A New Three Parameter Inverted Weibull Model: Simulation and Application to Medical Data and Engineering Data

Abstract

Here, we study the logarithmic Lomax–Inverted Weibull (Log-LIW) distribution, a two three-parameter lifetime model within the Lomax–G family, developed to provide good flexibility for modeling skewed and heavy-tailed data encountered in reliability and survival analysis. The model used the Exponential distribution as the baseline and incorporates two additional shape parameters. The resulting Hazard Rate Function (HRF) is highly flexible and can exhibit non-monotonic decreasing–increasing shapes based on the parameter values, making the model suitable for a wide range of lifetime data.  Fundamental statistical properties are investigated, including the probability density function, Cumulative Distribution Function (CDF), reliability and hazard functions, cumulative and reverse hazard rates, the Quantile Function (qf), Renyi and Tsallis entropies, Bonferroni, Lorenz and Zenga curves. Additional characteristics, including moments, incomplete moments, the Moment Generating Function (MGF), stochastic ordering, Probability Weighted Moments (PWM) and order statistics, are also investigated. The model parameters are estimated via maximum likelihood. The practical usefulness of the Log-LIW distribution is illustrated using a real dataset. Goodness-of-fit comparisons, based on log-likelihood, Akaike Information Criterion (AIC), Bayesian Information Criterion (BIC), and Kolmogorov–Smirnov (KS), Anderson-Darling (AD), and Cram´er-von Mises (CvM) statistics together with their corresponding p values, are performed against four competing models. The results consistently show that the proposed Log-LIW distribution outperforms the competing models, confirming its suitability as a flexible and reliable alternative for modeling lifetime data.