Modi linear failure rate distribution with application to survival time data

A new lifetime model, named the Modi linear failure rate distribution, is suggested. This flexible model is capable of accommodating a wide range of hazard rate shapes, including decreasing, increasing, bathtub, upside-down bathtub, and modified bathtub forms, making it particularly suitable for modeling diverse survival and reliability data. Our proposed model contains the Modi exponential distribution and the Modi Rayleigh distribution as sub-models. Numerous mathematical and reliability properties are derived, including the $r^{th}$ moment, moment generating function, $r^{th}$ conditional moment, quantile function, order statistics, mean deviations, R\'{e}nyi entropy, and reliability function. The method of maximum likelihood is employed to estimate the model parameters. Monte Carlo simulations are presented to examine how these estimators perform. The superior fit of our newly introduced model is proved through two real-world survival data sets.