qgamma3: qgamma3: The gamma Distribution (3 Parameter)

In r6qualitytools: R6-Based Statistical Methods for Quality Science

qgamma3: The gamma Distribution (3 Parameter)

Description

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

Usage

qgamma3(p, shape, scale, threshold, ...)

Arguments

p	A numeric vector of probabilities.
shape	The shape parameter, default is 1.
scale	The scale parameter, default is 1.
threshold	The threshold parameter, default is 0.
...	Additional arguments that can be passed to uniroot.

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.