| | Name | Function |
| | Beta |
where a, b > 0 are the shape parameters; B(.) is the Beta function; and I[0,1] is the indicator function. | | Exponential |
where µ is the mean. | | Extreme value |
where µ and σ are, respectively, the location and scale parameters. | | Gamma | , where a and b are the shape and scale parameters and is the Gamma function. | | Generalized extreme value |
where µ, σ, and k are, respectively, the location, scale, and shape parameters. | | Generalized Pareto |
where k, σ, and θ are, respectively, the shape, scale, and threshold parameters. | | Inverse Gaussian |
where µ and λ are, respectively, the mean and shape parameters. | | Logistic |
where µ and σ are, respectively, the mean and scale parameters. | | Log-logistic |
where µ and σ are, respectively, the mean and scale parameters. | | Log-normal |
where µ and σ are, respectively, the mean and scale parameters. | | Normal | If X follows the log-normal distribution with parameters µ and σ, then log(X) follows the normal distribution with mean µ and standard deviation σ. | | Weibull |
where σ and k are, respectively, the scale and shape parameters. |
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