×

Identification of models using failure rate and mean residual life of doubly truncated random variables. (English) Zbl 1050.62017

Summary: We study the relationship between the failure rate and the mean residual life of doubly truncated random variables. Accordingly, we develop characterizations for exponential, Pareto II and beta distributions. Further, we generalize the identities for the Pearson and the exponential family of distributions given, respectively, by N. U. Nair and P. G. Sankaran [IEEE Trans. Reliab. 40, 75–77 (1991)] and P. Consul [ibid. 44, 403–407 (1995)]. Applications of these measures in the context of length-biased models are also explored.

MSC:

62E10 Characterization and structure theory of statistical distributions
62N02 Estimation in survival analysis and censored data
PDFBibTeX XMLCite
Full Text: DOI

References:

[1] Blumenthal, S., Proportional sampling in life length studies, Technometrics, 9, 205-218 (1967) · doi:10.2307/1266418
[2] Consul, PC, Some characterizations for the exponential class of distributions, IEEE Trans. Reliability, 44, 403-407 (1995) · doi:10.1109/24.406573
[3] Cox DR (1962) Renewal Theory. Frome and Long, Butler and Tanner Ltd. · Zbl 0103.11504
[4] Galambos, J.; Kotz, S., Characterization of probability distributions (1978), New York: Springer Verlag, New York · Zbl 0381.62011
[5] Gupta, RC; Keating, JP, Relations for reliability measures under length biased sampling, Scand. J. Statist., 13, 49-56 (1986) · Zbl 0627.62098
[6] Gupta, RC; Kirmani, SNUA, The role of weighted distributions in stochastic modeling, Commun. Statist.-Theor. Meth., 19, 9, 3147-3162 (1990) · Zbl 0734.62093 · doi:10.1080/03610929008830371
[7] Johnson, NL; Kotz, S.; Balakrishnan, N., Continuous Univariate Distributions (1994), New York: John Wiley and Sons, New York · Zbl 0811.62001
[8] Kotz, S.; Shanbhag, DN, Some new approaches to probability distributions, Adv. Applied Prob., 12, 903-921 (1980) · Zbl 0454.62085 · doi:10.2307/1426748
[9] Meilijson, I., Limiting properties of the mean residual life function, Ann. Math. Statist., 43, 354-357 (1972) · Zbl 0278.60063 · doi:10.1214/aoms/1177692731
[10] Nair, NU; Sankaran, PG, Characterization of Pearson family of distributions, IEEE Trans. Reliability, 40, 75-77 (1991) · Zbl 0729.62622 · doi:10.1109/24.75339
[11] Patil GP, Rao CR (1977) The weighted distribution: A survey of their applications, In Applications of Statistics. P.R. Krishnaiah (ed.), North Holland Publ. Co., 383-405. · Zbl 0371.62034
[12] Navarro, J.; Franco, M.; Ruiz, JM, Characterization through moments of the residual life and conditional spacing, Sankhya A, 60, 36-48 (1998) · Zbl 0977.62010
[13] Navarro, J.; Ruiz, JM, Failure rate functions for doublytruncated random variables, IEEE Trans. Reliability, 45, 685-690 (1996) · doi:10.1109/24.556594
[14] Navarro, J.; del Aguila, Y.; Ruiz, JM, Characterization through reliability measures from weighted distributions, Statistical Papers, 42, 395-402 (2001) · Zbl 1099.62506 · doi:10.1007/s003620100066
[15] Rao, CR; Patil, G. P., On discrete distributions arising out of methods of ascertainments, Classical and Contagious Discrete Distributions, 320-332 (1965), Calcutta: Pergamon Press and Statistical Publishing Society, Calcutta
[16] Ruiz, JM; Navarro, J., Characterization of distributions by relationships between failure rate and mean residual life, IEEE Trans. Reliability, 43, 4, 640-644 (1994) · doi:10.1109/24.370215
[17] Ruiz, JM; Navarro, J., Characterizations based on conditional expectations of the doubled truncated distribution, Ann. Inst. Statist. Math., 48, 563-572 (1996) · Zbl 0925.62059 · doi:10.1007/BF00050855
[18] Scheaffer, RL, Size-biased sampling, Technometrics, 14, 635-644 (1972) · Zbl 0238.62011 · doi:10.2307/1267291
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.