Fuzzification of Linear Combination Based on Marshall-Olkin Bivariate Exponential Distribution
International Journal of Management and Fuzzy Systems
Volume 3, Issue 2, April 2017, Pages: 28-31
Received: Apr. 7, 2017;
Accepted: May 16, 2017;
Published: Jun. 16, 2017
Views 1990 Downloads 83
Yangjing Chong, Mathematics Department, Yanbian University, Yanji, P. R. China
Fangfang Guo, Mathematics Department, Yanbian University, Yanji, P. R. China
Wenyuan Sun, Mathematics Department, Yanbian University, Yanji, P. R. China
The exponential distribution is applied to a very wide range of life analysis models, therefore, the research on it is of great significance in the practice of life. Based on the basic theory of general reliability and fuzzy reliability, on account of the Marshall-Olkin binary exponential distribution model, by establishing the fuzzy probability density function of the linear combination of two - dimensional random variables, this paper gives the fuzzy reliability function of the linear combination of the most widely used two - dimensional exponential distribution in reliability engineering.
Fuzzification of Linear Combination Based on Marshall-Olkin Bivariate Exponential Distribution, International Journal of Management and Fuzzy Systems.
Vol. 3, No. 2,
2017, pp. 28-31.
Copyright © 2017 Authors retain the copyright of this article.
This article is an open access article distributed under the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0/
) which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Qiao Aifang. Generalized exponential distribution parameter change point analysis and its application [D]. Qinghai Normal University, 2016.
Liu Guoxiang. Relationship between exponential distribution and other distributions [J]. Journal of Chifeng University (Natural Science Edition), 2011, (12): 12-14.
Zeng Tianxiang. Application and Limitation of Exponential Distribution [J]. Actuation of Aviation, 1983, (06): 14-20.
Xi Li, Liu Ruiyuan. Two-dimensional exponential distribution [J] Qinghai University (Natural Science), 2007, (02): 86-88 + 94.
Zhang Ping. Statistical Analysis of Bivariate Exponential Distribution [D]. Shanghai Normal University, 2011.
Han Zhu. Research on Characterization and Parameter Estimation of Bivariate Exponential Distributions and Other Related Problems [D]. Ningbo University, 2009.
Arjun K,Gupta and SaraleesNadarajah. Exact and approximate distributions for the linear combination of inverted Dirichlet components [J]. Journal of Japan Statistical Society, 2006, 36 (2): 225-236.
Li Dongna, Zhang Minyue, Ma Changqing. Fuzzy reliability analysis of parallel series system [J]. Journal of Gansu science, 2007, (04): 141-144.
Li Tingjie, Gao He. Fuzzy Reliability of Series System [J]. Fuzzy Systems and Mathematics, 1989, (01): 38-45.
GuoYunfei, Yin Zhe. The distribution of linear combinations of non - independent random variables subjecting to two- dimensional exponential distribution [J]. Mathematical Practice and Understanding, 2010, 40 (16): 179-183.
Zhou Juling, Liang Xiaojia. Marshall-Olkin binary exponential distribution [J]. Journal of Xinjiang Normal University (Natural Science Edition), 2013, (04): 63-65.
Li Guoan. Independence and Uniqueness of Exponential Distribution of Binary Marshall ~ Olkin Type [J]. University Mathematics, 2013,29 (4): 91-93. DOI: 10.3969/ j.issn.1672-1454.2013.04.019.
Saralees Narajah and Samuel Kotz. Reliability for some Bivariate exponential distributions, Mathematical Problems in Engineering, 1-14, 2006.
LI Tingjie, Gao He. Fuzzy Reliability [J]. Systems Engineering and Electronics, 1988, (10): 1-9.
Cheng Kan, Cao Jinhua, Introduction to Reliability Mathematics. Beijing: Higher Education Press, 2006.
Guo Yunfei, Reliability function of linear combination of marshall and olkin’s bivariate exponential distribution, Scientific Advances Publishers, 2015.
Li Guoan. Exponential Distribution Sampling Fundamental Theorem and Its Application in Parameter Estimation of Two-parameter Binary Marshall-Olkin Exponential Distribution Parameter [J]. Statistical Research, 2016, (07): 98-102.
Wang Junfang, Zhang Minyue. Fuzzy reliability of [J]. Journal of Sichuan University of Science and Engineering two interdependent parts in parallel system and series system with cold standby components (NATURAL SCIENCE EDITION), 2015, (01): 80-82.
Li Tingjie, GaoHe. Reliability Design [M]. Beijing: Beijing University of Aeronautics and Astronautics Press, 1988.
Li Guoan. Characteristic and Parameter Estimation of Multivariate Marshall-Olkin Exponential Distribution [J]. Journal of Engineering Mathematics, 2005, (06): 109-116.