dgamma3: dgamma3: The gamma Distribution (3 Parameter)

In r6qualitytools: R6-Based Statistical Methods for Quality Science

dgamma3: The gamma Distribution (3 Parameter)

Description

Density function, distribution function, and quantile function for the Gamma distribution.

Usage

dgamma3(x, shape, scale, threshold)

Arguments

x	A numeric vector of quantiles.
shape	The shape parameter, default is 1.
scale	The scale parameter, default is 1.
threshold	The threshold parameter, default is 0.

Details

The Gamma distribution with scale parameter alpha, shape parameter c, and threshold parameter zeta has a density given by:

f(x) = \frac{c}{\alpha}\left(\frac{x-\zeta}{\alpha}\right)^{c-1}\exp\left(-\left(\frac{x-\zeta}{\alpha}\right)^c\right)

The cumulative distribution function is given by:

F(x) = 1 - \exp\left(-\left(\frac{x-\zeta}{\alpha}\right)^c\right)

Value

dgamma3 gives the density, pgamma3 gives the distribution function, and qgamma3 gives the quantile function.

Examples

dgamma3(x = 1, scale = 1, shape = 5, threshold = 0)
temp <- pgamma3(q = 1, scale = 1, shape = 5, threshold = 0)
temp
qgamma3(p = temp, scale = 1, shape = 5, threshold = 0)

r6qualitytools documentation built on Oct. 4, 2024, 1:09 a.m.