distribution
DateDownloadSize(KB)MD5 Hash
2011/11/1420111114-005.pdf6102d253c027de49d57def871b21726b20b

Keyword
Standard Birnbaum-Saunders(Fatigue Life) distribution,Probability Density Function(PDF),PDF:f(x)=(√x+√(1/x))/(2*γ*x)*φ((√x-√(1/x))/γ),φ is the probability density function of the standard normal distribution

Reference
[1]:NIST/SEMATECH e-Handbook of Statistical Methods:1.3.6.6.10. Birnbaum-Saunders (Fatigue Life) Distribution
[2]:WIKIPEDIA:Birnbaum–Saunders distribution

Remarks
・PDF:Probability Density Function
・CDF:Cumulative Distribution Function
・γ:Shape parameter
PDF Document:Standard Birnbaum-Saunders(Fatigue Life) distribution,Cumulative Distribution Function(CDF),CDF:F(x)=Φ((√x-√(1/x))/γ),Φ is the cumulative distribution function of the standard normal distribution
DateDownloadSize(KB)MD5 Hash
2011/11/1520111115-001.pdf79342f9e2f66b3bdb0c10a853813a9970da


Keyword
PDF Document:Standard Birnbaum-Saunders(Fatigue Life) distribution,Cumulative Distribution Function(CDF),CDF:F(x)=Φ((√x-√(1/x))/γ),Φ is the cumulative distribution function of the standard normal distribution

Reference
[1]:NIST/SEMATECH e-Handbook of Statistical Methods:1.3.6.6.10. Birnbaum-Saunders (Fatigue Life) Distribution
[2]:WIKIPEDIA:Birnbaum–Saunders distribution

Remarks
・PDF:Probability Density Function
・CDF:Cumulative Distribution Function
・γ:Shape parameter
PDF Document:Standard Birnbaum-Saunders(Fatigue Life) distribution,Hazard Function:h(x),h(x)=f(x)/(1-F(x))
DateDownloadSize(KB)MD5 Hash
2011/11/1520111115-002.pdf444c44f585729b4580001adb5b66a1a9413


Keyword
Standard Birnbaum-Saunders(Fatigue Life) distribution,Hazard Function:h(x),h(x)=f(x)/(1-F(x))


Reference
[1]:NIST/SEMATECH e-Handbook of Statistical Methods:1.3.6.6.10. Birnbaum-Saunders (Fatigue Life) Distribution
[2]:WIKIPEDIA:Birnbaum–Saunders distribution

Remarks
・PDF:Probability Density Function
・CDF:Cumulative Distribution Function
・γ:Shape parameter
PDF Document:Standard Birnbaum-Saunders(Fatigue Life) distribution,Survival Function:S(x),S(x)=1-F(x)
DateDownloadSize(KB)MD5 Hash
2011/11/1520111115-003.pdf790d9b6248fbb6be75b9553b290440bdba8

Keyword
Standard Birnbaum-Saunders(Fatigue Life) distribution,Survival Function:S(x),S(x)=1-F(x)

Reference
[1]:NIST/SEMATECH e-Handbook of Statistical Methods:1.3.6.6.10. Birnbaum-Saunders (Fatigue Life) Distribution
[2]:WIKIPEDIA:Birnbaum–Saunders distribution

Remarks
・PDF:Probability Density Function
・CDF:Cumulative Distribution Function
・γ:Shape parameter
PDF Document:Cumulative Distribution Function of the Standard Birnbaum-Saunders(Fatigue Life) distribution
DateDownloadSize(KB)MD5 Hash
2011/11/1720111117-001.pdf7084b69398170d73a61ea161ab6ed9d1ea


Keyword
Cumulative Distribution Function of the Standard Birnbaum-Saunders(Fatigue Life) distribution

Reference
[1]:NIST/SEMATECH e-Handbook of Statistical Methods:1.3.6.6.10. Birnbaum-Saunders (Fatigue Life) Distribution
[2]:WIKIPEDIA:Birnbaum–Saunders distribution

Remarks
・PDF:Probability Density Function
・CDF:Cumulative Distribution Function
・γ:Shape parameter
PDF Document:Standard Gamma Distribution,Probability Density Function(PDF),PDF:f(x)=x^(γ-1)*e^(-x)/Γ(γ),Γ:Gamma Function


