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

Year 2019, , 1859 - 1869, 08.12.2019
https://doi.org/10.15672/hujms.470452

Abstract

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.

References

  • [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.
Year 2019, , 1859 - 1869, 08.12.2019
https://doi.org/10.15672/hujms.470452

Abstract

References

  • [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.
There are 11 citations in total.

Details

Primary Language English
Subjects Mathematical Sciences
Journal Section Statistics
Authors

Hina Basharat 0000-0002-8120-9089

Saima Mustafa 0000-0002-0584-1445

Shahid Mahmood 0000-0002-7222-8181

Young Bae Jun 0000-0002-0181-8969

Publication Date December 8, 2019
Published in Issue Year 2019

Cite

APA Basharat, H., Mustafa, S., Mahmood, S., Jun, Y. B. (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. https://doi.org/10.15672/hujms.470452
AMA Basharat H, Mustafa S, Mahmood S, Jun YB. Inference for the linear combination of two independent exponential random variables based on fuzzy data. Hacettepe Journal of Mathematics and Statistics. December 2019;48(6):1859-1869. doi:10.15672/hujms.470452
Chicago Basharat, Hina, Saima Mustafa, Shahid Mahmood, and Young Bae Jun. “Inference for the Linear Combination of Two Independent Exponential Random Variables Based on Fuzzy Data”. Hacettepe Journal of Mathematics and Statistics 48, no. 6 (December 2019): 1859-69. https://doi.org/10.15672/hujms.470452.
EndNote Basharat H, Mustafa S, Mahmood S, Jun YB (December 1, 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.
IEEE H. Basharat, S. Mustafa, S. Mahmood, and Y. B. Jun, “Inference for the linear combination of two independent exponential random variables based on fuzzy data”, Hacettepe Journal of Mathematics and Statistics, vol. 48, no. 6, pp. 1859–1869, 2019, doi: 10.15672/hujms.470452.
ISNAD Basharat, Hina et al. “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.
JAMA Basharat H, Mustafa S, Mahmood S, Jun YB. Inference for the linear combination of two independent exponential random variables based on fuzzy data. Hacettepe Journal of Mathematics and Statistics. 2019;48:1859–1869.
MLA Basharat, Hina et al. “Inference for the Linear Combination of Two Independent Exponential Random Variables Based on Fuzzy Data”. Hacettepe Journal of Mathematics and Statistics, vol. 48, no. 6, 2019, pp. 1859-6, doi:10.15672/hujms.470452.
Vancouver Basharat H, Mustafa S, Mahmood S, Jun YB. Inference for the linear combination of two independent exponential random variables based on fuzzy data. Hacettepe Journal of Mathematics and Statistics. 2019;48(6):1859-6.