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A New Flexible Log-Logistic Distribution Based on a Nonhomogeneous Poisson Process: Properties, Classical and PINN-Based Estimation, and Applications |
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PP: 1545-1566 |
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doi:10.18576/amis/200607
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Author(s) |
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Sameer A. H. Al-Subh,
Hasanain Jalil Neamah Alsaedi,
Adel S. Hussain,
Emad A. Az-Zo’bi,
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Abstract |
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| This manuscript presents a novel and flexible lifetime distribution, called the Generalized Kavya–Manoharan Log-Logistic (GKMLL) distribution, which is built within the generalized Kavya–Manoharan (GKM-G) family using a nonhomogeneous Poisson process framework. The proposed model can describe a broad spectrum of hazard-rate behaviors, such as increasing, decreasing, bathtub- shaped, modified bathtub, upside-down bathtub and J-shaped, and is thus well suited to complex lifetime data. Moreover, the probability density function of the GKMLL distribution is highly flexible, with symmetric, skewed, and heavy-tailed shapes. Several key statistical properties of the distribution are derived, including the hazard rate, the quantile function, and entropy measures. Various classical estimation approaches, namely maximum likelihood, least squares, weighted least squares, Cramér–von Mises, Anderson–Darling, right-tail Anderson–Darling, maximum product of spacings, and percentile estimators, together with a modern physics-informed neural network (PINN) estimator, are used to estimate the model parameters. An extensive Monte Carlo simulation is conducted to assess the performance of the classical estimators, and it is shown that the maximum product of spacings method gives the best estimates in a range of situations. The practical usefulness of the GKMLL distribution is illustrated with two real-life datasets (gauge lengths and aircraft windshields). The results show that the proposed model achieves good performance on several goodness-of-fit (GOF) measures and graphical analyses compared with popular competing distributions. Moreover, the GOF results obtained with the PINN estimator are consistent with those obtained with maximum likelihood, which supports the efficiency of machine-learning-based inference. Overall, the GKMLL distribution is an effective and flexible tool for modeling complex lifetime data in reliability analysis and related tasks. |
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