DateFile NameSize(KB)MD5 Hash
2011/11/3020111130-001.pdf728e6f37c2162a173474359fe632b2b2f1a

Keyword

Standard Gamma Distribution,Probability Density Function(PDF),PDF:f(x)=x^(γ-1)*e^(-x)/Γ(γ),Γ:Gamma Function

Reference

[1]:NIST/SEMATECH e-Handbook of Statistical Methods:1.3.6.6.11. Gamma Distribution
[2]:WIKIPEDIA:Gamma distribution

Remarks

・PDF:Probability Density Function
・CDF:Cumulative Distribution Function
・γ:Shape parameter
PDF Document:Standard Gamma Distribution,Cumulative Distribution Function(CDF),CDF:F(x)=Γx(γ)/Γ(γ),Γ:Gamma Function , Γx:Incomplete Gamma Function


DateFile NameSize(KB)MD5 Hash
2011/11/3020111130-002.pdf7535c03dc2cd02cabbd2a982344d0412272

Keyword

Standard Gamma Distribution,Cumulative Distribution Function(CDF),CDF:F(x)=Γx(γ)/Γ(γ),Γ:Gamma Function , Γx:Incomplete Gamma Function

Reference

[1]:NIST/SEMATECH e-Handbook of Statistical Methods:1.3.6.6.11. Gamma Distribution
[2]:WIKIPEDIA:Gamma distribution

Remarks

・PDF:Probability Density Function
・CDF:Cumulative Distribution Function
・γ:Shape parameter
PDF Document:Standard Gamma Distribution,Hazard Function:h(x),h(x)=f(x)/(1-F(x)),f(x)=x^(γ-1)*e^(-x)/Γ(γ) , F(x)=Γx(γ)/Γ(γ)


DateFile NameSize(KB)MD5 Hash
2011/12/0120111201-001.pdf6959182958713c013085920ea7fff58afb6

Keyword

Standard Gamma Distribution,Hazard Function:h(x),h(x)=f(x)/(1-F(x)),f(x)=x^(γ-1)*e^(-x)/Γ(γ) , F(x)=Γx(γ)/Γ(γ)

Reference

[1]:NIST/SEMATECH e-Handbook of Statistical Methods:1.3.6.6.11. Gamma Distribution
[2]:WIKIPEDIA:Gamma distribution

Remarks

・PDF:Probability Density Function
・CDF:Cumulative Distribution Function
・γ:Shape parameter
PDF Document:Standard Gamma Distribution,Survival Function:S(x),S(x)=1-F(x),F(x)=Γx(γ)/Γ(γ)


DateFile NameSize(KB)MD5 Hash
2011/12/0220111201-002.pdf76301ed1bde865512ec12922a5abf4c5e2e

Keyword

Standard Gamma Distribution,Survival Function:S(x),S(x)=1-F(x),F(x)=Γx(γ)/Γ(γ)

Reference

[1]:NIST/SEMATECH e-Handbook of Statistical Methods:1.3.6.6.11. Gamma Distribution
[2]:WIKIPEDIA:Gamma distribution

Remarks

・PDF:Probability Density Function
・CDF:Cumulative Distribution Function
・γ:Shape parameter
PDF Document:Cumulative Distribution Function of the Standard Gamma Distribution,CDF:F(x)=Γx(γ)/Γ(γ) ※From 0 to x. γ=1


DateFile NameSize(KB)MD5 Hash
2011/12/0920111209-001.pdf59a135c34e9c0cf09abb28e5ea29aaad58

Keyword

Cumulative Distribution Function of the Standard Gamma Distribution,CDF:F(x)=Γx(γ)/Γ(γ) ※From 0 to x. γ=1

Reference

[1]:NIST/SEMATECH e-Handbook of Statistical Methods:1.3.6.6.11. Gamma Distribution
[2]:WIKIPEDIA:Gamma distribution

Remarks

・PDF:Probability Density Function
・CDF:Cumulative Distribution Function
・γ:Shape parameter
PDF Document:Double Exponential Distribution(Laplace distribution),Hazard Function:h(x),h(x)=f(x)/(1-F(x)),u=0

