10.1007/s40096-022-00485-x

The Exponential–Weibull logarithmic transformation with different estimation approaches under the right censoring scheme

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  • Seyed Rasuol Hosseini1,
  • Einolah Deiri*1,
  • Ezzatallah Baloui Jamkhaneh1,
  1. Department of Statistics, Qaemshahr Branch, Islamic Azad University, Qaemshahr, IR

Published in Issue 2022-07-13

How to Cite

Hosseini, S. R., Deiri, E., & Baloui Jamkhaneh, E. (2022). The Exponential–Weibull logarithmic transformation with different estimation approaches under the right censoring scheme. Mathematical Sciences, 18(1 (March 2024). https://doi.org/10.1007/s40096-022-00485-x
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Abstract

Abstract In this paper, we concentrated on a new lifetime distribution based on the Exponential–Weibull distribution and the logarithmic transformation named EW–LT. The novel EW–LT distribution is compatible with different kinds of data, with different shapes of the probability function. Also, in the EW–LT distribution, there is no extra parameter in the model than the other baseline distribution, which indicates parsimonious parameters. The probability density function of the EW–LT distribution is included monotone and unimodal with different types of skewness shapes. We provided some statistical properties of the EW–LT distribution including non-central moments, incomplete moments, moment generating, and quantile functions. Several estimation methods such as maximum likelihood, Bayesian and Bayesian shrinkage are considered for the parameters of the EW–LT model under the right censoring scheme. The Bayesian and Bayesian shrinkage estimators are obtained under both square error and Al-Bayyati loss functions. The Bayesian estimators have been computed through the importance sampling method. Different estimation approaches of the parameters of the EW–LT distribution are evaluated through a rich Monte Carlo simulation study. The privilege of the EW–LT distribution in modeling real data is demonstrated by four clinical data sets among other competitive models.

Keywords

  • Exponential–Weibull,
  • Importance sampling,
  • Logarithmic transformation,
  • Bayesian shrinkage,
  • Chickenpox disease

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