Statistical inference on sine-exponential distribution parameter

Akeem Ajibola Adepoju; Akanji Olalekan Bello; Alhaji Modu Isa; Akinrefon Adesupo; Jamiu S. Olumoh

doi:10.32890/jcia2024.3.2.6

Authors

Akeem Ajibola Adepoju University of Science and Technology, Nigeria
Akanji Olalekan Bello Ahmadu Bello University, Nigeria
Alhaji Modu Isa Borno State University, Nigeria
Akinrefon Adesupo Adama University, Nigeria
Jamiu S. Olumoh American University of Nigeria, Nigeria

DOI:

https://doi.org/10.32890/jcia2024.3.2.6

Keywords:

Anderson-Darling, Cramer-von-Mises, maximum product, mean square error, sine-exponential distribution

Abstract

The Sine-Exponential (Sine-E) distribution is a probability distribution that combines the periodic behavior of the sine function with the decay characteristic of the exponential function. This study addresses the problem of identifying the most accurate and reliable estimation method for the parameter of the Sine-E distribution. The objective is to evaluate various parameter estimation techniques, including Maximum Likelihood Estimation (MLE), Least Squares Estimation (LSE), Weighted Least Squares Estimation (WLSE), Maximum Product of Spacing Estimation (MPSE), Cramer-von-Mises Estimation (CVME), and Anderson-Darling Estimation (ADE), using Mean Square Error (MSE) as the criterion for determining the technique with the minimum error. The study’s findings reveal that as sample size increases, the parameter estimates for all techniques converge to the true parameter value, with decreases in bias, MSE, and mean relative estimates. Among the techniques evaluated, the MPSE method consistently provides estimates closest to the true parameter value and exhibits the least bias and lowest MSE across small, moderate, and large sample sizes, making it the best estimator for the Sine-E distribution.

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