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

#### Hina BASHARAT [1] , Saima MUSTAFA [2] , Shahid MAHMOOD [3] , Young Bae JUN [4]

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.
Linear combination, Exponential distribution, Parameter estimation, Fuzzy numbers, Fuzzy logics
• [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.
Primary Language en Mathematics Statistics Orcid: 0000-0002-8120-9089Author: Hina BASHARAT (Primary Author)Institution: PMAS Arid Agriculture UniversityCountry: Pakistan Orcid: 0000-0002-0584-1445Author: Saima MUSTAFA Institution: PMAS Arid Agriculture UniversityCountry: Pakistan Orcid: 0000-0002-7222-8181Author: Shahid MAHMOOD Institution: Sarhad University of Science & ITCountry: Pakistan Orcid: 0000-0002-0181-8969Author: Young Bae JUN Institution: Gyeongsang National UniversityCountry: South Korea Publication Date : December 8, 2019
 Bibtex @research article { hujms470452, journal = {Hacettepe Journal of Mathematics and Statistics}, issn = {2651-477X}, eissn = {2651-477X}, address = {}, publisher = {Hacettepe University}, year = {2019}, volume = {48}, pages = {1859 - 1869}, doi = {10.15672/hujms.470452}, title = {Inference for the linear combination of two independent exponential random variables based on fuzzy data}, key = {cite}, author = {BASHARAT, Hina and MUSTAFA, Saima and MAHMOOD, Shahid and JUN, Young Bae} } APA BASHARAT, H , MUSTAFA, S , MAHMOOD, S , JUN, Y . (2019). Inference for the linear combination of two independent exponential random variables based on fuzzy data. Hacettepe Journal of Mathematics and Statistics , 48 (6) , 1859-1869 . DOI: 10.15672/hujms.470452 MLA BASHARAT, H , MUSTAFA, S , MAHMOOD, S , JUN, Y . "Inference for the linear combination of two independent exponential random variables based on fuzzy data". Hacettepe Journal of Mathematics and Statistics 48 (2019 ): 1859-1869 Chicago BASHARAT, H , MUSTAFA, S , MAHMOOD, S , JUN, Y . "Inference for the linear combination of two independent exponential random variables based on fuzzy data". Hacettepe Journal of Mathematics and Statistics 48 (2019 ): 1859-1869 RIS TY - JOUR T1 - Inference for the linear combination of two independent exponential random variables based on fuzzy data AU - Hina BASHARAT , Saima MUSTAFA , Shahid MAHMOOD , Young Bae JUN Y1 - 2019 PY - 2019 N1 - doi: 10.15672/hujms.470452 DO - 10.15672/hujms.470452 T2 - Hacettepe Journal of Mathematics and Statistics JF - Journal JO - JOR SP - 1859 EP - 1869 VL - 48 IS - 6 SN - 2651-477X-2651-477X M3 - doi: 10.15672/hujms.470452 UR - https://doi.org/10.15672/hujms.470452 Y2 - 2019 ER - EndNote %0 Hacettepe Journal of Mathematics and Statistics Inference for the linear combination of two independent exponential random variables based on fuzzy data %A Hina BASHARAT , Saima MUSTAFA , Shahid MAHMOOD , Young Bae JUN %T Inference for the linear combination of two independent exponential random variables based on fuzzy data %D 2019 %J Hacettepe Journal of Mathematics and Statistics %P 2651-477X-2651-477X %V 48 %N 6 %R doi: 10.15672/hujms.470452 %U 10.15672/hujms.470452 ISNAD BASHARAT, Hina , MUSTAFA, Saima , MAHMOOD, Shahid , JUN, Young Bae . "Inference for the linear combination of two independent exponential random variables based on fuzzy data". Hacettepe Journal of Mathematics and Statistics 48 / 6 (December 2019): 1859-1869 . https://doi.org/10.15672/hujms.470452 AMA BASHARAT H , MUSTAFA S , MAHMOOD S , JUN Y . Inference for the linear combination of two independent exponential random variables based on fuzzy data. Hacettepe Journal of Mathematics and Statistics. 2019; 48(6): 1859-1869. Vancouver BASHARAT H , MUSTAFA S , MAHMOOD S , JUN Y . Inference for the linear combination of two independent exponential random variables based on fuzzy data. Hacettepe Journal of Mathematics and Statistics. 2019; 48(6): 1869-1859.