dgamma_mix: Gamma Mixture Density

In matheuscastro43/finiteMix: Finite Mixture Models

Gamma Mixture Density

Description

Gives the density value of a univariate Gamma Mixture.

Usage

dgamma_mix(x, pi, alpha, beta, log = FALSE)

Arguments

x	value or vector of values, to apply in the mixture probability density function.
pi	vector of mixture weights.
alpha	shape parameters.
beta	scale parameters.
log	logical; if TRUE, probabilities p are given as log(p).

Details

Each component of the mixture has density

f_j(x) = 1/(β_j^(α_j) Gamma(α_j)) x^(α_j-1) e^-(x/β_j)

where α_j is the shape parameter of the jth component and β_j is the scale parameter of the jth component. j = 1, 2, ..., g.

Author(s)

CASTRO, M. O.; MONTALVO, G. S. A.

Examples

f <- function(x){dgamma_mix(x, pi = c(0.1, 0.9), alpha = c(1, 3), beta = c(5, 2))}
## Plot using graphics package
require(graphics)
curve(f, 0, 25)

require(ggplot2)
## Plot using ggplot2 package
ggplot(data.frame(x=c(0, 25)), aes(x)) +
  stat_function(fun=f, size = 1L, colour = "#0c4c8a") +
  theme_minimal()

## Integrate
integrate(f, 0, "Inf")$value

matheuscastro43/finiteMix documentation built on March 30, 2022, 12:49 p.m.