article · Mikailalsys Journal of Mathematics and Statistics
Classical statistical distributions like the exponential, gamma, and Weibull models often struggle to capture skewed, kurtotic, and non-monotonic hazard behaviours found in medical and engineering lifetime data. To address these limitations, a new statistical model named the Alpha Power Transformed Ishita Distribution combines the Alpha Power Transformed family with the Ishita distribution. Mathematical properties of this model, including its moments, characteristic functions, reliability measures, and order statistics, have been established, alongside parameter estimation using maximum likelihood techniques. When tested on real-world data covering bladder cancer remission times, turbocharger failure times, and Australian athlete body fat percentages, the model consistently demonstrated superior fit compared to alternatives such as the Ishita, transmuted Ishita, sine-Ishita, Akash, and Lindley distributions based on standard selection criteria.
Accurately analysing survival and failure times is vital for assessing patient outcomes in medicine and predicting equipment breakdowns in engineering. Standard mathematical models often fail when data behaves irregularly. Providing a more flexible statistical distribution allows researchers and analysts to describe real-world survival and failure patterns with greater precision, leading to better diagnostic assessments and more reliable machinery monitoring.
This work represents early-stage, applied mathematical research that could be incorporated into statistical software packages used by reliability engineers and medical researchers. Potential users include clinical data analysts studying patient recovery timelines and industrial maintenance teams predicting component failure, such as turbocharger wear. While tested on real-world datasets, direct commercial deployment would require embedding the distribution and its estimation algorithms into accessible analytical toolkits or diagnostic software.
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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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DOI: 10.58578/mjms.v4i1.7674
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