DateFile NameSize(KB)MD5 Hash
2011/12/3020111230-001.pdf649e7a15c636a55a3b303387885b590d68e

Keyword

Double Exponential Distribution(Laplace distribution),Hazard Function:h(x),h(x)=f(x)/(1-F(x)),u=0

Reference

[1]:NIST/SEMATECH e-Handbook of Statistical Methods:1.3.6.6.12. Double Exponential Distribution
[2]:WIKIPEDIA:Laplace distribution

Remarks

・PDF:Probability Density Function
・CDF:Cumulative Distribution Function
・β:Scale parameter
・u:Location parameter
PDF Document:Double Exponential Distribution(Laplace distribution),Survival Function:S(x),S(x)=1-F(x),u=0

DateFile NameSize(KB)MD5 Hash
2011/12/3020111230-002.pdf729ece59d1d423a736b59c616032b4e156b

Keyword

Double Exponential Distribution(Laplace distribution),Survival Function:S(x),S(x)=1-F(x),u=0

Reference

[1]:NIST/SEMATECH e-Handbook of Statistical Methods:1.3.6.6.12. Double Exponential Distribution
[2]:WIKIPEDIA:Laplace distribution

Remarks

・PDF:Probability Density Function
・CDF:Cumulative Distribution Function
・β:Scale parameter
・u:Location parameter
PDF Document:Cumulative Distribution Function of the Double Exponential Distribution(Laplace distribution),CDF:F(x)=0.5*[1+sgn(x-u)*(1-e^(-|x-u|/β))] ※From -∞ to x. u=0,β=1

DateFile NameSize(KB)MD5 Hash
2011/12/3020111230-003.pdf59b2675d79dacec98e8d202a9871c95bbd

Keyword

Cumulative Distribution Function of the Double Exponential Distribution(Laplace distribution),CDF:F(x)=0.5*[1+sgn(x-u)*(1-e^(-|x-u|/β))] ※From -∞ to x. u=0,β=1

Reference

[1]:NIST/SEMATECH e-Handbook of Statistical Methods:1.3.6.6.12. Double Exponential Distribution
[2]:WIKIPEDIA:Laplace distribution

Remarks

・PDF:Probability Density Function
・CDF:Cumulative Distribution Function
・β:Scale parameter
・u:Location parameter
PDF Document:Power Normal Distribution,Probability Density Function(PDF),PDF:f(x)=p*φ(x)*(Φ(-x))^(p-1),u=0,σ=1

DateFile NameSize(KB)MD5 Hash
2012/01/0220120102-001.pdf271d70628fdbe42e00d445c733c4ee36751

Keyword

Power Normal Distribution,Probability Density Function(PDF),PDF:f(x)=p*φ(x)*(Φ(-x))^(p-1),u=0,σ=1

Reference

[1]:NIST/SEMATECH e-Handbook of Statistical Methods:1.3.6.6.13. Power Normal Distribution

Remarks

・PDF:Probability Density Function
・CDF:Cumulative Distribution Function
・h:Hazard function
・S:Survival function
・p: Shape parameter (Power parameter)
・σ:Scale parameter
・u:Location parameter
PDF Document:Power Normal Distribution,Cumulative Distribution Function(CDF),CDF:F(x)=1-(Φ(-x))^p,u=0,σ=1

DateFile NameSize(KB)MD5 Hash
2012/01/0220120102-002.pdf356bfd520540e8eaa6d2c9f5d0569a49293

Keyword

Power Normal Distribution,Cumulative Distribution Function(CDF),CDF:F(x)=1-(Φ(-x))^p,u=0,σ=1

Reference

[1]:NIST/SEMATECH e-Handbook of Statistical Methods:1.3.6.6.13. Power Normal Distribution

Remarks

・PDF:Probability Density Function
・CDF:Cumulative Distribution Function
・h:Hazard function
・S:Survival function
・p: Shape parameter (Power parameter)
・σ:Scale parameter
・u:Location parameter
PDF Document:Power Normal Distribution,Hazard Function:h(x),h(x)=p*φ(x)/Φ(-x),u=0,σ=1

DateFile NameSize(KB)MD5 Hash
2012/01/0220120102-003.pdf2912a763fd2394f8addd4740c8f9fa43001

