par_logn_mix_known

This function estimates the parameters of a Pareto and a lognormal density, assuming a known threshold.

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

par_logn_mix_known function

<dl><dt>y</dt>
<dd>non-negative numerical vector: random sample from the mixture.</dd>
<dt>prior1</dt>
<dd>scalar (0&lt;prior1&lt;1): starting value of the prior probability.</dd>
<dt>th</dt>
<dd>positive scalar: threshold.</dd>
<dt>alpha</dt>
<dd>non-negative scalar: starting value of the Pareto shape parameter.</dd>
<dt>mu</dt>
<dd>scalar: starting value of the lognormal parameter mu.</dd>
<dt>sigma</dt>
<dd>positive scalar: starting value of the lognormal parameter sigma.</dd></dl>

Arguments

Estimate the parameters of a lognormal-Pareto density, assuming a known threshold — par_logn_mix_known

<dl>

<dt>y</dt>
<dd>non-negative numerical vector: random sample from the mixture.</dd>


<dt>prior1</dt>
<dd>scalar (0&lt;prior1&lt;1): starting value of the prior probability.</dd>


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


<dt>alpha</dt>
<dd>non-negative scalar: starting value of the Pareto shape parameter.</dd>


<dt>mu</dt>
<dd>scalar: starting value of the lognormal parameter mu.</dd>


<dt>sigma</dt>
<dd>positive scalar: starting value of the lognormal parameter sigma.</dd>

</dl>

par_logn_mix_known: Estimate the parameters of a lognormal-Pareto density, assuming a known threshold

Description

Usage

Value

Arguments

Examples