NONE 20260602115532799 wseas/wseas content-registration-form+ja@crossref.org content-registration-form WSEAS TRANSACTIONS ON SYSTEMS 1109-2777 2224-2678 Wikanda Phaphan Department of Applied Statistics, Faculty of Applied Science, King Mongkut’s University of Technology North Bangkok, Bangkok 10800, THAILAND https://orcid.org/0000-0002-6082-4779 Nattawut Khansai Department of Mathematics, Faculty of Applied Science, King Mongkut’s University of Technology North Bangkok, Bangkok 10800, THAILAND https://orcid.org/0000-0001-7053-0072 Ibrahim Abdullahi Department of Mathematics and Statistics, Faculty of Science, Yobe State University, Damaturu 500501, NIGERIA https://orcid.org/0000-0002-7280-3035 Chalermrat Nontapa Department of Statistics, Faculty of Science, Chiang Mai University, Chiang Mai 50200, THAILAND https://orcid.org/0009-0006-0628-697X 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. 06 02 2026 06 02 2026 352 28 https://creativecommons.org/licenses/by/4.0/deed.en_US 10.37394/23202.2026.25.28 https://wseas.com/journals/systems/2026/a565106-2262.pdf Pollard, J.H., Valkovics, E.J.: The gompertz distribution and its applications. 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