Rényi’s residual entropy: A quantile approach

In the present paper, we introduce a quantile based Renyi’s entropy function and its residual version. We study certain properties and applications of the measure. Unlike the residual Renyi’s entropy function, the quantile version uniquely determines the distribution.

[1]  P. Sankaran,et al.  Nonparametric estimation of hazard quantile function , 2009 .

[2]  Jafar Ahmadi,et al.  Characterizations of symmetric distributions based on Rényi entropy , 2012 .

[3]  W. Gilchrist,et al.  Statistical Modelling with Quantile Functions , 2000 .

[4]  N. Balakrishnan,et al.  Total Time on Test Transforms , 2013 .

[5]  S. Sunoj,et al.  Quantile based entropy function , 2012 .

[6]  SOME NEW RESULTS ON RÉNYI ENTROPY OF RESIDUAL LIFE AND INACTIVITY TIME , 2011, Probability in the Engineering and Informational Sciences.

[7]  Marshall Freimer,et al.  a study of the generalized tukey lambda family , 1988 .

[8]  Robin K. S. Hankin,et al.  A NEW FAMILY OF NON‐NEGATIVE DISTRIBUTIONS , 2006 .

[9]  John W. Tukey,et al.  Nonparametric Statistical Data Modeling: Comment , 1979 .

[10]  Narayanaswamy Balakrishnan,et al.  Advances in Distribution Theory, Order Statistics, and Inference , 2007 .

[11]  K. Song.  Rényi information, loglikelihood and an intrinsic distribution measure , 2001 .

[12]  P. Sankaran,et al.  Modelling lifetimes by quantile functions using Parzen's score function , 2012 .

[13]  Somayeh Zarezadeh,et al.  Results on residual Rényi entropy of order statistics and record values , 2010, Inf. Sci..

[14]  Quantile based entropy function in past lifetime , 2013 .

[15]  G. M. Borzadaran,et al.  Information Measures for Some Well-Known Families , 2007 .

[16]  Bruce W. Schmeiser,et al.  An approximate method for generating symmetric random variables , 1972, CACM.

[17]  Jafar Ahmadi,et al.  Characterizations based on Rényi entropy of order statistics and record values , 2008 .

[18]  Bovas Abraham,et al.  Renyi's entropy for residual lifetime distribution , 2006 .

[19]  N. Unnikrishnan Nair,et al.  Quantile-Based Reliability Analysis , 2009 .

[20]  M. Asadi,et al.  Information Measures for Pareto Distributions and Order Statistics , 2006 .

[21]  Inder Jeet Taneja,et al.  On Generalized Information Measures and Their Applications , 1989 .

[22]  Study on RNorm Residual Entropy , 2006 .

[23]  N. Unnikrishnan Nair,et al.  A quantile based test for comparing cumulative incidence functions of competing risks models , 2010 .

[24]  Nader Ebrahimi,et al.  Residual entropy and its characterizations in terms of hazard function and mean residual life function , 2000 .

[25]  Nader Ebrahimi,et al.  Dynamic generalized information measures , 2005 .

[26]  Claude E. Shannon,et al.  A Mathematical Theory of Communications , 1948 .

[27]  Nader Ebrahimi,et al.  New partial ordering of survival functions based on the notion of uncertainty , 1995, Journal of Applied Probability.

[28]  Paul Jacobus Van Staden,et al.  Method of L-moment estimation for the generalized lambda distribution , 2009 .