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<p>This paper proposes and investigates a new probability distribution called the additive negative Perks–Lindley distribution. It is created by adding the hazard rate functions of the negative Perks and Lindley distributions. Its mathematical, structural and survival properties are studied. Among our results, the additive negative Perks–Lindley distribution is found to be more flexible than the negative Perks, Lindley and many other known distributions. In order to analyze the comparative behavior, stochastic ordering property is established. For the statistical aspect, the method of maximum likelihood estimation is provided to estimate the unknown parameters. A simulation algorithm for generating random samples from the negative Perks–Lindley distribution is described, together with a simulation analysis to assess the performances of the estimates. Finally, two sets of real data are fitted to show that this distribution provides a better fit to the data than any of the other distributions considered.</p>

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Additive negative Perks–Lindley distribution with increasing, decreasing and bathtub-shaped hazard rate function

  • 期刊论文

  • 发表日期：

    2026年2月5日

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  • Sunekh Pal,
  • Vivek Tyagi,
  • Christophe Chesneau,
  • Vikas Kumar Sharma

摘要

This paper proposes and investigates a new probability distribution called the additive negative Perks–Lindley distribution. It is created by adding the hazard rate functions of the negative Perks and Lindley distributions. Its mathematical, structural and survival properties are studied. Among our results, the additive negative Perks–Lindley distribution is found to be more flexible than the negative Perks, Lindley and many other known distributions. In order to analyze the comparative behavior, stochastic ordering property is established. For the statistical aspect, the method of maximum likelihood estimation is provided to estimate the unknown parameters. A simulation algorithm for generating random samples from the negative Perks–Lindley distribution is described, together with a simulation analysis to assess the performances of the estimates. Finally, two sets of real data are fitted to show that this distribution provides a better fit to the data than any of the other distributions considered.