Tail Probability Estimation for a Gamma Shape Mixture Model

Description

predict method for class "gsm". This function allows to estimate the tail probability of a Gamma Shape Mixture Model using the output of the estim.gsm or estim.gsm_theta procedures.

Usage

## S4 method for signature 'gsm'
predict(object, thresh, start = 1, ...)

Arguments

Details

The tail probability is estimated by applying the standard Rao-Blackwellized estimator on the Gibbs sampling realizations obtained through the estim.gsm or estim.gsm_theta procedures.

Value

A numerical vector containing the posterior draws for the tail probability exceeding the value of thresh.

Author(s)

Sergio Venturini sergio.venturini@unibocconi.it

References

Venturini, S., Dominici, F. and Parmigiani, G. (2008), "Gamma shape mixtures for heavy-tailed distributions". Annals of Applied Statistics, Volume 2, Number 2, 756–776. http://projecteuclid.org/euclid.aoas/1215118537

See Also

estim.gsm, estim.gsm_theta, predict-methods, plot-methods.

Examples

set.seed(2040)
y <- rgsm(500, c(.1, .3, .4, .2), 1)
burnin <- 5
mcmcsim <- 10
J <- 250
gsm.out <- estim.gsm(y, J, 300, burnin + mcmcsim, 6500, 340, 1/J)
thresh <- c(0.1, 0.5, 0.75, 1, 2)
tail.prob.est <- tail.prob.true <- rep(NA, length(thresh))
for (i in 1:length(thresh)){
   tail.prob.est[i] <- mean(predict(gsm.out, thresh[i]))
   tail.prob.true[i] <- sum(y > thresh[i])/length(y)
}
qqplot(tail.prob.true, tail.prob.est, main = "Q-Q plot of true vs. estimated tail probability")
abline(0, 1, lty = 2)

Results

R version 3.3.1 (2016-06-21) -- "Bug in Your Hair"
Copyright (C) 2016 The R Foundation for Statistical Computing
Platform: x86_64-pc-linux-gnu (64-bit)

R is free software and comes with ABSOLUTELY NO WARRANTY.
You are welcome to redistribute it under certain conditions.
Type 'license()' or 'licence()' for distribution details.

R is a collaborative project with many contributors.
Type 'contributors()' for more information and
'citation()' on how to cite R or R packages in publications.

Type 'demo()' for some demos, 'help()' for on-line help, or
'help.start()' for an HTML browser interface to help.
Type 'q()' to quit R.

> library(GSM)
Loading required package: gtools
Package GSM (1.3.2) loaded.
To cite, see citation("GSM")

> png(filename="/home/ddbj/snapshot/RGM3/R_CC/result/GSM/predict-methods.Rd_%03d_medium.png", width=480, height=480)
> ### Name: predict-methods
> ### Title: Tail Probability Estimation for a Gamma Shape Mixture Model
> ### Aliases: predict-methods predict,ANY-method predict,gsm-method
> ### Keywords: methods
> 
> ### ** Examples
> 
> set.seed(2040)
> y <- rgsm(500, c(.1, .3, .4, .2), 1)
> burnin <- 5
> mcmcsim <- 10
> J <- 250
> gsm.out <- estim.gsm(y, J, 300, burnin + mcmcsim, 6500, 340, 1/J)
> thresh <- c(0.1, 0.5, 0.75, 1, 2)
> tail.prob.est <- tail.prob.true <- rep(NA, length(thresh))
> for (i in 1:length(thresh)){
+    tail.prob.est[i] <- mean(predict(gsm.out, thresh[i]))
+    tail.prob.true[i] <- sum(y > thresh[i])/length(y)
+ }
> qqplot(tail.prob.true, tail.prob.est, main = "Q-Q plot of true vs. estimated tail probability")
> abline(0, 1, lty = 2)
> 
> 
> 
> 
> 
> dev.off()
null device 
          1 
>