DOI QR코드

DOI QR Code

Some applications for the difference of two CDFs

  • Received : 2013.12.13
  • Accepted : 2014.01.06
  • Published : 2014.01.31

Abstract

It is known that the dierence in the length between two location parameters of two random variables is equivalent to the difference in the area between two cumulative distribution functions. In this paper, we suggest two applications by using the difference of distribution functions. The first is that the difference of expectations of a certain function of two continuous random variables such as the differences of two kth moments and two moment generating functions could be defined by using the difference between two univariate distribution functions. The other is that the difference in the volume between two empirical bivariate distribution functions is derived. If their covariance is estimated to be zero, the difference in the volume between two empirical bivariate distribution functions could be defined as the difference in two certain areas.

Keywords

References

  1. Holland, P. W. (2002). Two measures of change in the gaps between the CDFs of test-score distributions. Journal of Educational and Behavioral Statistics, 27, 3-17. https://doi.org/10.3102/10769986027001003
  2. Hong, C. S. (2002). Theory of statistical probability distributions, 2nd Ed., Parkyoung Sa.
  3. Hong, C. S. (2013). The difference between two distribution functions. Journal of the Korean Data & Information Science Society, 24, 1449-1454. https://doi.org/10.7465/jkdi.2013.24.6.1449
  4. Mood, A. M., Graybill, F. A. and Boes, D. C. (1974) Introduction to the theory of statistics, 3rd Ed, McGraw-Hill, International Edition, Singapore.