Parameters Estimation for the [0, 1] Truncated Nadarajah Haghighi Rayleigh Distribution

Abstract

This paper investigates the estimation of three unknown parameters for the [0, 1] Truncated Nadarajah Haghighi Rayleigh distribution, denoted as ([0, 1] TNHR). It explores eight different estimation methods, namely the maximum likelihood, maximum product spacing, Anderson-Darling, Right Anderson-Darling, ordinary least squares, weighted least squares, Cramer-von Mises, and percentiles for point estimation. Detailed analyses were conducted to compare the effectiveness of these estimators in terms of bias and mean squared errors through extensive simulation experiments. The simulation results indicate that all the estimators perform well according to these criteria and exhibit similar values when the sample size is large. Some statistical properties of the new distribution are also derived. Additionally, the estimators were applied to two real life datasets, and the results of the Kolmogorov-Smirnov statistics were reported for each of them. Finally, the [0, 1] Truncated Nadarajah Haghighi Rayleigh distribution was applied to two real world datasets, its performance was compared to other famous extensions of Rayleigh distribution using four different selection criteria.

Keywords

• Truncated
• Rayleigh distribution
• Anderson-Darling
• simulation
• application