The conditional hybrid Pareto mixture distribution

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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

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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.

Author(s)

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

See Also

condmixt.nll, condmixt.fwd

Examples

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# 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

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