OICC Press Mathematical Sciences 2251-7456 18 1 (March 2024) 2022 07 13 The Exponential–Weibull logarithmic transformation with different estimation approaches under the right censoring scheme 10.1007/s40096-022-00485-x EN Seyed Rasuol Hosseini Department of Statistics, Qaemshahr Branch, Islamic Azad University, Qaemshahr, IR Einolah Deiri Department of Statistics, Qaemshahr Branch, Islamic Azad University, Qaemshahr, IR Ezzatallah Baloui Jamkhaneh Department of Statistics, Qaemshahr Branch, Islamic Azad University, Qaemshahr, IR Journal Article 2022 07 13 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.