Volume 4, Issue 3, May 2015, Page: 118-124
Entropy for Past Residual Life Time Distributions
Arif Habib, College of applied Medical Sciences - Khamis Mushait;,King Khalid University, Kingdome of Saudi Arabia
Meshiel Alalyani, College of Nursing – Khamis Mushait, King Khalid University, Kingdome of Saudi Arabia
Received: Feb. 27, 2015;       Accepted: Mar. 16, 2015;       Published: Apr. 21, 2015
DOI: 10.11648/j.ajtas.20150403.17      View  4152      Downloads  254
Abstract
As we are familiar that existence of life is uncertain. In the context of reliability and lifetime distributions, there are some measures such as the hazard rate function or the mean residual lifetime function that have been used to characterize or compare the aging process of a component. This definition deals with random variable truncated above some t, i.e. the support of the random variable is taken to be (0, t). We outline some common methods for past residual lifetime distributions with the aim to provide some insights on general construction mechanisms. Some applications are given to provide the readers a possible source of ideas to draw upon. Applications of past residual lifetime distributions in reliability, survival analysis and mortality studies are briefly discussed.
Keywords
Differential Entropy, Past Residual Entropy, Life Time Distributions
To cite this article
Arif Habib, Meshiel Alalyani, Entropy for Past Residual Life Time Distributions, American Journal of Theoretical and Applied Statistics. Vol. 4, No. 3, 2015, pp. 118-124. doi: 10.11648/j.ajtas.20150403.17
Reference
[1]
Asaid, M. and Ebrahimi, N., (2000), “Residual entropy and its characterizations in terms of hazard function and mean residual life function”. Statist. Prob. Lett. 49: 263-269.
[2]
Awad, A.M., (1987), “A statistical information measure”. Dirasat XIV (12): 7- 20
[3]
Belzunce, F., Navarror, J., Ruiz, J.M. and Aguila, Y., (2004), “Some results on residual entropy function”.Metrika 59:147-161.
[4]
Chandra, N.K. and Roy, D., (2001), “Some results on reversed hazard rate”. Prob. Eng. Inf. Sci. 15: 95-102.
[5]
Crescenzo, A. D. and Longobardi, M., (2002), “Entropy based measure of uncertainty in past life time distributions”. J.of applied probability 39: 434-440.
[6]
Crescenzo, A.D. and Longobardi, M., (2004), “A measure of discrimination between past life time distributions” Stat. Prob.Lett. 67: 173-182
[7]
Ebrahimi, N., (1996), “How to measure uncertainty in the life time distributions”.Sankhya. vol. 58, Ser.A 48-57
[8]
Ebrahimi, N., (1997) “Testing whether life time distribution is decreasing uncertainty”.J.Statist.Plann.Infer. 64:9-19
[9]
Ebrahimi, N. and Kirmani, S.N.U.A., (1996), “Some results on ordering of survival function through uncertainty”. Statist. Prob.Lett. 29:167-176
[10]
Ebrahimi, N. and Pellerey, F., (1995), “New partial ordering of survival functions based on the notion of uncertainty”. Journal of Applied probability. 32: 202-211
[11]
Gupta, R.D. and Nanda, A.K., (2002), “ and entropies and relative entropies ofdistributions”.J.of Statistical Theory and Applications 3:177-190
[12]
Hart, P.E., (1975), “Moment distributions in economics, an exposition”. Journal of Royal Statistical Society, Series A 138: 423-434.
[13]
Kapur, J.N., (1994), “Measures of information and their applications”. Willy Eastern Limited.
[14]
Kapur, J.N. and Kesavan, H.K., (1990), “Generalized maximum entropy principle withapplications”. Sand-Ford Educational Press of the University of Waterloo, Canada.
[15]
Kurths, J., Voss, A., Saparin, P., Witt, A., Klein, H.j., and Wessel, N., (1995), “QuantitativeAnalysis of heart rate variability”. Chaos 1: 88-94
[16]
Morales, D., Pardo, L., and Vajda, I., (1997), “Some new statistics for testing hypotheses inparametric models”. Journal of Multivariate Analysis, 62: 137-168.
[17]
Nair, K.R.M. and Rajesh, G., (1998), “Characterization of probability distributions using theresidual entropy function”.J.Indian Statist.Assoc. 36:157-166
[18]
Nanda, A.K. and Paul, P., (2006) “Some properties of past entropy and their applactions”.Metrika. 64: 47-61
[19]
Nanda, A.K. and Paul, P., (2006) “Some results on generalized residual entropy”.Information Science 176: 27-47.
[20]
Nanda, A.K. and Paul, P., (2006) “Some results on generalized past entropy” .Journal of StatisticalPlanning and Inference. 136 : 3659-3674.
[21]
Renyi, A., (1961), “On measure of entropy and information”.Proceeding of the FourthBerkeley Symposium on Math. Statist. Prob.Vol 1, University of California Press, Berkely,547-561.
[22]
Sankaran, P.G. and Gupta, R.P., (1999), “Characterization of the life time distributions using measure of uncertainty”. Calcutta Statistical Association Bulletin. 49:154-166.
[23]
Shannon, C.E.,(1948), “A mathematical theory of communication”. Bell System TechnicalJ. 27:379-423.
[24]
Sankaran, P.G. and Gleeja, V.L., (2006),“ On bivariate reversed hazard rates”. J.Japan Statist. Soc. 36: 213-224.
[25]
Song, K., (2001), “Renyi information, loglikelihood and an intrinsic distributionmeasure”. Journal of Statistical Planning and inference 93: 51-69
[26]
Jiang R, Murthy DNP. Impact of quality variations on product reliability. Reliability Engineering and System Safety 2009; 94:490–496.
[27]
Wong KL. A new framework for part failure-rate prediction models. IEEE Transactions on Reliability 1995; 44(1):139–146.
[28]
FinkelsteinM. Understanding the shape of the mixture failure rate (with engineering and demographic applications). Applied Stochastic Modelsin Business and Industry 2009; 25:643–663.
[29]
Finkelstein M. Failure Rate Modeling for Reliability and Risk. Springer: London, 2008.
[30]
Ghitany ME, Al-Awadhi FA, Alkhalfan LA. Marshall-Olkin extended Lomax distribution and its application. Communications in Statistics:Theory and Methods 2007; 36:1855–1866.
[31]
Meeker WQ, Escobar LA. Statistical Methods for Reliability Data. John Wiley & Sons: New York, 1998.
Browse journals by subject