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The generalized inverse Lindley distribution: A new inverse statistical model for the study of upside-down bathtub data

Author

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  • Vikas Kumar Sharma
  • Sanjay Kumar Singh
  • Umesh Singh
  • Faton Merovci

Abstract

In this article, a two-parameter generalized inverse Lindley distribution capable of modeling a upside-down bathtub-shaped hazard rate function is introduced. Some statistical properties of proposed distribution are explicitly derived here. The method of maximum likelihood, least square, and maximum product spacings are used for estimating the unknown model parameters and also compared through the simulation study. The approximate confidence intervals, based on a normal and a log-normal approximation, are also computed. Two algorithms are proposed for generating a random sample from the proposed distribution. A real data set is modeled to illustrate its applicability, and it is shown that our distribution fits much better than some other existing inverse distributions.

Suggested Citation

  • Vikas Kumar Sharma & Sanjay Kumar Singh & Umesh Singh & Faton Merovci, 2016. "The generalized inverse Lindley distribution: A new inverse statistical model for the study of upside-down bathtub data," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 45(19), pages 5709-5729, October.
    • Handle: RePEc:taf:lstaxx:v:45:y:2016:i:19:p:5709-5729
    DOI: 10.1080/03610926.2014.948206
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    Citations

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    Cited by:

    1. Sanku Dey & Indranil Ghosh & Devendra Kumar, 2019. "Alpha-Power Transformed Lindley Distribution: Properties and Associated Inference with Application to Earthquake Data," Annals of Data Science, Springer, vol. 6(4), pages 623-650, December.
    2. Friday Ikechukwu Agu & Joseph Thomas Eghwerido, 2021. "Agu-Eghwerido distribution, regression model and applications," Statistics in Transition New Series, Polish Statistical Association, vol. 22(4), pages 59-76, December.
    3. Komal Shekhawat & Vikas Kumar Sharma, 2021. "An Extension of J-Shaped Distribution with Application to Tissue Damage Proportions in Blood," Sankhya B: The Indian Journal of Statistics, Springer;Indian Statistical Institute, vol. 83(2), pages 548-574, November.
    4. Agu Friday Ikechukwu & Eghwerido Joseph Thomas, 2021. "Agu-Eghwerido distribution, regression model and applications," Statistics in Transition New Series, Statistics Poland, vol. 22(4), pages 59-76, December.
    5. Morad Alizadeh & Emrah Altun & Gamze Ozel & Mahmoud Afshari & Abbas Eftekharian, 2019. "A New Odd Log-Logistic Lindley Distribution with Properties and Applications," Sankhya A: The Indian Journal of Statistics, Springer;Indian Statistical Institute, vol. 81(2), pages 323-346, December.
    6. Yuancheng Si & Saralees Nadarajah, 2020. "Lindley Power Series Distributions," Sankhya A: The Indian Journal of Statistics, Springer;Indian Statistical Institute, vol. 82(1), pages 242-256, February.
    7. Siyi Chen & Wenhao Gui, 2020. "Statistical Analysis of a Lifetime Distribution with a Bathtub-Shaped Failure Rate Function under Adaptive Progressive Type-II Censoring," Mathematics, MDPI, vol. 8(5), pages 1-21, April.
    8. V. K. Rathaur & N. Chandra & Parmeet Kumar Vinit, 2024. "On Bayesian estimation of stress–strength reliability in multicomponent system for two-parameter gamma distribution," 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. 15(8), pages 3817-3832, August.

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