Keyword

Power Normal Distribution,Hazard Function:h(x),h(x)=p*φ(x)/Φ(-x),u=0,σ=1

Reference

[1]:NIST/SEMATECH e-Handbook of Statistical Methods:1.3.6.6.13. Power Normal Distribution

Remarks

・PDF:Probability Density Function
・CDF:Cumulative Distribution Function
・h:Hazard function
・S:Survival function
・p: Shape parameter (Power parameter)
・σ:Scale parameter
・u:Location parameter
PDF Document:Power Normal Distribution,Survival Function:S(x),S(x)=(Φ(-x))^p,u=0,σ=1

DateFile NameSize(KB)MD5 Hash
2012/01/0220120102-004.pdf3579e66a251d0b6283ff02c7459003652e7

Keyword

Power Normal Distribution,Survival Function:S(x),S(x)=(Φ(-x))^p,u=0,σ=1

Reference

[1]:NIST/SEMATECH e-Handbook of Statistical Methods:1.3.6.6.13. Power Normal Distribution

Remarks

・PDF:Probability Density Function
・CDF:Cumulative Distribution Function
・h:Hazard function
・S:Survival function
・p: Shape parameter (Power parameter)
・σ:Scale parameter
・u:Location parameter
PDF Document:Cumulative Distribution Function of the Power Normal Distribution,CDF:F(x)=1-(Φ(-x))^p ※From -∞ to x. u=0,σ=1

DateFile NameSize(KB)MD5 Hash
2012/01/0520120105-005.pdf462965b596041af8c69744bfdc4464d743c

Keyword

Cumulative Distribution Function of the Power Normal Distribution,CDF:F(x)=1-(Φ(-x))^p ※From -∞ to x. u=0,σ=1

Reference

[1]:NIST/SEMATECH e-Handbook of Statistical Methods:1.3.6.6.13. Power Normal Distribution

Remarks

・PDF:Probability Density Function
・CDF:Cumulative Distribution Function
・h:Hazard function
・S:Survival function
・p: Shape parameter (Power parameter)
・σ:Scale parameter
・u:Location parameter
PDF Document:The Standard Form of the Power Lognormal Distribution,Probability Density Function(PDF),PDF:f(x)=p/(x*σ)*φ(ln(x)/σ)*(Φ(-ln(x)/σ))^(p-1),u=0,σ=1

DateFile NameSize(KB)MD5 Hash
2012/01/0920120109-001.pdf4792c91399c2f9a53ab9bcde2cd30a2c2f7

Keyword

The Standard Form of the Power Lognormal Distribution,Probability Density Function(PDF),PDF:f(x)=p/(x*σ)*φ(ln(x)/σ)*(Φ(-ln(x)/σ))^(p-1),u=0,σ=1

Reference

[1]:NIST/SEMATECH e-Handbook of Statistical Methods:1.3.6.6.14. Power Lognormal Distribution

Remarks

・PDF:Probability Density Function
・CDF:Cumulative Distribution Function
・h:Hazard function
・S:Survival function
・p:Shape parameter (Power parameter)
・σ:Shape parameter
・u:Location parameter
PDF Document:The Standard Form of the Power Lognormal Distribution,Cumulative Distribution Function(CDF),CDF:F(x)=1-(Φ(-ln(x)/σ))^p,u=0,σ=1

DateFile NameSize(KB)MD5 Hash
2012/01/0920120109-002.pdf36629472cade3b523e9557ee59ad7519c6d

Keyword

The Standard Form of the Power Lognormal Distribution,Cumulative Distribution Function(CDF),CDF:F(x)=1-(Φ(-ln(x)/σ))^p,u=0,σ=1

Reference

[1]:NIST/SEMATECH e-Handbook of Statistical Methods:1.3.6.6.14. Power Lognormal Distribution

Remarks

・PDF:Probability Density Function
・CDF:Cumulative Distribution Function
・h:Hazard function
・S:Survival function
・p:Shape parameter (Power parameter)
・σ:Shape parameter
・u:Location parameter
PDF Document:The Standard Form of the Power Lognormal Distribution,Hazard Function:h(x),h(x)=p/(x*σ)*φ(ln(x)/σ)/(Φ(-ln(x)/σ)),u=0,σ=1

