Some Properties and Parameter Estimation of Length-Biased of Maxwell-Boltzmann Distribution

The primary objective of this article is to verify the theoretical properties of a reliability distribution that is the Length-biased Maxwell-Boltzmann distribution. The maximum likelihood estimator for the distribution parameters is obtained through the utilization of the “optimise” and “maxLik” functions within the R programming language. Furthermore, the article includes a comprehensive analysis that compares the estimates derived from a closed-form expression with those obtained using the “optimise” and “maxLik” functions. Finally, the construction of the Wald confidence interval for the Length-biased Maxwell-Boltzmann distribution is presented,