Posterior Distribution with Parameters of GPD

Description

MCMC runs of posterior distribution of data with parameters of Generalized Pareto Distribution (GPD), with parameters sigma and xi.

Usage

posterior.gpd(data, threshold, int)

Arguments

Value

The program has as result a matrix with dimensions int x 2, where the first represents points of posterior points of sigma parameter of GPD and the second column is posterior points of xi parameter. The joint priordistribution for these parameters is the Jeffreys prior Given as Castellanos and Cabras (2007).

References

Castellanos, M. A. and Cabras, S. (2007). A default Bayesian procedure for the generalized Pareto distribution, Journal of Statistical Planning and Inference, 137, 473-483.

Examples

# Obtaining posterior distribution of a vector of simulated points 
x=rgpd(300,xi=0.3,mu=9,beta=2) # in this case beta is the scale parameter sigma
# Obtaning 1000 points of posterior distribution
ajuste=posterior.gpd(x,9,1000)
# Histogram of posterior distribution of the parameters,with 95% credibility intervals
par(mfrow=c(1,2))
hist(ajuste[,1],freq=FALSE,main="mu")
abline(v=quantile(ajuste[,1],0.025),lwd=2)
abline(v=quantile(ajuste[,1],0.975),lwd=2)
hist(ajuste[,2],freq=FALSE,main="sigma")
abline(v=quantile(ajuste[,2],0.025),lwd=2)
abline(v=quantile(ajuste[,2],0.975),lwd=2)
# Danish data for evir package, modelling losses over 10
data(danish)
out=posterior.gpd(danish,10,300)

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(MCMC4Extremes)
Loading required package: evir
> png(filename="/home/ddbj/snapshot/RGM3/R_CC/result/MCMC4Extremes/posterior.gpd.Rd_%03d_medium.png", width=480, height=480)
> ### Name: posterior.gpd
> ### Title: Posterior Distribution with Parameters of GPD
> ### Aliases: posterior.gpd
> 
> ### ** Examples
> 
> # Obtaining posterior distribution of a vector of simulated points 
> x=rgpd(300,xi=0.3,mu=9,beta=2) # in this case beta is the scale parameter sigma
> # Obtaning 1000 points of posterior distribution
> ajuste=posterior.gpd(x,9,1000)
[1] 0.006666667
[1] 0.01333333
[1] 0.02
[1] 0.02666667
[1] 0.03333333
[1] 0.04
[1] 0.04666667
[1] 0.05333333
[1] 0.06
[1] 0.06666667
[1] 0.07333333
[1] 0.08
[1] 0.08666667
[1] 0.09333333
[1] 0.1
[1] 0.1066667
[1] 0.1133333
[1] 0.12
[1] 0.1266667
[1] 0.1333333
[1] 0.14
[1] 0.1466667
[1] 0.1533333
[1] 0.16
[1] 0.1666667
[1] 0.1733333
[1] 0.18
[1] 0.1866667
[1] 0.1933333
[1] 0.2
[1] 0.2066667
[1] 0.2133333
[1] 0.22
[1] 0.2266667
[1] 0.2333333
[1] 0.24
[1] 0.2466667
[1] 0.2533333
[1] 0.26
[1] 0.2666667
[1] 0.2733333
[1] 0.28
[1] 0.2866667
[1] 0.2933333
[1] 0.3
[1] 0.3066667
[1] 0.3133333
[1] 0.32
[1] 0.3266667
[1] 0.3333333
[1] 0.34
[1] 0.3466667
[1] 0.3533333
[1] 0.36
[1] 0.3666667
[1] 0.3733333
[1] 0.38
[1] 0.3866667
[1] 0.3933333
[1] 0.4
[1] 0.4066667
[1] 0.4133333
[1] 0.42
[1] 0.4266667
[1] 0.4333333
[1] 0.44
[1] 0.4466667
[1] 0.4533333
[1] 0.46
[1] 0.4666667
[1] 0.4733333
[1] 0.48
[1] 0.4866667
[1] 0.4933333
[1] 0.5
[1] 0.5066667
[1] 0.5133333
[1] 0.52
[1] 0.5266667
[1] 0.5333333
[1] 0.54
[1] 0.5466667
[1] 0.5533333
[1] 0.56
[1] 0.5666667
[1] 0.5733333
[1] 0.58
[1] 0.5866667
[1] 0.5933333
[1] 0.6
[1] 0.6066667
[1] 0.6133333
[1] 0.62
[1] 0.6266667
[1] 0.6333333
[1] 0.64
[1] 0.6466667
[1] 0.6533333
[1] 0.66
[1] 0.6666667
[1] 0.6733333
[1] 0.68
[1] 0.6866667
[1] 0.6933333
[1] 0.7
[1] 0.7066667
[1] 0.7133333
[1] 0.72
[1] 0.7266667
[1] 0.7333333
[1] 0.74
[1] 0.7466667
[1] 0.7533333
[1] 0.76
[1] 0.7666667
[1] 0.7733333
[1] 0.78
[1] 0.7866667
[1] 0.7933333
[1] 0.8
[1] 0.8066667
[1] 0.8133333
[1] 0.82
[1] 0.8266667
[1] 0.8333333
[1] 0.84
[1] 0.8466667
[1] 0.8533333
[1] 0.86
[1] 0.8666667
[1] 0.8733333
[1] 0.88
[1] 0.8866667
[1] 0.8933333
[1] 0.9
[1] 0.9066667
[1] 0.9133333
[1] 0.92
[1] 0.9266667
[1] 0.9333333
[1] 0.94
[1] 0.9466667
[1] 0.9533333
[1] 0.96
[1] 0.9666667
[1] 0.9733333
[1] 0.98
[1] 0.9866667
[1] 0.9933333
[1] 1
> # Histogram of posterior distribution of the parameters,with 95% credibility intervals
> par(mfrow=c(1,2))
> hist(ajuste[,1],freq=FALSE,main="mu")
> abline(v=quantile(ajuste[,1],0.025),lwd=2)
> abline(v=quantile(ajuste[,1],0.975),lwd=2)
> hist(ajuste[,2],freq=FALSE,main="sigma")
> abline(v=quantile(ajuste[,2],0.025),lwd=2)
> abline(v=quantile(ajuste[,2],0.975),lwd=2)
> # Danish data for evir package, modelling losses over 10
> data(danish)
> out=posterior.gpd(danish,10,300)
[1] 0.02222222
[1] 0.04444444
[1] 0.06666667
[1] 0.08888889
[1] 0.1111111
[1] 0.1333333
[1] 0.1555556
[1] 0.1777778
[1] 0.2
[1] 0.2222222
[1] 0.2444444
[1] 0.2666667
[1] 0.2888889
[1] 0.3111111
[1] 0.3333333
[1] 0.3555556
[1] 0.3777778
[1] 0.4
[1] 0.4222222
[1] 0.4444444
[1] 0.4666667
[1] 0.4888889
[1] 0.5111111
[1] 0.5333333
[1] 0.5555556
[1] 0.5777778
[1] 0.6
[1] 0.6222222
[1] 0.6444444
[1] 0.6666667
[1] 0.6888889
[1] 0.7111111
[1] 0.7333333
[1] 0.7555556
[1] 0.7777778
[1] 0.8
[1] 0.8222222
[1] 0.8444444
[1] 0.8666667
[1] 0.8888889
[1] 0.9111111
[1] 0.9333333
[1] 0.9555556
[1] 0.9777778
[1] 1
> 
> 
> 
> 
> 
> dev.off()
null device 
          1 
>