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

The Inverse Xgamma Distribution: Statistical Properties and Different Methods of Estimation 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. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Annals of Data Science Springer Journals

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

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References (24)

Publisher
Springer Journals
Copyright
Copyright © Springer-Verlag GmbH Germany, part of Springer Nature 2019
Subject
Business and Management; Business and Management, general; Statistics for Business, Management, Economics, Finance, Insurance; Artificial Intelligence
ISSN
2198-5804
eISSN
2198-5812
DOI
10.1007/s40745-019-00211-w
Publisher site
See Article on Publisher Site

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.

Journal

Annals of Data ScienceSpringer Journals

Published: Apr 16, 2019

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