Posterior Distribution with GEV, where xi=0

Description

MCMC runs of posterior distribution of data with parameters of Generalized Extreme Value (GEV) density, in the particular case where xi=0 with parameters mu,sigma.

Usage

posterior.gumbel(data, block, int)

Arguments

Value

The program has as result a matrix with dimensions int x 2, where the first represents points of posterior points of mu parameter of GEV, and the second column is posterior points of sigma parameter. The non-informative prior distribution of these parameters are Normal(0,1000) for the parameter mu and Gamma(0.001,0.001) for the parameter sigma. During the MCMC runs, screen shows the proportion of iteractions made.

Examples

# Obtaining posterior distribution of a vector of simulated points
x=rgev(200,xi=0.0001,mu=10,sigma=5)
# Obtaning 600 points of posterior distribution
ajuste=posterior.gumbel(x,1,600)
# 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)
# Maxima of each month in river nidd data
data(nidd.annual)
out=posterior.gumbel(nidd.annual,1,500)
# Predictive distribution for 15 day maxima ibovespa returns
data(ibovespa)
postibv=posterior.gumbel(ibovespa[,4],15,500)
datai=gev(ibovespa[,4],15)$data
predictive.gumbel(postibv,datai)

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.gumbel.Rd_%03d_medium.png", width=480, height=480)
> ### Name: posterior.gumbel
> ### Title: Posterior Distribution with GEV, where xi=0
> ### Aliases: posterior.gumbel
> 
> ### ** Examples
> 
> # Obtaining posterior distribution of a vector of simulated points
> x=rgev(200,xi=0.0001,mu=10,sigma=5)
> # Obtaning 600 points of posterior distribution
> ajuste=posterior.gumbel(x,1,600)
[1] 0.01111111
[1] 0.02222222
[1] 0.03333333
[1] 0.04444444
[1] 0.05555556
[1] 0.06666667
[1] 0.07777778
[1] 0.08888889
[1] 0.1
[1] 0.1111111
[1] 0.1222222
[1] 0.1333333
[1] 0.1444444
[1] 0.1555556
[1] 0.1666667
[1] 0.1777778
[1] 0.1888889
[1] 0.2
[1] 0.2111111
[1] 0.2222222
[1] 0.2333333
[1] 0.2444444
[1] 0.2555556
[1] 0.2666667
[1] 0.2777778
[1] 0.2888889
[1] 0.3
[1] 0.3111111
[1] 0.3222222
[1] 0.3333333
[1] 0.3444444
[1] 0.3555556
[1] 0.3666667
[1] 0.3777778
[1] 0.3888889
[1] 0.4
[1] 0.4111111
[1] 0.4222222
[1] 0.4333333
[1] 0.4444444
[1] 0.4555556
[1] 0.4666667
[1] 0.4777778
[1] 0.4888889
[1] 0.5
[1] 0.5111111
[1] 0.5222222
[1] 0.5333333
[1] 0.5444444
[1] 0.5555556
[1] 0.5666667
[1] 0.5777778
[1] 0.5888889
[1] 0.6
[1] 0.6111111
[1] 0.6222222
[1] 0.6333333
[1] 0.6444444
[1] 0.6555556
[1] 0.6666667
[1] 0.6777778
[1] 0.6888889
[1] 0.7
[1] 0.7111111
[1] 0.7222222
[1] 0.7333333
[1] 0.7444444
[1] 0.7555556
[1] 0.7666667
[1] 0.7777778
[1] 0.7888889
[1] 0.8
[1] 0.8111111
[1] 0.8222222
[1] 0.8333333
[1] 0.8444444
[1] 0.8555556
[1] 0.8666667
[1] 0.8777778
[1] 0.8888889
[1] 0.9
[1] 0.9111111
[1] 0.9222222
[1] 0.9333333
[1] 0.9444444
[1] 0.9555556
[1] 0.9666667
[1] 0.9777778
[1] 0.9888889
[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)
> # Maxima of each month in river nidd data
> data(nidd.annual)
> out=posterior.gumbel(nidd.annual,1,500)
[1] 0.01333333
[1] 0.02666667
[1] 0.04
[1] 0.05333333
[1] 0.06666667
[1] 0.08
[1] 0.09333333