DateFile NameSize(KB)MD5 Hash
2012/01/0920120109-003.pdf3896e9e13dec50838b9d2210d6497411fe8

Keyword

The Standard Form of the Power Lognormal Distribution,Hazard Function:h(x),h(x)=p/(x*σ)*φ(ln(x)/σ)/(Φ(-ln(x)/σ)),u=0,σ=1

Reference

[1]:NIST/SEMATECH e-Handbook of Statistical Methods:1.3.6.6.14. Power Lognormal Distribution

Remarks

・PDF:Probability Density Function
・CDF:Cumulative Distribution Function
・h:Hazard function
・S:Survival function
・p:Shape parameter (Power parameter)
・σ:Shape parameter
・u:Location parameter
PDF Document:The Standard Form of the Power Lognormal Distribution,Survival Function:S(x),S(x)=(Φ(-ln(x)/σ))^p,u=0,σ=1

DateFile NameSize(KB)MD5 Hash
2012/01/0920120109-004.pdf3662b9f232a2946cf26cd41f8f76233200f

Keyword

The Standard Form of the Power Lognormal Distribution,Survival Function:S(x),S(x)=(Φ(-ln(x)/σ))^p,u=0,σ=1

Reference

[1]:NIST/SEMATECH e-Handbook of Statistical Methods:1.3.6.6.14. Power Lognormal Distribution

Remarks

・PDF:Probability Density Function
・CDF:Cumulative Distribution Function
・h:Hazard function
・S:Survival function
・p:Shape parameter (Power parameter)
・σ:Shape parameter
・u:Location parameter
PDF Document:Cumulative Distribution Function of the Standard Form of the Power Lognormal Distribution,CDF:F(x)=1-(Φ(-ln(x)/σ))^p ※From 0 to x. u=0,σ=1,p=1

DateFile NameSize(KB)MD5 Hash
2012/01/0920120109-005.pdf91bafd365829b19720ff281cb57c4a8b47

Keyword

Cumulative Distribution Function of the Standard Form of the Power Lognormal Distribution,CDF:F(x)=1-(Φ(-ln(x)/σ))^p ※From 0 to x. u=0,σ=1,p=1

Reference

[1]:NIST/SEMATECH e-Handbook of Statistical Methods:1.3.6.6.14. Power Lognormal Distribution

Remarks

・PDF:Probability Density Function
・CDF:Cumulative Distribution Function
・h:Hazard function
・S:Survival function
・p:Shape parameter (Power parameter)
・σ:Shape parameter
・u:Location parameter
PDF Document:The Standard Gumbel distribution(Extreme Value Type I Distribution),Probability Density Function(PDF),PDF:f(x)=1/β*e^(-(x-u)/β-e^(-(x-u)/β)),u=0

DateFile NameSize(KB)MD5 Hash
2012/01/2420120124-005.pdf58797550b5fad70cb753d3728ee63b8971b

Keyword

The Standard Gumbel distribution(Extreme Value Type I Distribution),Probability Density Function(PDF),PDF:f(x)=1/β*e^(-(x-u)/β-e^(-(x-u)/β)),u=0

Reference

[1]:NIST/SEMATECH e-Handbook of Statistical Methods:1.3.6.6.16. Extreme Value Type I Distribution
[2]:Wikipedia:Gumbel distribution

Remarks

・PDF:Probability Density Function
・CDF:Cumulative Distribution Function
・h:Hazard function
・S:Survival function
・β:Shape parameter
・u:Location parameter
PDF Document:The Standard Gumbel distribution(Extreme Value Type I Distribution),Cumulative Distribution Function(CDF),CDF:F(x)=e^(-e^(-(x-u)/β)),u=0

DateFile NameSize(KB)MD5 Hash
2012/01/2420120124-006.pdf68036cc5ae4ac7fa6b575ca09f521d645ec

Keyword

The Standard Gumbel distribution(Extreme Value Type I Distribution),Cumulative Distribution Function(CDF),CDF:F(x)=e^(-e^(-(x-u)/β)),u=0

Reference

[1]:NIST/SEMATECH e-Handbook of Statistical Methods:1.3.6.6.16. Extreme Value Type I Distribution
[2]:Wikipedia:Gumbel distribution

