On unbiased estimators for functions of the rate parameter of the exponential distribution

TL;DR

This paper derives explicit unbiased estimators for various functions of the exponential distribution's rate parameter and proves their asymptotic normality, enhancing statistical inference methods for this distribution.

Contribution

It provides new explicit formulas for unbiased estimators of multiple functions of the rate parameter, complementing existing results and establishing their asymptotic properties.

Findings

Explicit unbiased estimators for functions of the rate parameter

Asymptotic normality of the estimators

Extension of existing formulas for exponential distribution

Abstract

In this paper, we explicitly derive unbiased estimators for various functions of the rate parameter of the exponential distribution in the absence of a location parameter, including powers of the rate parameter, the $q$th quantile, the $p$th moment, the survival function, the maximum, minimum, probability density function, mean past lifetime, moment generating function, and others. This work non-trivially complements established formulas for unbiased estimators of functions of parameters of the location-rate exponential distribution. Additionally, we establish a result demonstrating the asymptotic normality of the proposed unbiased estimators.