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A new one-parameter lifetime distribution and its regression model with applications

Author

Listed:
  • M S Eliwa
  • Emrah Altun
  • Ziyad Ali Alhussain
  • Essam A Ahmed
  • Mukhtar M Salah
  • Hanan Haj Ahmed
  • M El-Morshedy

Abstract

Lifetime distributions are an important statistical tools to model the different characteristics of lifetime data sets. The statistical literature contains very sophisticated distributions to analyze these kind of data sets. However, these distributions have many parameters which cause a problem in estimation step. To open a new opportunity in modeling these kind of data sets, we propose a new extension of half-logistic distribution by using the odd Lindley-G family of distributions. The proposed distribution has only one parameter and simple mathematical forms. The statistical properties of the proposed distributions, including complete and incomplete moments, quantile function and Rényi entropy, are studied in detail. The unknown model parameter is estimated by using the different estimation methods, namely, maximum likelihood, least square, weighted least square and Cramer-von Mises. The extensive simulation study is given to compare the finite sample performance of parameter estimation methods based on the complete and progressive Type-II censored samples. Additionally, a new log-location-scale regression model is introduced based on a new distribution. The residual analysis of a new regression model is given comprehensively. To convince the readers in favour of the proposed distribution, three real data sets are analyzed and compared with competitive models. Empirical findings show that the proposed one-parameter lifetime distribution produces better results than the other extensions of half-logistic distribution.

Suggested Citation

  • M S Eliwa & Emrah Altun & Ziyad Ali Alhussain & Essam A Ahmed & Mukhtar M Salah & Hanan Haj Ahmed & M El-Morshedy, 2021. "A new one-parameter lifetime distribution and its regression model with applications," PLOS ONE, Public Library of Science, vol. 16(2), pages 1-19, February.
    • Handle: RePEc:plo:pone00:0246969
    DOI: 10.1371/journal.pone.0246969
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    References listed on IDEAS

    as
    1. Morad Alizadeh & Ahmed Z. Afify & M. S. Eliwa & Sajid Ali, 2020. "The odd log-logistic Lindley-G family of distributions: properties, Bayesian and non-Bayesian estimation with applications," Computational Statistics, Springer, vol. 35(1), pages 281-308, March.
    2. Rodrigo R. Pescim & Edwin M. M. Ortega & Gauss M. Cordeiro & Morad Alizadeh, 2017. "A new log-location regression model: estimation, influence diagnostics and residual analysis," Journal of Applied Statistics, Taylor & Francis Journals, vol. 44(2), pages 233-252, January.
    3. Ayman Alzaatreh & Carl Lee & Felix Famoye, 2013. "A new method for generating families of continuous distributions," METRON, Springer;Sapienza Università di Roma, vol. 71(1), pages 63-79, June.
    4. Emrah Altun, 2021. "The log-weighted exponential regression model: alternative to the beta regression model," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 50(10), pages 2306-2321, May.
    5. 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.
    6. M. S. Eliwa & M. El-Morshedy & Sajid Ali, 2021. "Exponentiated odd Chen-G family of distributions: statistical properties, Bayesian and non-Bayesian estimation with applications," Journal of Applied Statistics, Taylor & Francis Journals, vol. 48(11), pages 1948-1974, August.
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