The Korean Journal of Applied Statistics (응용통계연구)

The Korean Statistical Society (한국통계학회)
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Modified Kolmogorov-Smirnov Statistic for Credit Evaluation

신용평가를 위한 Kolmogorov-Smirnov 수정통계량

  • Hong, C.S. (Dept. of Statistics, Sungkyunkwan University) ;
  • Bang, G. (Research Institute of Applied Statistics, Sungkyunkwan University)
  • 홍종선 (성균관대학교 통계학) ;
  • 방글 (성균관대학교 응용통계연구소)
  • Published : 2008.12.31
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Abstract

For the model validation of credit rating models, Kolmogorov-Smirnov(K-S) statistic has been widely used as a testing method of discriminatory power from the probabilities of default for default and non-default. For the credit rating works, K-S statistics are to test two identical distribution functions which are partitioned from a distribution. In this paper under the assumption that the distribution is known, modified K-S statistic which is formulated by using known distributions is proposed and compared K-S statistic.

신용평가모형 개발과 적합성 검정 연구에서 부도율분포로부터 부도기업과 정상기업의 판별력을 검정하는 방법으로 비모수적인 방법인 Kolmogorov-Smirnov(K-S) 검정방법을 많이 사용한다. 모집단에 대한 누적분포함수를 알고있으며 이 분포함수가 두 개의 분포함수로 분할되었다는 가정하에서 두 분포함수 동일성을 검정하는 신용평가 연구에서 스코어 또는 부도율이 다양한 확률분포를 따른다고 가정하고 기존의 K-S 통계량과 수정된 K-S 통계량을 비교 토론한다.

Keywords

References

  1. 송문섭, 박창순, 이정진 (2003). , 자유아카데미
  2. Azzalini, A. (1985). A class of distributions which includes the normal ones, Scandinavian Journal of Statistics, 12, 171-178
  3. Azzalini, A. and Capitanio, A. (1999). Statistical applications of the multivariate skew normal distribution, Journal of the Royal Statistical Society, Series B, 61, 579-602 https://doi.org/10.1111/1467-9868.00194
  4. Barton, D. E. and Mallows, C L. (1965). Some aspects of the random sequence, Annals of Mathematical Statistics, 36, 236-260 https://doi.org/10.1214/aoms/1177700286
  5. Buccianti, A. (2005). Meaning of the .A parameter of skew-normal and log-skew normal distributions in fluid geochemistry, CODAWORK'05, 19-21
  6. Chang, F. C, Gupta, A. K. and Huang, W. J. (2002). Some skew-symmetric models, Random Operators and Stochastic Equations, 10, 133-140 https://doi.org/10.1515/rose.2002.10.2.133
  7. Chiogna, M. (1998). Some results on the scalar skew-normal distribution, Journal of the Italian Statistical Society, 7, 1-13 https://doi.org/10.1007/BF03178918
  8. Daniel, W. W. (1990). Applied Nonparametric Statistics, 2nd ed., PWS-KENT, Boston
  9. Darling, D. A. (1957). The Kolmogorov-Smirnov, Cramer-von mises tests, Annals of Mathematical Statistics, 28, 823-838 https://doi.org/10.1214/aoms/1177706788
  10. Genton, M. G. (2005). Discussion of the skew-normal, Scandinavia Journal of Statistics, 32, 189-198 https://doi.org/10.1111/j.1467-9469.2005.00427.x
  11. Gupta, A. K. and Chen, T. (2001). Goodness-of-fit test for the skew-normal distribution, Communications in Statistics-Simulation and Computation, 30, 907-930 https://doi.org/10.1081/SAC-100107788
  12. Gupta, A. K., Nguyen, T. and Sanqui, J. A. T. (2004). Characterization of the skew-normal distribution, Annals of the Institute of Statistical Mathematics, 56, 351-360 https://doi.org/10.1007/BF02530549
  13. Hajek, J., Sidak, Z. and Sen, P. K. (1998). Theory of Rank Tests, 2nd ed., Academic Press, New York
  14. Henze, N. (1986). A probabilistic representation of the skew-normal distribution, Scandinavian Journal of Statistics, 13, 271-275
  15. Joseph, M. P. (2005). A PD validation framework for Basel II internal rating-based systems, Credit Scoring and Credit Control, IX
  16. Liseo, B. (1990). The skew-normal class of densities: Inferential aspects from a Bayesian viewpoint, Statistica, 50, 71-82
  17. Salvan, A. (1986). Locally most powerful invariant tests of normality, Atti Della XXXIII Riunione Sci entifica Della Societa Italiana di Statistica, 2, 173-179
  18. Smirnov, N. V. (1939). On the estimation of the discrepancy between empirical curves of distribution for two independent samples, Bulletin of Mathematical University of Moscow, 2, 3-16
  19. Tasche, D. (2006). Validation of internal rating systems and PD estimates, Working paper, http://arxiv.org/ physics/0606071v1

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