[1] 0.1066667
[1] 0.12
[1] 0.1333333
[1] 0.1466667
[1] 0.16
[1] 0.1733333
[1] 0.1866667
[1] 0.2
[1] 0.2133333
[1] 0.2266667
[1] 0.24
[1] 0.2533333
[1] 0.2666667
[1] 0.28
[1] 0.2933333
[1] 0.3066667
[1] 0.32
[1] 0.3333333
[1] 0.3466667
[1] 0.36
[1] 0.3733333
[1] 0.3866667
[1] 0.4
[1] 0.4133333
[1] 0.4266667
[1] 0.44
[1] 0.4533333
[1] 0.4666667
[1] 0.48
[1] 0.4933333
[1] 0.5066667
[1] 0.52
[1] 0.5333333
[1] 0.5466667
[1] 0.56
[1] 0.5733333
[1] 0.5866667
[1] 0.6
[1] 0.6133333
[1] 0.6266667
[1] 0.64
[1] 0.6533333
[1] 0.6666667
[1] 0.68
[1] 0.6933333
[1] 0.7066667
[1] 0.72
[1] 0.7333333
[1] 0.7466667
[1] 0.76
[1] 0.7733333
[1] 0.7866667
[1] 0.8
[1] 0.8133333
[1] 0.8266667
[1] 0.84
[1] 0.8533333
[1] 0.8666667
[1] 0.88
[1] 0.8933333
[1] 0.9066667
[1] 0.92
[1] 0.9333333
[1] 0.9466667
[1] 0.96
[1] 0.9733333
[1] 0.9866667
[1] 1
> # Predictive distribution for 15 day maxima ibovespa returns
> data(ibovespa)
> postibv=posterior.gumbel(ibovespa[,4],15,500)
[1] 0.01333333
[1] 0.02666667
[1] 0.04
[1] 0.05333333
[1] 0.06666667
[1] 0.08
[1] 0.09333333
[1] 0.1066667
[1] 0.12
[1] 0.1333333
[1] 0.1466667
[1] 0.16
[1] 0.1733333
[1] 0.1866667
[1] 0.2
[1] 0.2133333
[1] 0.2266667
[1] 0.24
[1] 0.2533333
[1] 0.2666667
[1] 0.28
[1] 0.2933333
[1] 0.3066667
[1] 0.32
[1] 0.3333333
[1] 0.3466667
[1] 0.36
[1] 0.3733333
[1] 0.3866667
[1] 0.4
[1] 0.4133333
[1] 0.4266667
[1] 0.44
[1] 0.4533333
[1] 0.4666667
[1] 0.48
[1] 0.4933333
[1] 0.5066667
[1] 0.52
[1] 0.5333333
[1] 0.5466667
[1] 0.56
[1] 0.5733333
[1] 0.5866667
[1] 0.6
[1] 0.6133333
[1] 0.6266667
[1] 0.64
[1] 0.6533333
[1] 0.6666667
[1] 0.68
[1] 0.6933333
[1] 0.7066667
[1] 0.72
[1] 0.7333333
[1] 0.7466667
[1] 0.76
[1] 0.7733333
[1] 0.7866667
[1] 0.8
[1] 0.8133333
[1] 0.8266667
[1] 0.84
[1] 0.8533333
[1] 0.8666667
[1] 0.88
[1] 0.8933333
[1] 0.9066667
[1] 0.92
[1] 0.9333333
[1] 0.9466667
[1] 0.96
[1] 0.9733333
[1] 0.9866667
[1] 1
> datai=gev(ibovespa[,4],15)$data
> predictive.gumbel(postibv,datai)
  [1] 4.889710e-03 7.579767e-03 1.158679e-02 1.746824e-02 2.597531e-02
  [6] 3.810192e-02 5.513922e-02 7.873367e-02 1.109457e-01 1.543051e-01
 [11] 2.118588e-01 2.872048e-01 3.845073e-01 5.084876e-01 6.643849e-01
 [16] 8.578846e-01 1.095012e+00 1.381991e+00 1.725074e+00 2.130342e+00
 [21] 2.603489e+00 3.149599e+00 3.772919e+00 4.476657e+00 5.262785e+00
 [26] 6.131898e+00 7.083096e+00 8.113925e+00 9.220364e+00 1.039686e+01
 [31] 1.163643e+01 1.293077e+01 1.427044e+01 1.564508e+01 1.704361e+01
 [36] 1.845447e+01 1.986587e+01 2.126602e+01 2.264334e+01 2.398671e+01
 [41] 2.528560e+01 2.653025e+01 2.771182e+01 2.882244e+01 2.985532e+01
 [46] 3.080478e+01 3.166626e+01 3.243632e+01 3.311259e+01 3.369375e+01
 [51] 3.417945e+01 3.457026e+01 3.486756e+01 3.507346e+01 3.519072e+01
 [56] 3.522268e+01 3.517311e+01 3.504619e+01 3.484638e+01 3.457838e+01
 [61] 3.424702e+01 3.385725e+01 3.341400e+01 3.292223e+01 3.238679e+01
 [66] 3.181244e+01 3.120380e+01 3.056531e+01 2.990124e+01 2.921564e+01
 [71] 2.851235e+01 2.779496e+01 2.706688e+01 2.633122e+01 2.559091e+01
 [76] 2.484863e+01 2.410683e+01 2.336775e+01 2.263342e+01 2.190565e+01
 [81] 2.118609e+01 2.047618e+01 1.977720e+01 1.909026e+01 1.841633e+01
