Sine Power Unit Inverse Lindley Model: Bayesian Analysis and Practical Application

Techniques for trigonometric transformation have become an effective way to modify statistical distributions. These methods provide more flexibility in modeling various real-world phenomena by precisely adjusting skewness without adding complexity to the model. A novel, flexible two-parameter distribution, the sine power unit inverse Lindley (SPUIL) distribution, is proposed. This distribution is obtained by combining the power unit inverse Lindley distribution with the sine-G family. The SPUIL distribution demonstrates greater flexibility in modeling various hazard rate behaviors, including increasing, decreasing, N-shaped, U-shaped, and J-shaped patterns. The SPUIL distribution constitutes a sine inverse Lindley as a new sine model. Explicit expressions for key statistical properties are derived, such as the moment generating function, ordinary moments, quantile function, incomplete moments, and entropy measures. Reliability properties, including survival function, hazard rate, reversed hazard rate, mean residual life, and stress-strength reliability, are also investigated. For parameter estimation, both traditional maximum likelihood estimation and Bayesian estimation, incorporating symmetric and asymmetric loss functions, are considered. Since Bayesian estimation is computationally demanding, we use Markov Chain Monte Carlo methods using independent gamma and uniform priors. The parameter consistency of the proposed model is demonstrated using simulated analysis domains. Our simulation results confirmed the expected trend of improved accuracy for both maximum likelihood and Bayesian estimators as sample size increased. In all scenarios, the Bayesian estimates consistently outperformed the classical estimates. Notably, in certain cases, Bayesian estimates under the symmetric loss function yielded better results than those under the asymmetric loss function. Lastly, the suggested distribution's applicability is evaluated using actual data sets, and the suggested model's adaptability is demonstrated by comparing it to other models already in use.