mLf1

Return the marginal log-liklihood value of variable \(X_1\).

Implements the EM algorithm with one-step Gradient Descent method to estimate
the parameters of the Block-Basu bivariate Pareto distribution with location
and scale. We also found parametric bootstrap and asymptotic confidence
intervals based on the observed Fisher information of scale and shape parameters,
and exact confidence intervals for location parameters. Details are in
Biplab Paul and Arabin Kumar Dey (2023) <doi:10.48550/arXiv.1608.02199>
"An EM algorithm for absolutely continuous Marshall-Olkin bivariate Pareto
distribution with location and scale";
E L Lehmann and George Casella (1998) <doi:10.1007/b98854> "Theory of Point Estimation";
Bradley Efron and R J Tibshirani (1994) <doi:10.1201/9780429246593>
"An Introduction to the Bootstrap";
A P Dempster, N M Laird and D B Rubin
(1977) <www.jstor.org/stable/2984875> "Maximum Likelihood from Incomplete
Data via the EM Algorithm".

Biplab Paul

bvpa

Bivariate Pareto Distribution

Arabin Kumar Dey

mLf1 function

<dl><dt>I</dt>
<dd>baivariate observations.</dd>
<dt>mu1</dt>
<dd>value of \(\mu_1\).</dd>
<dt>s1</dt>
<dd>value of \(\sigma_1\).</dd>
<dt>a0</dt>
<dd>value of \(\alpha_0\).</dd>
<dt>a1</dt>
<dd>value of \(\alpha_1\).</dd>
<dt>a2</dt>
<dd>value of \(\alpha_2\).</dd></dl>

Arguments

Biplab Paul &lt;paul.biplab497@gmail.com&gt; and Arabin Kumar Dey &lt;arabin@iitg.ac.in&gt;

Author

Marginal log-liklihood function of variable X1 — mLf1

<dl>

<dt>I</dt>
<dd>baivariate observations.</dd>


<dt>mu1</dt>
<dd>value of \(\mu_1\).</dd>


<dt>s1</dt>
<dd>value of \(\sigma_1\).</dd>


<dt>a0</dt>
<dd>value of \(\alpha_0\).</dd>


<dt>a1</dt>
<dd>value of \(\alpha_1\).</dd>


<dt>a2</dt>
<dd>value of \(\alpha_2\).</dd>

</dl>

mLf1: Marginal log-liklihood function of variable X1

Description

Usage

Value

Arguments

Author

Examples