A New Probability Distribution with Applications to ReliefTimes, Fiber ‎Stress and Aircraft Failure Data

  • Authors

    • Muhammad Osama Department of Statistics, University of Peshawar, Pakistan
    • Sayed Muhammad Zeeshan Department of Statistics, University of Peshawar, Pakistan
    • Sayed Alamgir Shah Department of Statistics, University of Peshawar, Pakistan
    https://doi.org/10.14419/x5dcps51

    Received date: February 11, 2026

    Accepted date: April 19, 2026

    Published date: April 21, 2026

  • Fréchet Distribution; Moments; Moment Generating Function; Maximum Likelihood Estimation; Simulation Study; Goodness of Fit

  • Abstract

    In this article, a new flexible statistical model is developed, known as the Khalil New Generalized Fréchet (KNG-Fréchet) distribution, which ‎extends the classical Fréchet distribution to better capture complex data behaviors. Several statistical properties of the proposed distribution, ‎including its quantile function, moments, moment generating function, and characteristic function, are thoroughly explored. Parameter estimation is performed using the maximum likelihood estimation (MLE) method. A simulation study is conducted to evaluate the performance of ‎the MLEs in terms of bias and mean squared error (MSE). To validate the effectiveness of the proposed distribution in real-world scenarios, ‎the proposed distribution is applied to three real-life datasets and compared with existing models using goodness-of-fit criteria. The ‎results demonstrate that the proposed model provides a good fit compared to existing alternative distributions, consistently outperforming ‎them in terms of goodness-of-fit measures, parameter stability, and overall flexibility when applied to different datasets and sample sizes‎.

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