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

Author

Listed:
  • Abhimanyu Singh Yadav

    (Central University of Rajasthan)

  • Sudhansu S. Maiti

    (Visva-Bharati University)

  • Mahendra Saha

    (Central University of Rajasthan)

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.

Suggested Citation

  • Abhimanyu Singh Yadav & Sudhansu S. Maiti & Mahendra Saha, 2021. "The Inverse Xgamma Distribution: Statistical Properties and Different Methods of Estimation," Annals of Data Science, Springer, vol. 8(2), pages 275-293, June.
    • Handle: RePEc:spr:aodasc:v:8:y:2021:i:2:d:10.1007_s40745-019-00211-w
    DOI: 10.1007/s40745-019-00211-w
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    References listed on IDEAS

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    1. Manoj Kumar & Sanjay Kumar Singh & Umesh Singh, 2016. "Reliability Estimation for poisson-exponential model under Progressive type-II censoring data with binomial removal data," Statistica, Department of Statistics, University of Bologna, vol. 76(1), pages 3-26.
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