hparetomixt.negloglike {condmixt} R Documentation

## Maximum Likelihood Estimation for a Mixture of Hybrid Paretos

### Description

Negative log-likelihood and gradient (hparetomixt.negloglike), MLE of a hybrid Pareto distribution parameters (hparetomixt.fit) and out-of-sample negative log-likelihood estimation for a given number of components with nfold cross-validation (hparetomixt.cvtrain).

hparetomixt.fit applies the optimizer nlm to minimize the negative log-likelihood based on some starting values for the hybrid Pareto parameters.

### Usage

hparetomixt.negloglike(params, x)
hparetomixt.fit(params, x, ...)
hparetomixt.cvtrain(m, x, nfold=5, nstart=1, ...)


### Arguments

 params matrix of dimension 4 by m, where m is the number of components, each column of the matrix contains the mixture parameters of one component (pi, xi, mu, sigma) x a vector of length n of observations assumed to be sampled from a mixture of hybrid Paretos m number of mixture components nfold number of fold for cross-validation estimate, default is 5 nstart number of re-starts for the optimizer nlm with different initial parameters, default is 1 ... optional arguments for nlm

### Value

hparetomixt.negloglike returns a single value (the negative log-likelihood for given parameters and sample) and a vector, the gradient, which is passed as an attribute, while hparetomixt.fit returns a 4 by m matrix of MLE for the hybrid Pareto mixture parameters and hparetomixt.cvtrain returns a cross-validation estimate of the out-of-sample negative log-likelihood for a selected number of components

Julie Carreau

### References

Carreau, J. and Bengio, Y. (2009), A Hybrid Pareto Model for Asymmetric Fat-tailed Data: the Univariate Case, 12, Extremes

hparetomixt.init, hparetomixt.negloglike.tailpen
r <- rfrechet(500,loc=5,scale=5,shape=5)