dLnormParMix

This function computes the density of a mixture of a lognormal and a Pareto r.v.

mixture.

Estimates a lognormal-Pareto mixture by means of the Expectation-Conditional-Maximization-Either algorithm and by maximizing the profile likelihood function. A likelihood ratio test for discriminating between lognormal and Pareto tail is also implemented. See Bee, M. (2022) <doi:10.1007/s11634-022-00497-4>.

Marco Bee

LNPar

Estimation and Testing for a Lognormal-Pareto Mixture

dLnormParMix function

<dl><dt>x</dt>
<dd>non-negative numerical vector: values where the density has to be evaluated.</dd>
<dt>pi</dt>
<dd>scalar, 0 &lt; p &lt; 1: mixing weight.</dd>
<dt>mu</dt>
<dd>scalar: expected value of the lognormal distribution on the log scale.</dd>
<dt>sigma</dt>
<dd>positive scalar: standard deviation of the lognormal distribution on the log scale.</dd>
<dt>xmin</dt>
<dd>positive scalar: threshold.</dd>
<dt>alpha</dt>
<dd>positive scalar: Pareto shape parameter.</dd></dl>

Arguments

density of a mixture of a lognormal and a Pareto r.v. — dLnormParMix

<dl>

<dt>x</dt>
<dd>non-negative numerical vector: values where the density has to be evaluated.</dd>


<dt>pi</dt>
<dd>scalar, 0 &lt; p &lt; 1: mixing weight.</dd>


<dt>mu</dt>
<dd>scalar: expected value of the lognormal distribution on the log scale.</dd>


<dt>sigma</dt>
<dd>positive scalar: standard deviation of the lognormal distribution on the log scale.</dd>


<dt>xmin</dt>
<dd>positive scalar: threshold.</dd>


<dt>alpha</dt>
<dd>positive scalar: Pareto shape parameter.</dd>

</dl>

dLnormParMix: density of a mixture of a lognormal and a Pareto r.v.

Description

Usage

Value

Arguments

Examples