Methods and formulas for distributions in Individual Distribution Identification

Probability density function, Cumulative density function, Mean, Standard deviation

Normal distribution

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CDF
Mean	μ
Standard deviation	σ

Term	Description
μ	Location parameter
σ	Scale parameter

Lognormal distribution

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CDF
Mean
Standard deviation

Term	Description
μ	Scale parameter
σ	Shape parameter

3-parameter lognormal distribution

PDF
CDF
Mean
Standard deviation

Term	Description
μ	Scale parameter
σ	Shape parameter
λ	Threshold parameter

Exponential distribution

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CDF
Mean	θ
Standard deviation	θ

Term	Description
θ	Scale parameter

2-parameter exponential distribution

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CDF
Mean	θ + λ
Standard deviation	θ

Term	Description
θ	Scale parameter
λ	Threshold parameter

Weibull distribution

PDF
CDF
Mean
Standard deviation

Term	Description
α	Scale parameter
β	Shape parameter

3-parameter Weibull distribution

PDF
CDF
Mean
Standard deviation

Term	Description
α	Scale parameter
β	Shape parameter
λ	Threshold parameter

Largest extreme value distribution

PDF
CDF
Mean
Standard deviation

Term	Description
μ	Location parameter
σ	Scale parameter
γ	Euler's constant (approximately equals 0.5772)

Smallest extreme value distribution

PDF
CDF
Mean
Standard deviation

Term	Description
μ	Location parameter
σ	Scale parameter
γ	Euler's constant (approximately equals 0.5772)

Gamma distribution

PDF
CDF
Mean
Standard deviation

Term	Description
α	Shape parameter
β	Scale parameter

3-parameter gamma distribution

PDF
CDF
Mean
Standard deviation

Term	Description
α	Shape parameter
β	Scale parameter
γ	Threshold parameter

Logistic distribution

PDF
CDF
Mean	μ
Standard deviation

Term	Description
μ	Location parameter
σ	Scale parameter

Loglogistic distribution

PDF
CDF
Mean
Standard deviation

Term	Description
μ	Location parameter
σ	Scale parameter

3-parameter loglogistic distribution

PDF
CDF
Mean
Standard deviation

Term	Description
μ	Location parameter
σ	Scale parameter
λ	Threshold parameter