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Journal : RAGAM: Journal of Statistics and Its Application

COMPARISON OF SIX NORMAL DISTRIBUTION PARAMETER ESTIMATION METHODS: MONTE CARLO SIMULATION STUDY WITH COMPREHENSIVE EVALUATION Pardomuan Robinson Sihombing
RAGAM: Journal of Statistics & Its Application Vol 4, No 2 (2025): RAGAM: Journal of Statistics & Its Application
Publisher : Universitas Lambung Mangkurat

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.20527/ragam.v4i2.17104

Abstract

Estimating normal distribution parameters is one of the fundamental problems in statistics that has attracted the attention of researchers for more than two centuries. This study aims to analyse and compare the performance of six normal distribution parameter estimation methods, which include Method of Moments (MoM), Maximum Likelihood Estimation (MLE), Least Squares Estimation (LSE), Bayesian Estimation, Percentile Matching, and Generalised Method of Moments (GMM), through a systematic and comprehensive approach. The methodology of this study combines rigorous theoretical mathematical derivation for each estimation method with empirical evaluation through extensive Monte Carlo simulations. Each method was derived mathematically from the basic principle to the final estimator formula, then implemented in a simulation with 500 replications on various sample sizes, i.e. n = 30, 50, 100, and 200, of the normal distribution of N (5, 4). In small samples with n = 30, Percentile Matching showed the highest MSE for   parameter estimation with a value of 0.162, while MoM, MLE, and LSE showed the best performance with MSE for μ parameter of 0.127 and MSE for parameter 0.067. The main conclusions of this study show that MLE provides an optimal balance between statistical accuracy and computational efficiency for most practical applications. Bayesian Estimation shows good stability at all sample sizes and is superior when informative prior information is available. 
Co-Authors Abdul Gofur Rochman Ade Famalika Ade Famalika Ade Marsinta Arsani Ade Marsinta Arsani Ade Marsinta Arsani Ade Marsinta Arsani Ade Marsinta Arsani Ade Marsinta Arsani Ade Marsinta Arsani Ade Marsinta Arsani Ade Marsinta Arsani Adina Astasia Ahid Nur Istinah Ahmaddien, Iskandar Aji, Lexi Jalu Al Aqilah, Muhamad Refkhi Amin Prawiro Madhani Anang Kurnia Anita, Tiurida Lily Arsani, Ade Marsinta Artha Satwika Astawa, I Gede Putu Banu Avior Ocean Noya Bagus Sartono Bekti Endar Susilowati Bekti Endar Susilowati Bekti Endar Susilowati Bertho Tantular Bungkus Sasongko Purnomo Bungkus Sasongko Purnomo Busminoloan Busminoloan Cahya Alkahfi Daqiqil Id, Ibnu Deden Achmad Sunarjo Desak Ari Gita Wahyuni Deva A. Nurul Huda Devitama Patria Nagara Dhinnessa Prabowo Drajat Indra Purnama DRAJAT INDRA PURNAMA Dwi Muslianti Dyah Purwanti Ekowati Retnaningsih Erfiani Erfiani Erfiani Erfiani, Erfiani Erica Indryani Fadlol Muhammad Fajar Faiza Aina Nurrizqi Feri Fernandes Fitri Mudia Sari Frisca Adriana Gregorius Ivan Aditya Purwahendra Gultom, Yulifar Amin Gunawan, Ghina Hanifa HAMIDAH Hastoro Dwinantoaji Hema Malini, Hema Hendiva Tri Nugraha Hendry Frananda, Hendry Herman, Nur Ashilah Raihanah I Dewa Gede Sunanjaya I Gede Heprin Prayasta I Gede Heprin Prayasta Ida Ayu Candrawati Ida Ayu Candrawati Iis Hayyun Nurul Islam Ine Ratna Dewi Irma Nurmala Dewi Istiqomatul Fajriyah Yuliati Istiqomatul Fajriyah Yuliati Jaka Wijaya Kusuma Januar Ramadhan Karel Fauzan Hakim Kartika Maulidya Irzain Khairil Anwar Notodiputro Krisdianto, Boby Febri Kuat Sidik Wahyono Kurnia, Anang Leni Merdawati Lina Sari Lisna Sari Lisna Sari Luh Putu Widya Adnyani Mahuda, Isnaini Marta Sundari Marta Sundari Maryani, Sri Masruri Mochtar Maydita Ayu Nursaskiawati Mella Anisa Miftahul Huda Miftakhul Jannah Mohamad Arif Kurniawan Mohamad Arif Kurniawan Muchtar, Masruri Muhammad Hafiz Fadhilah Muhammad Heru Akhmadi Muhammad Ramadhan Zulfi Muliantino, Mulyanti Roberto Mun'im, Akhmad Neni Nur Laili Ersela Zain Ng, Kah Choon Ni Kadek Sinarwati Novitha, Irni Nurhidayati Nurhidayati Nurhidayati Nurhidayati Nuryanto Nuryanto Oki Prasetia Hendarsin Padhilah Dikri Pascal, Emilio Pradita Galih Sekar Palupi Puput Puspito Rini Putri Indi Rahayu Putu Pande Wahyu Diatmika Putu Widya Adnyani, Luh Rahayu, Putri Indi Rahmi Lathifah Islami Rama Bhaskara Praja Ramadhisa Fadli, Diva Aisyaliani Rini Rahani Risqi Nurika Fatha Hidayati Saeful Hidayat Sarah Sholikhatun Risma Septie Wulandary Sigit Budiantono Sigit Budiantono Sigit Budiantono Sigit Budiantono Sigit Budiantono Simbolon, Zefanya Grace Enos Sinarta Putra P. Surbakti Sodiqin, Achmad Sri Murdaningrum Stephanus, Matthew Sundari, Marta Supriatna, Yayat Suryadiningrat Suryadiningrat Suryadiningrat SYAMSUL HIDAYAT Taufik Febriyanto Temy Setiawan, Temy Triana Mauliasih Aritonang Triana Mauliasih Aritonang Ulfa Anggraini Usep Nugraha Wahyu Puji Lestari Widdia Angraini Wijaya, Lianna Wiradinata Lambok Silaban Wiranegara, Hanny Wahidin Wisnu Pratiko Y Yunita Yanti, Ni Komang Semara Yesi, Desri Yoshep Paulus Apri Caraka Yuda Yudhie Andriyana Yuninda Anggraini Putri Yunita Yunita Yunita Zain Yudha Prawira Zakir, Supratman