r6qualitytools (version 1.0.1)

dgamma3: dgamma3: The gamma Distribution (3 Parameter)

Description

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

Usage

dgamma3(x, shape, scale, threshold)

Value

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

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:

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

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)