Estimation of hazard rate and mean residual life ordering for fuzzy random variable. (English) Zbl 1434.60006

Ramasubramanian, S.; Mahendran, P.

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

Summary: \(L_2\)-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 \(Y\).

MSC:

60A86	Fuzzy probability
62N86	Fuzziness, and survival analysis and censored data

References:

[1]	Kwakernaak, H., Fuzzy random variables. I. Definitions and theorems, Information Sciences, 15, 1, 1-29, (1978) · Zbl 0438.60004 · doi:10.1016/0020-0255(78)90019-1
[2]	Puri, M. L.; Ralescu, D. A., Fuzzy random variables, Journal of Mathematical Analysis and Applications, 114, 2, 409-422, (1986) · Zbl 0592.60004 · doi:10.1016/0022-247x(86)90093-4
[3]	Ruiz, J. M.; Navarro, J., Characterization of distributions by relationships between failure rate and mean residual life, IEEE Transactions on Reliability, 43, 4, 640-644, (1994) · doi:10.1109/24.370215
[4]	Gupta, R. C.; Tailie, C.; Patil, G. P.; Baldessar, B. A., On the mean residual life function in survival studies, Statistical Distribution in Scientific works. Statistical Distribution in Scientific works, NATO Advanced study Institutes Series, 79, 327-334, (1981), Dordrecht, The Netherlands: Reidel, Dordrecht, The Netherlands · doi:10.1007/978-94-009-8552-0_26
[5]	Gupta, R. C.; Olcay Akman, H., Mean residual life function for certain types of non-monotonic ageing, Communications in Statistics. Stochastic Models, 11, 1, 219-225, (1995) · Zbl 0813.60081 · doi:10.1080/15326349508807340
[6]	Finkelstein, M. S., On the shape of the mean residual lifetime function, Applied Stochastic Models in Business and Industry, 18, 2, 135-146, (2002) · Zbl 1007.62084 · doi:10.1002/asmb.461
[7]	Akbari, M. G. H.; Rezaei, A. H.; Waghei, Y., Statistical inference about the variance of fuzzy random variables, The Indian Journal of Statistics B, 71, 2, 206-221, (2009) · Zbl 1192.60010
[8]	Shanthikumar, J. G.; Yao, D. D., Bivariate characterization of some stochastic order relations, Advances in Applied Probability, 23, 3, 642-659, (1991) · Zbl 0745.62054 · doi:10.2307/1427627
[9]	Itoh, T.; Ishii, H., One machine scheduling problem with fuzzy random due-dates, Fuzzy Optimization and Decision Making, 4, 1, 71-78, (2005) · Zbl 1079.90054 · doi:10.1007/s10700-004-5571-4
[10]	Piriyakumar, J. E. L.; Ramasubramanian, S., Bivariate characterization of stochastic orderings of fuzzy random variables, Proceedings of the International Conference in Management Sciences and Decision Making, Tamkang University
[11]	Rausand, M.; Hoyla, A., System Reliability Theory, Models, Statistical Methods and Applications, (2004), John Wiley & Sons · Zbl 1052.93001
[12]	Wang, G.-Y.; Zhang, Y., The theory of fuzzy stochastic processes, Fuzzy Sets and Systems, 51, 2, 161-178, (1992) · Zbl 0782.60039 · doi:10.1016/0165-0114(92)90189-b
[13]	Wu, H.-C., Probability density functions of fuzzy random variables, Fuzzy Sets and Systems, 105, 1, 139-158, (1999) · Zbl 0936.60001 · doi:10.1016/s0165-0114(97)00241-8