Abstract and Applied Analysis

Estimation of Hazard Rate and Mean Residual Life Ordering for Fuzzy Random Variable

S. Ramasubramanian and P. Mahendran

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L2-metric is used to find the distance between triangular fuzzy numbers. The mean and variance of a fuzzy random variable are also determined by this concept. The hazard rate is estimated and its relationship with mean residual life ordering of fuzzy random variable is investigated. Additionally, we have focused on deriving bivariate characterization of hazard rate ordering which explicitly involves pairwise interchange of two fuzzy random variables X and Y.

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Abstr. Appl. Anal., Volume 2015 (2015), Article ID 164795, 5 pages.

First available in Project Euclid: 17 August 2015

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Ramasubramanian, S.; Mahendran, P. Estimation of Hazard Rate and Mean Residual Life Ordering for Fuzzy Random Variable. Abstr. Appl. Anal. 2015 (2015), Article ID 164795, 5 pages. doi:10.1155/2015/164795. https://projecteuclid.org/euclid.aaa/1439816234

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  • H. Kwakernaak, “Fuzzy random variables. I. Definitions and theorems,” Information Sciences, vol. 15, no. 1, pp. 1–29, 1978.
  • M. L. Puri and D. A. Ralescu, “Fuzzy random variables,” Journal of Mathematical Analysis and Applications, vol. 114, no. 2, pp. 409–422, 1986.
  • J. M. Ruiz and J. Navarro, “Characterization of distributions by relationships between failure rate and mean residual life,” IEEE Transactions on Reliability, vol. 43, no. 4, pp. 640–644, 1994.
  • R. C. Gupta, “On the mean residual life function in survival studies,” in Statistical Distribution in Scientific works, C. Tailie, G. P. Patil, and B. A. Baldessar, Eds., vol. 79 of NATO Advanced study Institutes Series, pp. 327–334, Reidel, Dordrecht, The Netherlands, 1981.
  • R. C. Gupta and H. Olcay Akman, “Mean residual life function for certain types of non-monotonic ageing,” Communications in Statistics. Stochastic Models, vol. 11, no. 1, pp. 219–225, 1995.
  • M. S. Finkelstein, “On the shape of the mean residual lifetime function,” Applied Stochastic Models in Business and Industry, vol. 18, no. 2, pp. 135–146, 2002.
  • M. G. H. Akbari, A. H. Rezaei, and Y. Waghei, “Statistical inference about the variance of fuzzy random variables,” The Indian Journal of Statistics B, vol. 71, no. 2, pp. 206–221, 2009.
  • J. G. Shanthikumar and D. D. Yao, “Bivariate characterization of some stochastic order relations,” Advances in Applied Probability, vol. 23, no. 3, pp. 642–659, 1991.
  • T. Itoh and H. Ishii, “One machine scheduling problem with fuzzy random due-dates,” Fuzzy Optimization and Decision Making, vol. 4, no. 1, pp. 71–78, 2005.
  • J. E. L. Piriyakumar and S. Ramasubramanian, “Bivariate characterization of stochastic orderings of fuzzy random variables,” in Proceedings of the International Conference in Management Sciences and Decision Making, pp. 25–31, Tamkang University, Taipei, Taiwan, 2010.
  • M. Rausand and A. Hoyla, System Reliability Theory, Models, Statistical Methods and Applications, John Wiley & Sons, 2004.
  • G.-Y. Wang and Y. Zhang, “The theory of fuzzy stochastic processes,” Fuzzy Sets and Systems, vol. 51, no. 2, pp. 161–178, 1992.
  • H.-C. Wu, “Probability density functions of fuzzy random variables,” Fuzzy Sets and Systems, vol. 105, no. 1, pp. 139–158, 1999. \endinput