Journal of Statistical Theory and Practice

, Volume 11, Issue 1, pp 26–40

# The Maxwell length-biased distribution: Properties and estimation

Article

## Abstract

The concept of length-biased distribution can be employed in the development of proper models for the lifetime data. Length-biased distribution is a special case of the more general form known as the weighted distribution. This article introduces a new class of Maxwell length-biased distribution. The statistical properties of the proposed distribution are determined, including shape, kth moment, reliability function, hazard function, reverse hazard function, and so on. The maximum likelihood estimate (MLE), method of moments (MM) estimate, and Bayesian estimate of the unknown parameter are derived. An illustrative example demonstrates the application of the proposed distribution in real life.

## Keywords

Bayes estimate maximum likelihood estimate Maxwell length-biased distribution reliability function sufficient statistic

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