The inverse xgamma distribution: statistical properties and different methods of estimation

TL;DR

This paper introduces the inverse xgamma distribution (IXGD), explores its mathematical properties, compares various estimation methods, and demonstrates its applicability with real data examples.

Contribution

The paper proposes a new distribution, derives its properties, compares multiple estimation techniques, and applies it to real data, expanding statistical modeling options.

Findings

Derived reliability characteristics, moments, and order statistics of IXGD.

Compared estimators via simulation, analyzing their accuracy and confidence intervals.

Validated the distribution's practical use with real data sets.

Abstract

This paper proposed a new probability distribution named as inverse xgamma distribution (IXGD). Different mathematical and statistical properties,viz., reliability characteristics, moments, inverse moments, stochastic ordering and order statistics of the proposed distribution have been derived and discussed. The estimation of the parameter of IXGD has been approached by different methods of estimation, namely, maximum likelihood method of estimation (MLE), Least square method of estimation (LSE), Weighted least square method of estimation (WLSE), Cram'er-von-Mises method of estimation (CME) and maximum product spacing method of estimation (MPSE). Asymptotic confidence interval (ACI) of the parameter is also obtained. A simulation study has been carried out to compare the performance of the obtained estimators and corresponding ACI in terms of average widths and corresponding coverage probabilities. Finally, two real data sets have been used to demonstrate the applicability of IXGD in real life situations.