pgsm | R Documentation |
Computes cumulative distribution function (cdf) of the gamma shape mixture (GSM) model. The general form for the cdf of the GSM model is given by
F(x,{Θ}) = ∑_{j=1}^{K}ω_j F(x,j,β),
where
F(x,j,β) = \int_{0}^{x} \frac{β^j}{Γ(j)} y^{j-1} \exp\bigl( -β y\bigr) dy,
in which Θ=(ω_1,…,ω_K, β)^T is the parameter vector and known constant K is the number of components. The vector of mixing parameters is given by ω=(ω_1,…,ω_K)^T where ω_js sum to one, i.e., ∑_{j=1}^{K}ω_j=1. Here β is the rate parameter that is equal for all components.
pgsm(data, omega, beta, log.p = FALSE, lower.tail = TRUE)
data |
Vector of observations. |
omega |
Vector of the mixing parameters. |
beta |
The rate parameter. |
log.p |
If |
lower.tail |
If |
A vector of the same length as data
, giving the cdf of the GSM model.
Mahdi Teimouri
S. Venturini, F. Dominici, and G. Parmigiani, 2008. Gamma shape mixtures for heavy-tailed distributions, The Annals of Applied Statistics, 2(2), 756–776.
data<-seq(0,20,0.1) omega<-c(0.05, 0.1, 0.15, 0.2, 0.25, 0.25) beta<-2 pgsm(data, omega, beta)
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