# Transmuted Inverse Xgamma Distribution: Statistical Properties, Classical Estimation Methods and Data Modeling

## DOI:

https://doi.org/10.6092/issn.1973-2201/15277## Keywords:

Transmuted inverse Xgamma distribution, Lifetime distribution, Hazard rate function, Classical estimation, Simulation## Abstract

In this article, a new variant of Inverse Xgamma distribution is introduced by using the quadratic rank transmutation map (QRTM), named as Transmuted Inverse Xgamma (TIXG) distribution. The proposed model is positively skewed and has flexibility in the hazard rate function. A comprehensive account of mathematical and statistical properties of the newly obtained lifetime model are provided. Explicit expressions for moments, moment generating function, quantile functions, stochastic orderings, ageing intensity function and order statistics are formulated. We briefly discuss different classical estimations, including the maximum likelihood, maximum product spacings, least square, weighted least square and Cram`er-Von-Mises estimation methods. Monte Carlo simulation is carried out to compare the performance of the different estimation methods. Finally, to demonstrate the applicability of the model in real life, an illustrative example is performed by analyzing an environmental science dataset.

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*83*(1), 123–149. https://doi.org/10.6092/issn.1973-2201/15277

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