A Comparison of Parameter Estimation Methods for the Inverted Modified Lindley Distribution

The Inverted Modified Lindley (IML) distribution has been shown to exhibit superior fitting capabilities compared to the exponential and Lindley distributions. This study investigates the parameter estimation of the IML distribution using the Least Squares (LS), Cramer von Misses (CvM), and Maximum Likelihood (ML) methods. A Monte Carlo simulation study is conducted to compare the efficiency of the ML, LS, and CvM methods in estimating the parameters of the IML distribution. Moreover, real data applications from various fields are provided using related estimation methods. The fitting performance of these methods is evaluated using root mean squared error, coefficient of determination, and the Kolmogorov-Smirnov test. According to the application results, the CvM estimates describe the considered data for the IML distribution best, while the simulation study favors ML estimation among the considered methods.