ll_lnormparmix

This function evaluates the log-likelihood function with respect to xmin for a mixture of a lognormal and a Pareto r.v.,
assuming to know the numerical values of all the other parameters.

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

ll_lnormparmix function

<dl><dt>x</dt>
<dd>positive scalar: value of xmin where the function is evaluated.</dd>
<dt>pi</dt>
<dd>scalar, 0 &lt; pi &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>alpha</dt>
<dd>non-negative scalar: Pareto shape parameter.</dd>
<dt>y</dt>
<dd>(nx1) vector: random sample from the mixture.</dd></dl>

Arguments

Log-likelihood with respect to xmin — ll_lnormparmix

<dl>

<dt>x</dt>
<dd>positive scalar: value of xmin where the function is evaluated.</dd>


<dt>pi</dt>
<dd>scalar, 0 &lt; pi &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>alpha</dt>
<dd>non-negative scalar: Pareto shape parameter.</dd>


<dt>y</dt>
<dd>(nx1) vector: random sample from the mixture.</dd>

</dl>

ll_lnormparmix: Log-likelihood with respect to xmin

Description

Usage

Value

Arguments

Examples