mgamma {extrememix}R Documentation

The Gamma Mixture Distribution

Description

Density, distribution function, quantile function and random generation for the mixture of Gamma distribution.

Usage

dmgamma(x, mu, eta, w, log = FALSE)

pmgamma(q, mu, eta, w, lower.tail = TRUE)

qmgamma(p, mu, eta, w, lower.tail = TRUE)

rmgamma(N, mu, eta, w)

Arguments

x, q

vector of quantiles.

mu

means of the gamma mixture components (vector).

eta

shapes of the gamma mixture components (vector).

w

weights of the gamma mixture components (vector). Must sum to one.

log

logical; if TRUE, probabilities p are given as log(p).

lower.tail

logical; if TRUE (default), probabilities are P(X\leq x) otherwise P(X>x).

p

vector of probabilities.

N

number of observations.

Details

The Gamma distribution has density

f_{GA}(x|\mu,\eta)= \frac{(\eta/\mu)^\eta}{\Gamma(\eta)}x^{\eta-1}\exp(-(\eta/\mu)x), \hspace{1cm} x>0,

where \mu>0 is the mean of the distribution and \eta>0 is its shape. The density of a mixture of Gamma distributions with k components is defined as

f_{MG}(x|\mu,\eta,w)=\sum_{i=1}^k w_if_{GA}(x|\mu_i,\eta_i),

where w_i,\mu_i,\eta_i >0, for i=1,\dots,k, w_1+\cdots+w_k=1, \mu=(\mu_1,\dots,\mu_k), \eta = (\eta_1,\dots,\eta_k) and w=(w_1,\dots,w_k).

Value

dmgamma gives the density, pmgamma gives the distribution function, qmgamma gives the quantile function, and rmgamma generates random deviates.

The length of the result is determined by N for rmgamma and by the length of x, q or p otherwise.

References

Wiper, Michael, David Rios Insua, and Fabrizio Ruggeri. "Mixtures of gamma distributions with applications." Journal of Computational and Graphical Statistics 10.3 (2001): 440-454.

Examples

dmgamma(3, mu = c(2,3), eta = c(1,2), w = c(0.3,0.7))


[Package extrememix version 0.0.1 Index]