<![CDATA[Modeling lifetime and reliability data in medicine and engineering often requires highly flexible statistical distributions capable of capturing skewed, kurtotic, and non-monotonic hazard behaviors, for which classical models such as the exponential, gamma, and Weibull distributions are often inadequate. To address this limitation, numerous generalized families of distributions have been developed, including the Alpha Power Transformed (APT) family, which has gained attention due to its simplicity and capacity to enhance the flexibility and tail behavior of some classical distributions, and the Ishita distribution, which has proven useful for modeling lifetime data with increasing or decreasing hazard rates in medical and reliability contexts. Building on these developments, this study proposes a new extension of the Ishita model known as the Alpha Power Transformed Ishita Distribution (APTID). The study derives and investigates important properties of this distribution, including its moments, moment-generating and characteristic functions, reliability measures, and order statistics, and estimates its parameters using the maximum likelihood method. The performance of the proposed APTID is evaluated using three real-life datasets, namely the remission times of bladder cancer patients, failure times of turbocharger, and body fat percentages of Australian athletes. Model selection criteria such as AIC, BIC, CAIC, and Kolmogorov–Smirnov tests indicate that the APTID consistently outperforms the transmuted Ishita, sine-Ishita, Ishita, Akash, and Lindley distributions. These results confirm that the proposed APTID will be a robust and versatile method for modeling diverse medical and engineering lifetime data.]]>
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