Optimizing Poisson-Lindley Parameter Estimation: LQM and Reliability Analysis Applied to Guinea Pig Survival Data

The main objective of this work is to estimate the scale parameter of the Poisson Lindley distribution by means of multiple approaches, such as Poisson Linear Quantile-Moment and Maximum Likelihood. Based on mean square error criteria(MSE), Akaike information criterion (AIC), and Bayesian information criterion (BIC), Linear Quantile-Moment is the most efficient estimator among these techniques. The study focuses on reliability analysis and investigates the probability functions of the distribution to create a theoretical framework for parameter estimation by Using R programming language for in-depth analysis. Through simulation and real data analysis, several estimation techniques are compared and contrasted, demonstrating the superiority of the Linear Quantile Moment approach in terms of accuracy and model fit. The Poisson Lindley Distribution parameter estimation is improved in this work, which has implications for environmental research, finance, and epidemiology. Moreover, variance estimates for the known parameters and the related Kolmogorov–Smirnov (K–S) statistics, along with their corresponding p-values for the Poisson-Lindley Distribution (PLD), are analyzed using actual data on guinea pig survival times under various tubercle bacilli dosages. An observation indicating a strong fit with the optimal estimator with (LQM=4.190217) and the lowest MSE (78.71956) is made in light of the small K–S distance and the significant p-value for the test.