Gamma Distribution

Two-parameter Gamma distribution with scale \(\beta\) and shape \(\alpha\). The distribution is supported on \(x > 0\) and is widely used for modelling positively skewed variables such as precipitation amounts. Density, distribution, quantile, and random generation functions are provided via base R dgamma. Fitting is performed via closed-form L-moments through pelgam.

The probability density function is: $$f(x) = \frac{1}{\beta^\alpha \Gamma(\alpha)} x^{\alpha-1} \exp\left(-\frac{x}{\beta}\right), \quad x > 0$$ where:

• \(\beta\) — scale parameter (scale)

• \(\alpha\) — shape parameter (shape)

Usage

dgamma(x, scale, shape)

pgamma(q, scale, shape)

qgamma(p, scale, shape)

rgamma(n, scale, shape)

Arguments

x, q

vector of quantiles.

scale

scale parameter.

shape

shape parameter.

p

vector of probabilities.

n

number of observations. If length(n) > 1, the length is taken as the number required.