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
Stdev σ
TermDescription
μLocation parameter
σScale parameter

Lognormal distribution

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CDF
Mean
Stdev
TermDescription
μScale parameter
σShape parameter

3-parameter lognormal distribution

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CDF
Mean
Stdev
TermDescription
μScale parameter
σShape parameter
λThreshold parameter

Exponential distribution

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CDF
Mean θ
Stdev θ
TermDescription
θScale parameter

2-parameter exponential distribution

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CDF
Mean θ + λ
Stdev θ
TermDescription
θScale parameter
λThreshold parameter

Weibull distribution

PDF
CDF
Mean
Stdev
TermDescription
αScale parameter
βShape parameter

3-parameter Weibull distribution

PDF
CDF
Mean
Stdev
TermDescription
αScale parameter
βShape parameter
λThreshold parameter

Largest extreme value distribution

PDF
CDF
Mean
Stdev

TermDescription
μLocation parameter
σScale parameter
γEuler's constant (approximately equals 0.5772)

Smallest extreme value distribution

PDF
CDF
Mean
Stdev

TermDescription
μLocation parameter
σScale parameter
γEuler's constant (approximately equals 0.5772)

Gamma distribution

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CDF
Mean αβ
Stdev αβ2
TermDescription
αShape parameter
βScale parameter

3-parameter gamma distribution

PDF
CDF
TermDescription
αShape parameter
βScale parameter
γThreshold parameter

Logistic distribution

PDF
CDF
Mean μ
Stdev
TermDescription
μLocation parameter
σScale parameter

Loglogistic distribution

PDF
CDF
Mean
Stdev
TermDescription
μLocation parameter
σScale parameter

3-parameter loglogistic distribution

PDF
CDF
Mean
Stdev
TermDescription
μLocation parameter
σScale parameter
λThreshold parameter
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