gamma_params: Calculate shape and scale (or rate) parameters of a gamma...

In DARTH-git/dampack: Decision-Analytic Modeling Package

Calculate shape and scale (or rate) parameters of a gamma distribution.

Description

Function to calculate the shape, \alpha, and scale, \theta, (or rate, \beta) parameters of a gamma distribution based on the method of moments (MoM) using the mean \mu and standard deviation \sigma of the random variable of interest.

Usage

gamma_params(mu, sigma, scale = TRUE)

Arguments

mu	scalar with the mean of the random variable.
sigma	scalar with the standard deviation of the random variable.
scale	logical variable indicating scale parameterization of the gamma distribution (Default is TRUE). If FALSE, rate parameterization is retrieved

Value

A list contianing the following:

shape Shape parameter of gamma distribution

scale Scale parameter of gamma distribution (If scale=TRUE)

rate Rate parameter of gamma distribution (If scale=FALSE)

Details

Based on method of moments. If \mu is the mean and \sigma is the standard deviation of the random variable, then the the shape, \alpha, scale, \theta, and rate, \beta, parameters are computed as follows

\alpha=\frac{\mu^2}{\sigma^2},

\theta = \frac{\sigma^2}{\mu}

and

\beta = \frac{\mu}{\sigma^2}

References

• Gamma distribution. (2018, February 7). In Wikipedia, The Free Encyclopedia. Retrieved 17:23, February 11, 2018, from https://en.wikipedia.org/w/index.php?title=Gamma_distribution&oldid=824541785

Examples

mu    <- 2
sigma <- 1
# Scale specification
gamma_params(mu, sigma)
# Rate specification
gamma_params(mu, sigma, scale = FALSE)

DARTH-git/dampack documentation built on Sept. 25, 2024, 4:48 p.m.