pctl.fun

Survival functions of pivots of estimators of locations \(\mu_1\) and \(\mu_2\).
These are required to calculate the critical value of confidence intervals for \(\mu_1\)
and \(\mu_2\).

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

pctl.fun function

<dl><dt>z</dt>
<dd>quantiles.</dd>
<dt>n</dt>
<dd>number of observations.</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>
<dt>pct</dt>
<dd>probabilities.</dd>
<dt>select</dt>
<dd>Allows to select the function for different location parameters. a single model term to be selected for printing.
e.g. if you just want the function for \(\mu_1\) set \(select=1\) (default).</dd></dl>

Arguments

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

Author

Survival functions of pivots of estimators of locations. — pctl.fun

<dl>

<dt>z</dt>
<dd>quantiles.</dd>


<dt>n</dt>
<dd>number of observations.</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>


<dt>pct</dt>
<dd>probabilities.</dd>


<dt>select</dt>
<dd>Allows to select the function for different location parameters. a single model term to be selected for printing.
e.g. if you just want the function for \(\mu_1\) set \(select=1\) (default).</dd>

</dl>

pctl.fun: Survival functions of pivots of estimators of locations.

Description

Usage

Value

Arguments

Author

Examples