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On progressively censored generalized inverted exponential distribution

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  • Sanku Dey
  • Tanujit Dey

Abstract

A generalized version of inverted exponential distribution (IED) is considered in this paper. This lifetime distribution is capable of modeling various shapes of failure rates, and hence various shapes of aging criteria. The model can be considered as another useful two-parameter generalization of the IED. Maximum likelihood and Bayes estimates for two parameters of the generalized inverted exponential distribution (GIED) are obtained on the basis of a progressively type-II censored sample. We also showed the existence, uniqueness and finiteness of the maximum likelihood estimates of the parameters of GIED based on progressively type-II censored data. Bayesian estimates are obtained using squared error loss function. These Bayesian estimates are evaluated by applying the Lindley's approximation method and via importance sampling technique. The importance sampling technique is used to compute the Bayes estimates and the associated credible intervals. We further consider the Bayes prediction problem based on the observed samples, and provide the appropriate predictive intervals. Monte Carlo simulations are performed to compare the performances of the proposed methods and a data set has been analyzed for illustrative purposes.

Suggested Citation

  • Sanku Dey & Tanujit Dey, 2014. "On progressively censored generalized inverted exponential distribution," Journal of Applied Statistics, Taylor & Francis Journals, vol. 41(12), pages 2557-2576, December.
    • Handle: RePEc:taf:japsta:v:41:y:2014:i:12:p:2557-2576
    DOI: 10.1080/02664763.2014.922165
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    References listed on IDEAS

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    1. Manoj Kumar Rastogi & Yogesh Mani Tripathi & Shuo-Jye Wu, 2012. "Estimating the parameters of a bathtub-shaped distribution under progressive type-II censoring," Journal of Applied Statistics, Taylor & Francis Journals, vol. 39(11), pages 2389-2411, July.
    2. Basak, Indrani & Basak, Prasanta & Balakrishnan, N., 2006. "On some predictors of times to failure of censored items in progressively censored samples," Computational Statistics & Data Analysis, Elsevier, vol. 50(5), pages 1313-1337, March.
    3. Sanjay Kumar Singh & Umesh Singh & Dinesh Kumar, 2013. "Bayesian estimation of parameters of inverse Weibull distribution," Journal of Applied Statistics, Taylor & Francis Journals, vol. 40(7), pages 1597-1607, July.
    4. Kundu, Debasis & Howlader, Hatem, 2010. "Bayesian inference and prediction of the inverse Weibull distribution for Type-II censored data," Computational Statistics & Data Analysis, Elsevier, vol. 54(6), pages 1547-1558, June.
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    Cited by:

    1. Liang Wang & Huizhong Lin & Yuhlong Lio & Yogesh Mani Tripathi, 2022. "Interval Estimation of Generalized Inverted Exponential Distribution under Records Data: A Comparison Perspective," Mathematics, MDPI, vol. 10(7), pages 1-20, March.
    2. Mahmoud R. Mahmoud & Hiba Z. Muhammed & Ahmed R. El-Saeed, 2023. "Inference for Generalized Inverted Exponential Distribution Under Progressive Type-I Censoring Scheme in Presence of Competing Risks Model," Sankhya A: The Indian Journal of Statistics, Springer;Indian Statistical Institute, vol. 85(1), pages 43-76, February.
    3. Essam A. Ahmed, 2017. "Estimation and prediction for the generalized inverted exponential distribution based on progressively first-failure-censored data with application," Journal of Applied Statistics, Taylor & Francis Journals, vol. 44(9), pages 1576-1608, July.
    4. Maha A. Aldahlan & Rana A. Bakoban & Leena S. Alzahrani, 2022. "On Estimating the Parameters of the Beta Inverted Exponential Distribution under Type-II Censored Samples," Mathematics, MDPI, vol. 10(3), pages 1-37, February.
    5. Fatih Kızılaslan, 2018. "Classical and Bayesian estimation of reliability in a multicomponent stress–strength model based on a general class of inverse exponentiated distributions," Statistical Papers, Springer, vol. 59(3), pages 1161-1192, September.
    6. Wang, Liang & Wu, Shuo-Jye & Zhang, Chunfang & Dey, Sanku & Tripathi, Yogesh Mani, 2022. "Analysis for constant-stress model on multicomponent system from generalized inverted exponential distribution with stress dependent parameters," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 193(C), pages 301-316.
    7. Aisha Fayomi & Ehab M. Almetwally & Maha E. Qura, 2023. "Exploring New Horizons: Advancing Data Analysis in Kidney Patient Infection Rates and UEFA Champions League Scores Using Bivariate Kavya–Manoharan Transformation Family of Distributions," Mathematics, MDPI, vol. 11(13), pages 1-37, July.
    8. Kousik Maiti & Suchandan Kayal, 2019. "Estimation for the generalized Fréchet distribution under progressive censoring scheme," International Journal of System Assurance Engineering and Management, Springer;The Society for Reliability, Engineering Quality and Operations Management (SREQOM),India, and Division of Operation and Maintenance, Lulea University of Technology, Sweden, vol. 10(5), pages 1276-1301, October.
    9. Dey, Sanku & Dey, Tanujit & Luckett, Daniel J., 2016. "Statistical inference for the generalized inverted exponential distribution based on upper record values," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 120(C), pages 64-78.

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