Inference for the linear combination of two independent exponential random variables based on fuzzy data

Yıl 2019, Cilt: 48 Sayı: 6, 1859 - 1869, 08.12.2019

Hina Basharat , Saima Mustafa , Shahid Mahmood , Young Bae Jun

https://doi.org/10.15672/hujms.470452

Cited By: 2

Öz

In this article, we have derived the distribution of a linear combination of two independent exponential random variables. The parameter estimates of the proposed distribution are obtained by using the maximum likelihood estimation method and the method of moments from fuzzy data. The findings in this paper show that estimation expertise is still valuable to any organization based on the precise and certain information. The proposed research consisted in developing an estimation technique using fuzzy logic and this is often measured in terms of linguistic values, which is very helpful and beneficial  for the certain and precise results.

Anahtar Kelimeler

Linear combination, Exponential distribution, Parameter estimation, Fuzzy numbers, Fuzzy logics

Kaynakça

• [1] T. Denoeux, Maximum likelihood estimation from fuzzy data using the EM algorithm, Fuzzy Sets and Systems 183 (1), 72-91, 2011.
• [2] T.E. Dalkilic and K.S. Kula, Parameter Estimation for Pareto Distribution and Type- II Fuzzy Logic, Gazi University Journal of Science 30 (1), 251-258, 2017.
• [3] R.A. Fisher, On the Mathematical Foundations of Theoretical Statistics, Philos. Trans. Roy. Soc. A 222, 309-368, 1922.
• [4] A.H. Joarder, M.H. Omar and A.K. Gupta, The Distribution of a Linear Combination of Two Correlated Chi-Square Variables, Revista Colombiana de Estadistica 36 (2), 209-219, 2013.
• [5] B.M.G. Kibria and S. Nadarajah, Reliability Modeling: Linear Combination and Ratio of Exponential and Rayleigh, IEEE Transactions On Reliability 56 (1), 102-105, 2007.
• [6] N.B. Khoolenjani and F. Shahsanaie, Estimating the parameter of Exponential distribution under Type-II censoring from fuzzy data, J. Stat. Theory Appl. 15 (2), 181-195, 2016.
• [7] S. Nadarajah and S. Kotz, On the Linear Combination of Exponential and Gamma Random Variables, Entropy 7 (2), 161-171, 2005.
• [8] A. Pak, G.A. Parham and M. Saraj, Inference for the Weibull Distribution Based on Fuzzy Data, Revista Colombiana de Estadistica 36 (2), 337-356, 2013.
• [9] A. Pak, Statistical Inference for the parameter of Lindley distribution based on fuzzy data, Braz. J. Probab. Stat. (2), 1-16, 2016.
• [10] M. Shakil and B.M.G. Kibria, Exact Distributions of the Linear Combination of Gamma and Rayleigh Random Variables, Austrian Journal of Statistics 38 (1), 33- 44, 2009.
• [11] L.A. Zadeh, Probability Measures of Fuzzy Events, J. Math. Anal. Appl. 23, 421-427, 1968.