Estimation of Extension of Topp-Leone Distribution using Two Different Methods: Maximum Product Spacing and Maximum Likelihood Estimate

Abstract

Study’s Excerpt/Novelty

• This study provides a comprehensive evaluation of parameter estimation methods for the Log-Topp-Leone (L-T-L), Topp-Leone-Exponential (T-L-E), and Topp-Leone-Weibull (T-L-W) distributions using maximum likelihood (ML) and maximum product spacing (MPS) techniques.
• Through simulations conducted in R-Studio, the research demonstrates the consistency and adequacy of these estimators, particularly highlighting the unbiased and efficient performance of the ML estimator.
• The findings underscore the recommendation of ML over MPS for parameter estimation in Topp-Leone distribution extensions, contributing valuable insights into statistical methodology for complex distribution models.

Full Abstract

The parameters for Log-Topp-leone (L-T-L) distribution, Topp-leone-exponential (T-L-E) distribution, and Top-plane-Weibull (T-L-W)distribution were estimated via the methods of  ML (maximum likelihood) and MPS (maximum product spacing).  Simulations were carried out using R-Studio to estimate the parameters and check the efficiency of the estimators.  As a consequence, if the sample size (SS) increases, the outcome of the estimations tends to the true PV (parameter values), which proves the consistency and adequacy (C & A) of all the estimators.  Similarly, the MSE and biases using the two estimators approach zero, even though some MPS bias values fluctuated.  This shows the suitability of each estimator, and MLE is more unbiased and adequate.  The estimates using MLE and MPS were efficient.  Thus, we recommend that MLE be employed in assessing and computing the parameters of extensions of the Topp-Leone (TL) distribution.