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Keywords:
characterization; entropy; weighted residual (past) inaccuracy; proportional (reversed) hazard model
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.
References:
[1] Arnold, B. C.: Pareto Distributions. Statistical Distributions in Scientific Work 5 International Co-operative Publishing House, Burtonsville (1983). MR 0751409 | Zbl 1169.62307
[2] Azlarov, T. A., Volodin, N. A.: Characterization Problems Associated with the Exponential Distribution. Transl. from the Russian. Springer, New York (1986). MR 0841073 | Zbl 0624.62020
[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). MR 0114280 | Zbl 0093.15704
[4] Cox, D. R.: Renewal Theory. Methuen’s Monographs on Applied Probability and Statistics Methuen, London; John Wiley, New York (1962). MR 0153061 | Zbl 0103.11504
[5] Cox, D. R.: Regression models and life-tables. J. R. Stat. Soc., Ser. B 34 187-220 (1972). MR 0341758 | Zbl 0243.62041
[6] Crescenzo, A. Di: Some results on the proportional reversed hazards model. Stat. Probab. Lett. 50 313-321 (2000). DOI 10.1016/S0167-7152(00)00127-9 | MR 1802225 | Zbl 0967.60016
[7] Crescenzo, A. Di, Longobardi, M.: On weighted residual and past entropies. Sci. Math. Jpn. 64 255-266 (2006). MR 2254144 | Zbl 1106.62114
[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). DOI 10.1093/biomet/83.1.233 | MR 1399168 | Zbl 0865.62075
[9] Furman, E., Zitikis, R.: Weighted premium calculation principles. Insur. Math. Econ. 42 459-465 (2008). DOI 10.1016/j.insmatheco.2007.10.006 | MR 2392102 | Zbl 1141.91509
[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). MR 0513423 | Zbl 0381.62011
[11] Gupta, R. C., Gupta, R. D.: Proportional reversed hazard rate model and its applications. J. Stat. Plann. Inference 137 3525-3536 (2007). DOI 10.1016/j.jspi.2007.03.029 | MR 2363274 | Zbl 1119.62098
[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). DOI 10.1080/03610929808832134 | MR 1613497 | Zbl 0900.62534
[13] Gupta, R. C., Han, W.: Analyzing survival data by PRH models. International Journal of Reliability and Applications 2 (2001), 203-216.
[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). DOI 10.1080/03610929008830371 | MR 1089242 | Zbl 0734.62093
[15] Jain, K., Singh, H., Bagai, I.: Relations for reliability measures of weighted distributions. Commun. Stat., Theory Methods 18 4393-4412 (1989). DOI 10.1080/03610928908830162 | MR 1046715 | Zbl 0707.62197
[16] Kerridge, D. F.: Inaccuracy and inference. J. R. Stat. Soc., Ser. B 23 184-194 (1961). MR 0123375 | Zbl 0112.10302
[17] Kullback, S., Leibler, R. A.: On information and sufficiency. Ann. Math. Stat. 22 79-86 (1951). DOI 10.1214/aoms/1177729694 | MR 0039968 | Zbl 0042.38403
[18] Kumar, V., Taneja, H. C.: On length biased dynamic measure of past inaccuracy. Metrika 75 73-84 (2012). DOI 10.1007/s00184-010-0315-7 | MR 2878109 | Zbl 1241.62014
[19] Kumar, V., Taneja, H. C., Srivastava, R.: Length biased weighted residual inaccuracy measure. Metron 68 (2010), 153-160. DOI 10.1007/BF03263532 | MR 3038412 | Zbl 1301.62104
[20] Kumar, V., Taneja, H. C., Srivastava, R.: A dynamic measure of inaccuracy between two past lifetime distributions. Metrika 74 1-10 (2011). DOI 10.1007/s00184-009-0286-8 | MR 2804725 | Zbl 1216.62156
[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.
[22] Nair, K. R. M., Rajesh, G.: Geometric vitality function and its applications to reliability. IAPQR Trans. 25 1-8 (2000). MR 1949414 | Zbl 1277.62236
[23] Nanda, A. K., Jain, K.: Some weighted distribution results on univariate and bivariate cases. J. Stat. Plann. Inference 77 169-180 (1999). DOI 10.1016/S0378-3758(98)00190-6 | MR 1687954 | Zbl 0924.62018
[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). MR 0652546 | Zbl 0414.62015
[25] Rao, C. R.: Linear Statistical Inference and Its Applications. John Wiley & Sons, New York (1965). MR 0221616 | Zbl 0137.36203
[26] Sengupta, D., Singh, H., Nanda, A. K.: The proportional reversed hazard model. Technical Report 1999, Indian Statistical Institute, Calcutta.
[27] Shannon, C. E.: A mathematical theory of communication. Bell Syst. Tech. J. 27 379-423, 623-656 (1948). DOI 10.1002/j.1538-7305.1948.tb01338.x | MR 0026286 | Zbl 1154.94303
[28] Smitha, S.: A Study on the Kerridge's Inaccuracy Measure and Related Concepts. Doctoral Dissertation 2010, CUSAT.
[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). MR 2545115 | Zbl 1185.62032
[30] Wallis, G.: Using spatio-temporal correlations to learn invariant object recognition. Neural Netw. 9 1513-1519 (1996). DOI 10.1016/S0893-6080(96)00041-X
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