condhparetomixt {condmixt} R Documentation

## The conditional hybrid Pareto mixture distribution

### Description

Distribution function for the conditional hybrid Pareto mixture with and without discrete component at zero and density function for the conditional hybrid Pareto mixture without discrete component.

### Usage

pcondhparetomixt(params, m, y, trunc = TRUE)
pcondhparetomixt.dirac(params,m,y)
dcondhparetomixt(params,m,y,log=FALSE,trunc=TRUE)


### Arguments

 params m x 4 x n matrix of mixture parameters where n is the number of examples for condhparetomixt and (4m+1) x n matrix for condhparetomixt.dirac m Number of mixture components. y Vector of n dependent variables. log logical, if TRUE, probabilities p are given as log(p). trunc logical, if TRUE (default), the hybrid Pareto density is truncated below zero. A mixture with a Dirac component at zero is always truncated below zero.

### Details

params can be computed from the forward functions on the explanatory variables x of dimension d x n associated with y : condhparetomixt.fwd and condhparetomixt.dirac.fwd

### Value

Distribution function evaluated at n points for pcondhparetomixt and pcondhparetomixt.dirac and density function for dcondhparetomixt.

Julie Carreau

### References

Carreau, J. and Bengio, Y. (2009), A Hybrid Pareto Mixture for Conditional Asymmetric Fat-Tailed Distributions, 20, IEEE Transactions on Neural Networks

condmixt.nll, condmixt.fwd

### Examples

# generate train data with a mass at zero
ntrain <- 200
xtrain <- runif(ntrain,0,2*pi)
alpha.train <- sin(2*xtrain)/2+1/2
data.train <- rep(0,ntrain)
for (i in 1:ntrain){
if (sample(c(0,1),1,prob=c(1-alpha.train[i],alpha.train[i]))){
# rainy day, sample from a Frechet
data.train[i] <-rfrechet(1,loc=3*sin(2*xtrain[i])+4,scale=1/(1+exp(-(xtrain[i]-1))),
shape=(1+exp(-(xtrain[i]/5-2))))
}
}

plot(xtrain,data.train,pch=20)

h <- 4 # number of hidden units
m <- 2 # number of components

# initialize a conditional mixture with hybrid Pareto components and a dirac at zero
thetainit <- condhparetomixt.dirac.init(1,h,m,data.train)

# compute mixture parameters on test data
params.mixt <- condhparetomixt.dirac.fwd(thetainit,h,m,t(xtrain))

cdf <- pcondhparetomixt.dirac(params.mixt,m,data.train) # compute CDF on test data



[Package condmixt version 1.1 Index]