WSEAS Transactions on Systems
Print ISSN: 1109-2777, E-ISSN: 2224-2678
Volume 25, 2026
Estimating Parameters for the New Mixture Nakagami and Rayleigh Distributions: Mathematical Properties and Simulations
Authors: , , ,
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Abstract: This article proposes a new distribution called the mixture Nakagami-Rayleigh (mNR)
distribution, which is obtained by combining Nakagami and Rayleigh distributions. The maximum
likelihood estimator (MLE) is the primary approach we propose to estimate the parameters for the
mN-R distribution. This paper also presents related functions of the mNR distribution, such as the
survival function, the probability density function (PDF), the cumulative distribution function (CDF),
and the hazard function, along with the important mathematical properties of the mNR distribution.
Additionally, plots of the important functions of the mNR distribution are illustrated as line plots
and contour plots. Furthermore, we present a simulation study to demonstrate the flexibility of the
mNR distribution. Finally, the article concludes by summarizing the key outcomes and providing
recommendations for future work.
Keywords:
Nakagami distribution, Rayleigh distribution, Mixture Nakagami-Rayleigh distribution, Maximum likelihood estimator, Probability modeling in public health
Pages: 352-369
DOI: 10.37394/23202.2026.25.28