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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 Sihombing, Pardomuan Robinson
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 Ade Marsinta Arsani Adina Astasia Ahid Nur Istinah Ahmaddien, Iskandar Aji, Lexi Jalu Al Aqilah, Muhamad Refkhi Amin Prawiro Madhani Anang Kurnia Anindita Ramadhani Anita, Tiurida Lily Arhaninka, Dewi Arsani, Ade Marsinta Artha Satwika Astawa, I Gede Putu Banu Avior Ocean Noya Bagus Sartono Basmallah, Fikri Dias Bayu Adinugroho Bekti Endar Susilowati Bekti Endar Susilowati Bekti Endar Susilowati Bertho Tantular Budiantono, Sigit Bungkus Sasongko Purnomo Bungkus Sasongko Purnomo Busminoloan Busminoloan Busminoloan Busminoloan Cahya Alkahfi Daniel Pangaribuan 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 Dyah Purwanti Ekowati Retnaningsih Erfiani Erfiani 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 Gumilang, Gabiela Gunawan, Ghina Hanifa HAMIDAH Hastoro Dwinantoaji Hema Malini, Hema Hendiva Tri Nugraha Hendry Frananda, Hendry Herman, Nur Ashilah Raihanah Hertanto, Rus 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 Iskandar Ahmaddien Islami, Rahmi Lathifah Istiqomatul Fajriyah Yuliati Istiqomatul Fajriyah Yuliati Jaka Wijaya Kusuma Januar Ramadhan Karel Fauzan Hakim Kartika Maulidya Irzain Khairil Anwar Notodiputro Khairil Anwar Notodiputro Khalimi Khalimi, Khalimi Krisdianto, Boby Febri Kuat Sidik Wahyono Kurnia, Anang Leni Merdawati Lexi Jalu Aji Lina Sari Lisna Sari Lisna Sari Luh Putu Widya Adnyani Maharani, Arya Putri Mahuda, Isnaini Maisaroh Maisaroh Marselinus Nirwan Luru Marta Sundari Marta Sundari Martina Cecilia Adriana Maryani, Sri Masruri Mochtar Maulidiyah, Syafrina Maydita Ayu Nursaskiawati Mella Anisa Miftahul Huda 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 Nurhidayati Nurhidayati Nurul Islam, Iis Hayyun Nuryanto Nuryanto Octaviana, Aniek Oki Prasetia Hendarsin Olivia, Theresia Padhilah Dikri Pangaribuan, Daniel Pascal, Emilio Pradita Galih Sekar Palupi Pudjiono, Bjardianto Puput Puspito Rini Putri Indi Rahayu Putri, Ayudya Purwani Putu Pande Wahyu Diatmika Putu Widya Adnyani, Luh Rahayu, Putri Indi Rahmi Lathifah Islami Rama Bhaskara Praja Ramadhanti, Ajeng Taufina Ramadhisa Fadli, Diva Aisyaliani Rini Rahani Risqi Nurika Fatha Hidayati Saeful Hidayat Sagala, Eliza Clara Yeremia Sarah Sholikhatun Risma Septie Wulandary Setiawan, Prayoga Sigit Budiantono Sigit Budiantono Sigit Budiantono Sigit Budiantono Sigit Budiantono Simanjuntak, Johana Veronika Simbolon, Zefanya Grace Enos Sinarta Putra P. Surbakti Sitorus, Yosef Felix Sodiqin, Achmad Sri Murdaningrum Sri Murtiningsih Stephanus, Matthew Sukarsa, Galuh Prabaningrum Ayu Sundari, Marta Supriatna, Yayat Suryadiningrat Suryadiningrat Suryadiningrat SYAMSUL HIDAYAT Taufik Febriyanto Temy Setiawan, Temy Triana Mauliasih Aritonang Triana Mauliasih Aritonang Ulfa Anggraini Usep Nugraha Usep Nugraha Wahyu Puji Lestari Widdia Angraini Widdia Angraini Wijaya, Lianna Wiradinata Lambok Silaban Wiranegara, Hanny Wahidin Wisely Yahya Wisnu Pratiko 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