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Title: Characterizations based on length-biased weighted measure of inaccuracy for truncated random variables (English)
Author: Kundu, Chanchal
Language: English
Journal: Applications of Mathematics
ISSN: 0862-7940 (print)
ISSN: 1572-9109 (online)
Volume: 59
Issue: 6
Year: 2014
Pages: 697-714
Summary lang: English
Category: math
Summary: In survival studies and life testing, the data are generally truncated. Recently, authors have studied a weighted version of Kerridge inaccuracy measure for truncated distributions. In the present paper we consider weighted residual and weighted past inaccuracy measure and study various aspects of their bounds. Characterizations of several important continuous distributions are provided based on weighted residual (past) inaccuracy measure. (English)
Keyword: characterization
Keyword: entropy
Keyword: weighted residual (past) inaccuracy
Keyword: proportional (reversed) hazard model
MSC: 20B10
MSC: 60E15
MSC: 62E10
MSC: 62N05
idZBL: Zbl 06391457
idMR: MR3277734
DOI: 10.1007/s10492-014-0080-4
Date available: 2014-11-10T09:23:07Z
Last updated: 2020-07-02
Stable URL:
Reference: [1] Arnold, B. C.: Pareto Distributions.Statistical Distributions in Scientific Work 5 International Co-operative Publishing House, Burtonsville (1983). Zbl 1169.62307, MR 0751409
Reference: [2] Azlarov, T. A., Volodin, N. A.: Characterization Problems Associated with the Exponential Distribution. Transl. from the Russian.Springer, New York (1986). Zbl 0624.62020, MR 0841073
Reference: [3] Cox, D. R.: The analysis of exponentially distributed life-times with two types of failure.J. R. Stat. Soc., Ser. B 21 411-421 (1959). Zbl 0093.15704, MR 0114280
Reference: [4] Cox, D. R.: Renewal Theory.Methuen’s Monographs on Applied Probability and Statistics Methuen, London; John Wiley, New York (1962). Zbl 0103.11504, MR 0153061
Reference: [5] Cox, D. R.: Regression models and life-tables.J. R. Stat. Soc., Ser. B 34 187-220 (1972). Zbl 0243.62041, MR 0341758
Reference: [6] Crescenzo, A. Di: Some results on the proportional reversed hazards model.Stat. Probab. Lett. 50 313-321 (2000). Zbl 0967.60016, MR 1802225, 10.1016/S0167-7152(00)00127-9
Reference: [7] Crescenzo, A. Di, Longobardi, M.: On weighted residual and past entropies.Sci. Math. Jpn. 64 255-266 (2006). Zbl 1106.62114, MR 2254144
Reference: [8] Ebrahimi, N., Kirmani, S. N. U. A.: A characterisation of the proportional hazards model through a measure of discrimination between two residual life distributions.Biometrika 83 233-235 (1996). Zbl 0865.62075, MR 1399168, 10.1093/biomet/83.1.233
Reference: [9] Furman, E., Zitikis, R.: Weighted premium calculation principles.Insur. Math. Econ. 42 459-465 (2008). Zbl 1141.91509, MR 2392102, 10.1016/j.insmatheco.2007.10.006
Reference: [10] Galambos, J., Kotz, S.: Characterizations of Probability Distributions. A Unified Approach with an Emphasis on Exponential and Related Models.Lecture Notes in Mathematics 675 Springer, Berlin (1978). Zbl 0381.62011, MR 0513423, 10.1007/BFb0069530
Reference: [11] Gupta, R. C., Gupta, R. D.: Proportional reversed hazard rate model and its applications.J. Stat. Plann. Inference 137 3525-3536 (2007). Zbl 1119.62098, MR 2363274, 10.1016/j.jspi.2007.03.029
Reference: [12] Gupta, R. C., Gupta, P. L., Gupta, R. D.: Modeling failure time data by Lehman alternatives.Commun. Stat., Theory Methods 27 887-904 (1998). Zbl 0900.62534, MR 1613497, 10.1080/03610929808832134
Reference: [13] Gupta, R. C., Han, W.: Analyzing survival data by PRH models.International Journal of Reliability and Applications 2 (2001), 203-216.
