Log transformed transmuted exponential distribution‎: ‎an increasing hazard rate model to deal with cancer patients data

Document Type : Original Article

Authors

• Md Tahir
• Sanjay K. Singh
• Abhimanyu Singh Yadav

Department of Statistics, Institute of Science, Banaras Hindu University, Varanasi, India

10.22067/smps.2025.91480.1041

Abstract

‎In this paper‎, ‎we introduce a novel distribution called the log transformed transmuted exponential (LTTE)‎, ‎which is derived by applying a log transformation to the transmuted exponential distribution as the baseline model‎. ‎We derive several key mathematical and statistical properties of the LTTE distribution‎, ‎including its moments‎, ‎quantile function‎, ‎skewness‎, ‎kurtosis‎, ‎reliability function‎, ‎and hazard rate‎, ‎along with their respective shapes‎. ‎The maximum likelihood estimation method is used to estimate the parameters of the distribution‎. ‎The practical applicability of the LTTE distribution is demonstrated by fitting it to three real-life datasets related to cancer patients‎. ‎The results indicate that the LTTE distribution offers a superior fit‎, ‎as evidenced by better values of AIC‎, ‎BIC‎, ‎and the Kolmogorov--Smirnov (KS) statistic‎, ‎when compared to other existing lifetime models.‎

Keywords

• Maximum likelihood estimation
• ‎Moments
• ‎Transmuted exponential‎
• ‎Log transformation

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