The Inverse Xgamma Distribution: Statistical Properties and Different Methods of Estimation

Abhimanyu Singh Yadav, Sudhansu S. Maiti and Mahendra Saha ()
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Abhimanyu Singh Yadav: Central University of Rajasthan
Sudhansu S. Maiti: Visva-Bharati University
Mahendra Saha: Central University of Rajasthan

Annals of Data Science, 2021, vol. 8, issue 2, No 6, 275-293

Abstract: Abstract The paper proposes a new probability distribution, named inverse xgamma (IXG) distribution. Different mathematical and statistical properties, viz., reliability characteristics, inverse moments, quantile function, mean inverse residual life, stress-strength reliability, stochastic ordering and order statistics of the proposed distribution have been derived and discussed. Estimation of the parameter of IXG distribution has been approached by different methods, namely, maximum likelihood estimation, least squares estimation, weighted least squares estimation, Cramèr–von-Mises estimation and maximum product of spacing estimation (MPSE). A simulation study has been carried out to compare the performance of these estimators in terms of their mean squared errors. Asymptotic confidence interval of the parameter in terms of average widths and coverage probabilities is also obtained using MPSE of the parameter. Finally, a data set is used to demonstrate the applicability of IXG distribution in real life situations.

Keywords: Asymptotic confidence interval; Cramer–Von Mises estimate; Maximum likelihood estimate; Maximum product spacing estimate; Weighted least squares estimate (search for similar items in EconPapers)
Date: 2021
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Citations: View citations in EconPapers (1)

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DOI: 10.1007/s40745-019-00211-w

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