nConst_MC

This function evaluates via Monte Carlo simulation the normalizing constant of a Lognormal-GPD dynamic mixture,
with Cauchy or exponential weight.

dynamic

mixture.

Estimation of a dynamic lognormal - Generalized Pareto mixture via the Approximate Maximum Likelihood and the Cross-Entropy methods. See Bee, M. (2023) <doi:10.1016/j.csda.2023.107764>.

Marco Bee

FitDynMix

Estimation of Dynamic Mixtures

nConst_MC function

<dl><dt>x</dt>
<dd>if weight is equal to 'cau', (6 by 1) numerical vector: values of \(\mu_c\), \(\tau\), \(\mu\), \(\sigma\), \(\xi\), \(\beta\);
if weight is equal to 'exp', (5 by 1) numerical vector: values of \(\lambda\), \(\mu\), \(\sigma\), \(\xi\), \(\beta\).</dd>
<dt>nreps</dt>
<dd>number of replications to be used in the computation of the integral in the normalizing
constant.</dd>
<dt>xiInst</dt>
<dd>real: value of the shape parameter of the instrumental density. Default value equal to 3.</dd>
<dt>betaInst</dt>
<dd>non-negative real: value of the scale parameter of the instrumental density. Default value equal to 3.</dd>
<dt>weight</dt>
<dd>'cau' or 'exp': name of weight distribution.</dd></dl>

Arguments

Monte carlo approximation of the normalizing constant of a Lognormal-GPD dynamic mixture — nConst_MC

<dl>

<dt>x</dt>
<dd>if weight is equal to 'cau', (6 by 1) numerical vector: values of \(\mu_c\), \(\tau\), \(\mu\), \(\sigma\), \(\xi\), \(\beta\);
if weight is equal to 'exp', (5 by 1) numerical vector: values of \(\lambda\), \(\mu\), \(\sigma\), \(\xi\), \(\beta\).</dd>


<dt>nreps</dt>
<dd>number of replications to be used in the computation of the integral in the normalizing
constant.</dd>


<dt>xiInst</dt>
<dd>real: value of the shape parameter of the instrumental density. Default value equal to 3.</dd>


<dt>betaInst</dt>
<dd>non-negative real: value of the scale parameter of the instrumental density. Default value equal to 3.</dd>


<dt>weight</dt>
<dd>'cau' or 'exp': name of weight distribution.</dd>

</dl>

nConst_MC: Monte carlo approximation of the normalizing constant of a Lognormal-GPD dynamic mixture

Description

Usage

Value

Arguments

Examples