Fuzzification of Linear Combination Based on Marshall-Olkin Bivariate Exponential Distribution

Yangjing Chong; Fangfang Guo; Wenyuan Sun

doi:doi:10.11648/j.ijmfs.20170302.12

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Fuzzification of Linear Combination Based on Marshall-Olkin Bivariate Exponential Distribution

Yangjing Chong, Fangfang Guo, Wenyuan Sun

Published in International Journal of Management and Fuzzy Systems (Volume 3, Issue 2)

Received: 7 April 2017 Accepted: 16 May 2017 Published: 16 June 2017

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Abstract

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.

Published in	International Journal of Management and Fuzzy Systems (Volume 3, Issue 2)
DOI	10.11648/j.ijmfs.20170302.12
Page(s)	28-31
Creative Commons	This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited.
Copyright	Copyright © The Author(s), 2017. Published by Science Publishing Group

Keywords

Fuzzy Reliability, Binary Exponential Distribution, Non-Independent, Linear Combination

References

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[7]	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.
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[10]	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.
[11]	Zhou Juling, Liang Xiaojia. Marshall-Olkin binary exponential distribution [J]. Journal of Xinjiang Normal University (Natural Science Edition), 2013, (04): 63-65.
[12]	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.
[13]	Saralees Narajah and Samuel Kotz. Reliability for some Bivariate exponential distributions, Mathematical Problems in Engineering, 1-14, 2006.
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[16]	Guo Yunfei, Reliability function of linear combination of marshall and olkin’s bivariate exponential distribution, Scientific Advances Publishers, 2015.
[17]	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.
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[19]	Li Tingjie, GaoHe. Reliability Design [M]. Beijing: Beijing University of Aeronautics and Astronautics Press, 1988.
[20]	Li Guoan. Characteristic and Parameter Estimation of Multivariate Marshall-Olkin Exponential Distribution [J]. Journal of Engineering Mathematics, 2005, (06): 109-116.

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APA Style

Yangjing Chong, Fangfang Guo, Wenyuan Sun. (2017). Fuzzification of Linear Combination Based on Marshall-Olkin Bivariate Exponential Distribution. International Journal of Management and Fuzzy Systems, 3(2), 28-31. https://doi.org/10.11648/j.ijmfs.20170302.12

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ACS Style

Yangjing Chong; Fangfang Guo; Wenyuan Sun. Fuzzification of Linear Combination Based on Marshall-Olkin Bivariate Exponential Distribution. Int. J. Manag. Fuzzy Syst. 2017, 3(2), 28-31. doi: 10.11648/j.ijmfs.20170302.12

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AMA Style

Yangjing Chong, Fangfang Guo, Wenyuan Sun. Fuzzification of Linear Combination Based on Marshall-Olkin Bivariate Exponential Distribution. Int J Manag Fuzzy Syst. 2017;3(2):28-31. doi: 10.11648/j.ijmfs.20170302.12

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@article{10.11648/j.ijmfs.20170302.12,
  author = {Yangjing Chong and Fangfang Guo and Wenyuan Sun},
  title = {Fuzzification of Linear Combination Based on Marshall-Olkin Bivariate Exponential Distribution},
  journal = {International Journal of Management and Fuzzy Systems},
  volume = {3},
  number = {2},
  pages = {28-31},
  doi = {10.11648/j.ijmfs.20170302.12},
  url = {https://doi.org/10.11648/j.ijmfs.20170302.12},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ijmfs.20170302.12},
  abstract = {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.},
 year = {2017}
}

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TY  - JOUR
T1  - Fuzzification of Linear Combination Based on Marshall-Olkin Bivariate Exponential Distribution
AU  - Yangjing Chong
AU  - Fangfang Guo
AU  - Wenyuan Sun
Y1  - 2017/06/16
PY  - 2017
N1  - https://doi.org/10.11648/j.ijmfs.20170302.12
DO  - 10.11648/j.ijmfs.20170302.12
T2  - International Journal of Management and Fuzzy Systems
JF  - International Journal of Management and Fuzzy Systems
JO  - International Journal of Management and Fuzzy Systems
SP  - 28
EP  - 31
PB  - Science Publishing Group
SN  - 2575-4947
UR  - https://doi.org/10.11648/j.ijmfs.20170302.12
AB  - 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.
VL  - 3
IS  - 2
ER  -

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Author Information

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

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APA Style

Yangjing Chong, Fangfang Guo, Wenyuan Sun. (2017). Fuzzification of Linear Combination Based on Marshall-Olkin Bivariate Exponential Distribution. International Journal of Management and Fuzzy Systems, 3(2), 28-31. https://doi.org/10.11648/j.ijmfs.20170302.12

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ACS Style

Yangjing Chong; Fangfang Guo; Wenyuan Sun. Fuzzification of Linear Combination Based on Marshall-Olkin Bivariate Exponential Distribution. Int. J. Manag. Fuzzy Syst. 2017, 3(2), 28-31. doi: 10.11648/j.ijmfs.20170302.12

Copy | Download

AMA Style

Yangjing Chong, Fangfang Guo, Wenyuan Sun. Fuzzification of Linear Combination Based on Marshall-Olkin Bivariate Exponential Distribution. Int J Manag Fuzzy Syst. 2017;3(2):28-31. doi: 10.11648/j.ijmfs.20170302.12

Copy | Download

@article{10.11648/j.ijmfs.20170302.12,
  author = {Yangjing Chong and Fangfang Guo and Wenyuan Sun},
  title = {Fuzzification of Linear Combination Based on Marshall-Olkin Bivariate Exponential Distribution},
  journal = {International Journal of Management and Fuzzy Systems},
  volume = {3},
  number = {2},
  pages = {28-31},
  doi = {10.11648/j.ijmfs.20170302.12},
  url = {https://doi.org/10.11648/j.ijmfs.20170302.12},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ijmfs.20170302.12},
  abstract = {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.},
 year = {2017}
}

Copy | Download

TY  - JOUR
T1  - Fuzzification of Linear Combination Based on Marshall-Olkin Bivariate Exponential Distribution
AU  - Yangjing Chong
AU  - Fangfang Guo
AU  - Wenyuan Sun
Y1  - 2017/06/16
PY  - 2017
N1  - https://doi.org/10.11648/j.ijmfs.20170302.12
DO  - 10.11648/j.ijmfs.20170302.12
T2  - International Journal of Management and Fuzzy Systems
JF  - International Journal of Management and Fuzzy Systems
JO  - International Journal of Management and Fuzzy Systems
SP  - 28
EP  - 31
PB  - Science Publishing Group
SN  - 2575-4947
UR  - https://doi.org/10.11648/j.ijmfs.20170302.12
AB  - 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.
VL  - 3
IS  - 2
ER  -

Copy | Download