Reference: [14] Gupta, R. C., Kirmani, S. N. U. A.: The role of weighted distributions in stochastic modeling.Commun. Stat., Theory Methods 19 3147-3162 (1990). Zbl 0734.62093, MR 1089242, 10.1080/03610929008830371
Reference: [15] Jain, K., Singh, H., Bagai, I.: Relations for reliability measures of weighted distributions.Commun. Stat., Theory Methods 18 4393-4412 (1989). Zbl 0707.62197, MR 1046715, 10.1080/03610928908830162
Reference: [16] Kerridge, D. F.: Inaccuracy and inference.J. R. Stat. Soc., Ser. B 23 184-194 (1961). Zbl 0112.10302, MR 0123375
Reference: [17] Kullback, S., Leibler, R. A.: On information and sufficiency.Ann. Math. Stat. 22 79-86 (1951). Zbl 0042.38403, MR 0039968, 10.1214/aoms/1177729694
Reference: [18] Kumar, V., Taneja, H. C.: On length biased dynamic measure of past inaccuracy.Metrika 75 73-84 (2012). Zbl 1241.62014, MR 2878109, 10.1007/s00184-010-0315-7
Reference: [19] Kumar, V., Taneja, H. C., Srivastava, R.: Length biased weighted residual inaccuracy measure.Metron 68 (2010), 153-160. Zbl 1301.62104, MR 3038412, 10.1007/BF03263532
Reference: [20] Kumar, V., Taneja, H. C., Srivastava, R.: A dynamic measure of inaccuracy between two past lifetime distributions.Metrika 74 1-10 (2011). Zbl 1216.62156, MR 2804725, 10.1007/s00184-009-0286-8
Reference: [21] Nair, N. U., Gupta, R. P.: Characterization of proportional hazard models by properties of information measures.International Journal of Statistical Sciences 6 (2007), Special Issue, 223-231.
Reference: [22] Nair, K. R. M., Rajesh, G.: Geometric vitality function and its applications to reliability.IAPQR Trans. 25 1-8 (2000). Zbl 1277.62236, MR 1949414
Reference: [23] Nanda, A. K., Jain, K.: Some weighted distribution results on univariate and bivariate cases.J. Stat. Plann. Inference 77 169-180 (1999). Zbl 0924.62018, MR 1687954, 10.1016/S0378-3758(98)00190-6
Reference: [24] Patil, G. P., Ord, J. K.: On size-biased sampling and related form-invariant weighted distributions.Sankhy\=a, Ser. B 38 48-61 (1976). Zbl 0414.62015, MR 0652546
Reference: [25] Rao, C. R.: Linear Statistical Inference and Its Applications.John Wiley & Sons, New York (1965). Zbl 0137.36203, MR 0221616
Reference: [26] Sengupta, D., Singh, H., Nanda, A. K.: The proportional reversed hazard model.Technical Report 1999, Indian Statistical Institute, Calcutta.
Reference: [27] Shannon, C. E.: A mathematical theory of communication.Bell Syst. Tech. J. 27 379-423, 623-656 (1948). Zbl 1154.94303, MR 0026286, 10.1002/j.1538-7305.1948.tb01338.x
Reference: [28] Smitha, S.: A Study on the Kerridge's Inaccuracy Measure and Related Concepts.Doctoral Dissertation 2010, CUSAT.
Reference: [29] Taneja, H. C., Kumar, V., Srivastava, R.: A dynamic measure of inaccuracy between two residual lifetime distributions.Int. Math. Forum 4 1213-1220 (2009). Zbl 1185.62032, MR 2545115
Reference: [30] Wallis, G.: Using spatio-temporal correlations to learn invariant object recognition.Neural Netw. 9 1513-1519 (1996). 10.1016/S0893-6080(96)00041-X


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