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Home > Vol 33, No 3 (2023) > Yamrubboon

Anderson-Darling Parameter Estimation of the Marshall-Olkin Length-Biased Exponential Distribution with Applications in Engineering and Environment

Darika Yamrubboon, Areeya Sudsuk

Abstract


การศึกษาครั้งนี้มีวัตถุประสงค์เพื่อประยุกต์ใช้ตัวประมาณแอนเดอร์สัน-ดาร์ลิ่ง (minimum Anderson-Darling estimator: MADE) ในการประมาณค่าพารามิเตอร์ที่ไม่ทราบค่าของการแจงแจงแบบมาร์แชล์โอคินความยาวเอนเอียงเลขชี้กำลัง (Marshall-Olkin Length-Biased Exponential (MOLBE) distribution) ซึ่งการแจกแจงนี้เป็นการการแจกแจงที่ขยายจากการแจงแจงแบบความยาวเอนเอียงเลขชี้กำลัง (Length-Biased Exponential distribution) โดยใช้หลักการของมาร์แชลโอคิน (Marshall-Olkin scheme) อีกทั้งการแจกแจง MOLBE ยังเป็นการแจกแจงที่มีความยืดหยุ่นเป็นอย่างมากในการนำไปใช้อธิบายข้อมูลจริงที่มีลักษณะเบ้ขวา นอกจากนี้ประสิทธิผลของตัวประมาณ MADE ที่ใช้ในการประมาณค่าพารามิเตอร์ของการแจกแจง MOLBE ถูกนำเสนอผ่านข้อมูลจริงทางด้านวิศวกรรม และสิ่งแวดล้อมที่ไม่ถูกเซ็นเซอร์จำนวน 3 ชุดข้อมูล ซึ่งชุดข้อมูลที่นำมาใช้ประกอบไปด้วยข้อมูลที่มีหลากหลายรูปแบบเช่น เบ้ซ้าย เบ้ขวา และสมมาตร

This paper aims at applying the minimum Anderson–Darling estimator (MADE) to the Marshall-Olkin Length-Biased Exponential (MOLBE) distribution for estimating its unknown parameters. The MOLBE distribution, which extends the Length-Biased Exponential distribution based on the Marshall-Olkin scheme, seems more flexible in modeling real data with right skewed shape. The efficacy of the MADE for the MOLBE parameter estimation is shown through three uncensored real datasets in engineering and environment with various shapes such as slightly left skewed, right skewed and symmetrical.


Keywords



[1] O. Maxwell, S. O. Oyamakin, and E. J. Thomas, “The gompertz length biased exponential distribution and its application to uncensored data,” Curr Tre Biosta & Biometr, vol. 1, no. 3, pp. 52–57, 2019.

[2] O. Maxwell, A. I. Friday, and N. C. Chukwudike, “A theoretical analysis of the odd generalized exponentiated inverse Lomax distribution,” Biometrics & Biostatistics International Journal, vol. 8, no. 1, pp. 17–22, 2019.

[3] S. T. Dara and M. Ahmad, Recent Advances in Moment Distribution and their Hazard Rates. LAP LAMBERT Academic Publishing, 2012.

[4] R. A. Fisher, “The effect of methods of ascertainment upon the estimation of frequencies,” Annals of Eugenics, vol. 6, no. 1, pp. 13–25, 1934.

[5] M. A. ul Haq, R. M. Usman, S. Hashmi, and A. I. AI-Omeri, “The Marshall-Olkin length-biased exponential distribution and its applications,” Journal of King Saud University - Science, vol. 31, no. 2, pp. 246–251, 2019.

[6] Ç. Çetinkaya, “Optimal step stress accelerated life testing for the length-biased exponential cumulative exposure model,” İSTATİSTİK, vol. 13, no. 1, pp. 1–11, 2021.

[7] A. W. Marshall and I. Olkin, “A new method for adding a parameter to a family of distributions with application to the exponential and Weibull families,” Biometrika, vol. 84, no. 3, pp. 641–652, 1997.

[8] M. Raschke, “Opportunities of the minimum Anderson–Darling estimator as a variant of the maximum likelihood method,” Communications in Statistics - Simulation and Computation, vol. 46, no. 9, pp. 6879–6888, 2017.

[9] S. Dey, J. Mazucheli, and S. Nadarajah, “Kumaraswamy distribution: Different methods of estimation,” Computational and Applied Mathematics, vol. 37, no. 2, pp. 2094–2111, 2018.

[10] R. A. ZeinEldin, C. Chesneau, F. Jamal, and M. Elgarhy, “Different estimation methods for type I half-logistic Topp–Leone distribution,” Mathematics, vol. 7, no. 10, p. 985, 2019.

[11] H. Al-Mofleh, A. Z. Afify, and N. A. Ibrahim, “A new extended two-parameter distribution: Properties, estimation methods, and applications in medicine and geology,” Mathematics, vol. 8, no. 9, p. 985, 2020.

[12] D.D. Boos, “Minimum Anderson-Darling estimation,” Ommunications in Statistics - Theory and Methods, vol. 11, no. 24, pp. 2747–2774, 1982.

[13] R Core Team. (2021). R: A language and environment for statistical computing. R Foundation for Statistical Computing, Vienna, Austria. [Online]. Available: https://www.Rproject. org/.

[14] R. Kr. Singh, A. S. Yadav, S. K. Singh, and U. Singh, “Marshall-Olkin extended exponential distribution : different method of estimations,” Journal of Advanced Computing, vol. 5, no. 1, pp. 12–28, 2016.

[15] N. Ekhosuehi, G. E. Kenneth, and U. K. Kevin, “The Weibull length biased exponential distribution: Statistical properties and applications,” Journal of Statistical and Econometric Methods, vol. 9, no. 4, pp. 15–30, 2020.

[16] S. Nadarajah and S. Kotz, “Strength modeling using Weibull distributions,” Journal of Mechanical Science and Technology, vol. 22, no. 7, pp. 1247–1254, 2008.

[17] B. Makubate, F. Chipepa, B. Oluyede, and P.O. Peter, “The Marshall-Olkin half logistic-G family of distributions with applications,” International Journal of Statistics and Probability, vol. 10, no. 2, pp. 119–136, 2021.

[18] F. Chipepa , B. Oluyede, and P.O. Peter, “The Burr III-Topp-Leone-G family of distributions with applications,” Heliyon, vol. 7, no. 4, 2021.

[19] M. D. Nicholas and W. J. Padgett, “A bootstrap control chart for Weibull percentiles,” Quality and Reliability Engineering International, vol. 22, no. 2, pp. 141–151, 2005.

[20] M. M. Ristic, and N. Balakrishnan, “The gammaexponentiated exponential distribution,” Journal of Statistical Computation and Simulation, vol. 82, no. 8, pp. 1191–1206, 2012.

[21] R. A. ZeinEldin, F. Jamal, C. Chesneau, and M. Elgarhy, “Type II Topp–Leone inverted kumaraswamy distribution with statistical,” Symmetry, vol. 11, no. 12, pp. 1191–1206, 2019.

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DOI: 10.14416/j.kmutnb.2022.09.016

ISSN: 2985-2145