 [86] 1.775622e+01 1.711064e+01 1.648015e+01 1.586522e+01 1.526619e+01
 [91] 1.468334e+01 1.411685e+01 1.356683e+01 1.303330e+01 1.251624e+01
 [96] 1.201559e+01 1.153119e+01 1.106289e+01 1.061047e+01 1.017369e+01
[101] 9.752279e+00 9.345945e+00 8.954370e+00 8.577223e+00 8.214158e+00
[106] 7.864819e+00 7.528842e+00 7.205856e+00 6.895486e+00 6.597357e+00
[111] 6.311091e+00 6.036313e+00 5.772650e+00 5.519731e+00 5.277193e+00
[116] 5.044674e+00 4.821821e+00 4.608286e+00 4.403731e+00 4.207821e+00
[121] 4.020234e+00 3.840652e+00 3.668768e+00 3.504283e+00 3.346906e+00
[126] 3.196355e+00 3.052357e+00 2.914649e+00 2.782974e+00 2.657085e+00
[131] 2.536744e+00 2.421720e+00 2.311791e+00 2.206744e+00 2.106371e+00
[136] 2.010476e+00 1.918866e+00 1.831358e+00 1.747776e+00 1.667949e+00
[141] 1.591716e+00 1.518919e+00 1.449409e+00 1.383041e+00 1.319678e+00
[146] 1.259186e+00 1.201440e+00 1.146316e+00 1.093700e+00 1.043479e+00
[151] 9.955455e-01 9.497983e-01 9.061392e-01 8.644743e-01 8.247140e-01
[156] 7.867725e-01 7.505678e-01 7.160213e-01 6.830581e-01 6.516065e-01
[161] 6.215978e-01 5.929666e-01 5.656502e-01 5.395888e-01 5.147251e-01
[166] 4.910047e-01 4.683752e-01 4.467869e-01 4.261922e-01 4.065456e-01
[171] 3.878037e-01 3.699250e-01 3.528700e-01 3.366009e-01 3.210816e-01
[176] 3.062777e-01 2.921564e-01 2.786862e-01 2.658372e-01 2.535808e-01
[181] 2.418898e-01 2.307381e-01 2.201009e-01 2.099545e-01 2.002763e-01
[186] 1.910447e-01 1.822391e-01 1.738399e-01 1.658282e-01 1.581864e-01
[191] 1.508972e-01 1.439444e-01 1.373125e-01 1.309866e-01 1.249527e-01
[196] 1.191972e-01 1.137074e-01 1.084709e-01 1.034760e-01 9.871155e-02
[201] 9.416696e-02 8.983204e-02 8.569711e-02 8.175293e-02 7.799069e-02
[206] 7.440198e-02 7.097879e-02 6.771347e-02 6.459873e-02 6.162761e-02
[211] 5.879347e-02 5.609000e-02 5.351115e-02 5.105117e-02 4.870457e-02
[216] 4.646611e-02 4.433080e-02 4.229387e-02 4.035078e-02 3.849721e-02
[221] 3.672900e-02 3.504223e-02 3.343314e-02 3.189814e-02 3.043380e-02
[226] 2.903688e-02 2.770425e-02 2.643295e-02 2.522016e-02 2.406316e-02
[231] 2.295940e-02 2.190641e-02 2.090184e-02 1.994348e-02 1.902918e-02
[236] 1.815692e-02 1.732476e-02 1.653085e-02 1.577342e-02 1.505080e-02
[241] 1.436138e-02 1.370363e-02 1.307610e-02 1.247738e-02 1.190616e-02
[246] 1.136117e-02 1.084120e-02 1.034509e-02 9.871755e-03 9.420140e-03
[251] 8.989247e-03 8.578122e-03 8.185856e-03 7.811581e-03 7.454469e-03
[256] 7.113731e-03 6.788615e-03 6.478401e-03 6.182405e-03 5.899974e-03
[261] 5.630483e-03 5.373338e-03 5.127973e-03 4.893844e-03 4.670438e-03
[266] 4.457260e-03 4.253842e-03 4.059735e-03 3.874512e-03 3.697765e-03
[271] 3.529105e-03 3.368161e-03 3.214578e-03 3.068020e-03 2.928163e-03
[276] 2.794701e-03 2.667340e-03 2.545800e-03 2.429816e-03 2.319131e-03
[281] 2.213503e-03 2.112701e-03 2.016502e-03 1.924698e-03 1.837085e-03
[286] 1.753472e-03 1.673676e-03 1.597523e-03 1.524844e-03 1.455483e-03
[291] 1.389285e-03 1.326108e-03 1.265811e-03 1.208265e-03 1.153343e-03
[296] 1.100924e-03 1.050896e-03 1.003147e-03 9.575742e-04 9.140780e-04
[301] 8.725634e-04
> 
> 
> 
> 
> 
> dev.off()
null device 
          1 
>