Classical and Bayesian Inference of Engineering and Disability Data: Using the Kavya Manoharan Power Chris-Jerry Distribution under Hybrid Censoring

Abstract

In this article, we study and introduce the Kavya-Manoharan power ChrisJerry distribution (KMPCJD) which is a new generation of the power Chris-Jerry distribution (PCJD) which is suitable for engineering and disability data. The probability density curves of KMPCJD demonstrate that it has practical applications in analyzing engineering and disability data in Saudi Arabia. Researchers have a lot of flexibility when developing statistical models for research on disability issues, since the hazard rate function (HRF) for KMPCJD can exhibit J-shaped, increasing, and decreasing trends. In addition, several significant KMPCJD features are calculated, including moments, reliability metrics, moment-generating function, and order statistics. Using data on engineering and disability difficulties, we estimate the parameters of KMPCJD and use classical and Bayesian techniques to assess their reliability and HRF under hybrid censored schemes. Asymptotic confidence/credible intervals are calculated. The numerical results show that when the sample size n increases while keeping other factors like r and T constant, the estimators for δ and λ show improved performance in terms of reduced Bias, mean square error (MSE), and narrower confidence intervals. Also, the Bayesian method also produces shorter credible intervals (LCCI) compared to the traditional confidence intervals (LACI) from ML and MPS methods, suggesting higher precision. To show the utility of the suggested distribution, it was tested in five datasets related to engineering and disability issues in Saudi Arabia. The KMPCJD performed better in terms of goodness of fit than a number of models, including the Kavya Manoharan Rayleigh inverted Weibull distribution, Kavya Manoharan Burr X distribution, exponentiated generalized power Lindley distribution, Weibull power Lindley distribution, power Lindley distribution, Kavya Manoharan generalized exponential distribution, power XLindley distribution, Kavya Manoharan unit exponentiated half logistic distribution, and PCJD. Due to its superior fit capabilities, the KMPCJD is suggested for data modeling in disciplines including engineering and disability difficulties.OPEN ACCESS Received: 27/08/2025 Accepted: 19/09/2025 Published: 27/11/2025

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