Remarks

・PDF:Probability Density Function
・CDF:Cumulative Distribution Function
・h:Hazard function
・S:Survival function
・β:Shape parameter
・u:Location parameter
PDF Document:The Standard Gumbel distribution(Extreme Value Type I Distribution),Hazard Function:h(x),h(x)=f(x)/(1-F(x)),u=0

DateFile NameSize(KB)MD5 Hash
2012/02/1020120210-001.pdf650943173fb83d13c3933d8761206bfe178

Keyword

The Standard Gumbel distribution(Extreme Value Type I Distribution),Hazard Function:h(x),h(x)=f(x)/(1-F(x)),u=0

Reference

[1]:NIST/SEMATECH e-Handbook of Statistical Methods:1.3.6.6.16. Extreme Value Type I Distribution
[2]:Wikipedia:Gumbel distribution

Remarks

・PDF:Probability Density Function
・CDF:Cumulative Distribution Function
・h:Hazard function
・S:Survival function
・β:Shape parameter
・u:Location parameter
PDF Document:The Standard Gumbel distribution(Extreme Value Type I Distribution),Survival Function:S(x),S(x)=1-F(x),u=0

DateFile NameSize(KB)MD5 Hash
2012/02/1020120210-002.pdf6728a733b8d5069f09f4c3cb126f2ac0c25

Keyword

The Standard Gumbel distribution(Extreme Value Type I Distribution),Survival Function:S(x),S(x)=1-F(x),u=0

Reference

[1]:NIST/SEMATECH e-Handbook of Statistical Methods:1.3.6.6.16. Extreme Value Type I Distribution
[2]:Wikipedia:Gumbel distribution

Remarks

・PDF:Probability Density Function
・CDF:Cumulative Distribution Function
・h:Hazard function
・S:Survival function
・β:Shape parameter
・u:Location parameter
PDF Document:Cumulative Distribution Function of The Standard Gumbel distribution(Extreme Value Type I Distribution)

DateFile NameSize(KB)MD5 Hash
2012/02/1020120210-003.pdf103b1d980239349ddbba6dd5567e2820fdb

Keyword

Cumulative Distribution Function of The Standard Gumbel distribution(Extreme Value Type I Distribution)

Reference

[1]:NIST/SEMATECH e-Handbook of Statistical Methods:1.3.6.6.16. Extreme Value Type I Distribution
[2]:Wikipedia:Gumbel distribution

Remarks

・PDF:Probability Density Function
・CDF:Cumulative Distribution Function
・h:Hazard function
・S:Survival function
・β:Shape parameter
・u:Location parameter
PDF Document:Double Exponential Distribution(Laplace distribution),Probability Density Function(PDF),PDF:f(x)=e^(-|x-u|/β)/(2*β),u=0


DateFile NameSize(KB)MD5 Hash
2011/12/1120111211-005.pdf6322b7c9036b7f621f034b164c6ce7fd1ab

Keyword

Double Exponential Distribution(Laplace distribution),Probability Density Function(PDF),PDF:f(x)=e^(-|x-u|/β)/(2*β),u=0

Reference

[1]:NIST/SEMATECH e-Handbook of Statistical Methods:1.3.6.6.12. Double Exponential Distribution
[2]:WIKIPEDIA:Laplace distribution

Remarks

・PDF:Probability Density Function
・CDF:Cumulative Distribution Function
・β:Scale parameter
PDF Document:Double Exponential Distribution(Laplace distribution),Cumulative Distribution Function(CDF),CDF:F(x)=0.5*[1+sgn(x-u)*(1-e^(-|x-u|/β))],u=0


DateFile NameSize(KB)MD5 Hash
2011/12/1120111211-006.pdf739f2643c4a5e359f62adb5d32d21a367a8

Keyword

Double Exponential Distribution(Laplace distribution),Cumulative Distribution Function(CDF),CDF:F(x)=0.5*[1+sgn(x-u)*(1-e^(-|x-u|/β))],u=0

Reference

[1]:NIST/SEMATECH e-Handbook of Statistical Methods:1.3.6.6.12. Double Exponential Distribution
[2]:WIKIPEDIA:Laplace distribution

Remarks

・PDF:Probability Density Function
・CDF:Cumulative Distribution Function
・β:Scale parameter