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Inverse Gompertz Distribution: Properties and Different Estimation Methods with Application to Complete and Censored Data

Author

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  • M. S. Eliwa

    (Mansoura University)

  • M. El-Morshedy

    (Mansoura University)

  • Mohamed Ibrahim

    (Damietta University)

Abstract

In this article, we introduce inverse Gompertz distribution with two parameters. Some statistical properties are presented such as hazard rate function, quantile, probability weighted (moments), skewness, kurtosis, entropies function, mean residual lifetime and mean inactive lifetime. The model parameters are estimated by the method of maximum likelihood, bootstrap, least squares, weighted least squares and Cramér-von Mises. Further, Monte Carlo simulations are carried out to compare the long-run performance of the estimators based on complete and type II right censored data. Finally, we estimate the parameters based on behavioral sciences data and fatigue life of 10 bearing of a certain type in hours censored data, which explain that the model fits the data better than some models.

Suggested Citation

  • M. S. Eliwa & M. El-Morshedy & Mohamed Ibrahim, 2019. "Inverse Gompertz Distribution: Properties and Different Estimation Methods with Application to Complete and Censored Data," Annals of Data Science, Springer, vol. 6(2), pages 321-339, June.
    • Handle: RePEc:spr:aodasc:v:6:y:2019:i:2:d:10.1007_s40745-018-0173-0
    DOI: 10.1007/s40745-018-0173-0
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    References listed on IDEAS

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    1. Clifford M. Hurvich & Chih‐Ling Tsai, 1993. "A Corrected Akaike Information Criterion For Vector Autoregressive Model Selection," Journal of Time Series Analysis, Wiley Blackwell, vol. 14(3), pages 271-279, May.
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    Cited by:

    1. Dina H. Abdelhady & Yasser M. Amer, 2021. "On the Inverse Power Gompertz Distribution," Annals of Data Science, Springer, vol. 8(3), pages 451-473, September.
    2. M. S. Eliwa & Ziyad Ali Alhussain & M. El-Morshedy, 2020. "Discrete Gompertz-G Family of Distributions for Over- and Under-Dispersed Data with Properties, Estimation, and Applications," Mathematics, MDPI, vol. 8(3), pages 1-26, March.
    3. Mohamed A. W. Mahmoud & Mohamed G. M. Ghazal & Hossam M. M. Radwan, 2023. "Bayesian Estimation and Optimal Censoring of Inverted Generalized Linear Exponential Distribution Using Progressive First Failure Censoring," Annals of Data Science, Springer, vol. 10(2), pages 527-554, April.

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