A Novel Two-Parameter Sine Model: Bayesian and Non-Bayesian Analysis with Application

Statistical methods are widely used in various real-life applications. Researchers are particularly interested in creating new probability models through different functions. However, few studies have explored the use of trigonometric functions to create new probability models. This paper introduces the sine power inverted Topp-Leone (SPITL) model, a novel two-parameter model constructed through a trigonometric-based transformation. The SPITL model features a hazard rate function that can take various forms, including inverted bathtub-shaped, increasing, decreasing, reversed J-shaped, or upside-down, along with a probability density function that is unimodal and positively skewed. The probability density function, cumulative distribution function, quantile function, moment-generating function, incomplete moments, Lorenz and Bonferroni curves, residual life and reversed residual life functions, stochastic ordering, stress-strength reliability, and entropy measures are among the important characteristics of the model that are examined in this work. Parameter estimation is conducted using both maximum likelihood and Bayesian methods with simulations to verify the model's effectiveness. Finally, two real-world datasets from agriculture and water resources are analyzed to demonstrate the model's flexibility. The SPITL model is compared with several competing distributions and is shown to outperform them according to standard statistical criteria. Furthermore, the likelihood ratio test is employed to assess the compatibility of the sine-inverted Topp-Leone model as a special case. The results confirm that the SPITL framework effectively captures the data's characteristics while maintaining statistical consistency with its sub-models, offering fresh avenues for further study in these fields.