Maximum Likelihood Estimations Based on Upper Record Values for Probability Density Function and Cumulative Distribution Function in Exponential Family and Investigating Some of Their Properties

TL;DR

This paper develops maximum likelihood estimators based on upper record values for a subfamily of the exponential family, analyzing their properties and relations to estimators from random samples, especially for large samples.

Contribution

It introduces MLEs based on upper record values for a specific exponential family subfamily and investigates their properties and relationships to standard estimators.

Findings

MLEs based on record values are effective for large samples.

Relations between record-based MLEs and sample-based estimators are established.

Some properties of these estimators are proven to hold asymptotically.

Abstract

In this paper a useful subfamily of the exponential family has been considered. The ML estimation based on upper record values has been calculated for the parameter, Cumulative Density Function, and Probability Density Function of the family. Also, the relations between MLE based on record values and a random sample has been discussed. Additionally, some properties of these estimators have been investigated. Finally, it has been proven that these estimators have some useful properties for samples with large size