Journal of the Korean Data and Information Science Society

The Korean Data and Information Science Society (한국데이터정보과학회)
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Generalized Kullback-Leibler information and its extensions to censored and discrete cases

  • Park, Sangun (Department of Applied Statistics, Yonsei University)
  • Received : 2012.10.11
  • Accepted : 2012.11.05
  • Published : 2012.11.30
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Abstract

In this paper, we propose a generalized Kullback-Leibler (KL) information for measuring the distance between two distribution functions where the extension to the censored case is immediate. The generalized KL information has the nonnegativity and characterization properties, and its censored version has the additional property of monotonic increase. We also extend the discussion to the discrete case and propose a generalized censored measure which is comparable to Pearson's chi-square statistic.

Keywords

References

  1. Cramer, H. (1955). The elements of probability theory, John Wiley and Sons, NY.
  2. David, H. A. and Nagaraja, H. N. (2003), Order statistics, 3rd Ed., John Wiley and Sons, NY.
  3. Efron, B. and Johnstone, I. (1990). Fisher information in terms of the hazard rate. Annals of Statistics 18, 38-62. https://doi.org/10.1214/aos/1176347492
  4. Kullback, S. (1959). Information theory and statistics, John Wiley and Sons, NY.
  5. Lim, J. and Park, S. (2007). Censored Kullback-Leibler information and goodness of t test with Type II censored data. Journal of Applied Statistics, 34, 1051-1064. https://doi.org/10.1080/02664760701592000
  6. Park, S. and Shin, M. (2012). Kullback-Leibler information of Type I censored variable and its application. Submitted.

Cited by

  1. On scaled cumulative residual Kullback-Leibler information vol.24, pp.6, 2013, https://doi.org/10.7465/jkdi.2013.24.6.1497