Modified Test Statistic for Identity of Two Distribution on Credit Evaluation

Title & Authors
Modified Test Statistic for Identity of Two Distribution on Credit Evaluation
Hong, C.S.; Park, H.S.;

Abstract
The probability of default on the credit evaluation study is represented as a linear combination of two distributions of default and non-default, and the distribution of the probability of default are generally known in most cases. Except the well-known Kolmogorov-Smirnov statistic for testing the identity of two distribution, Kuiper, Cramer-Von Mises, Anderson-Darling, and Watson test statistics are introduced in this work. Under the assumption that the population distribution is known, modified Cramer-Von Mises, Anderson-Darling, and Watson statistics are proposed. Based on score data generated from various probability density functions of the probability of default, the modified test statistics are discussed and compared.
Keywords
Credit rating model;score;discriminatory power;distribution function;nonparametric test;probability of default;skewness;validation;
Language
Korean
Cited by
References
1.
송문섭, 박창순, 이정진(2003). , 자유아카데미

2.
홍종선, 방글 (2008). 신용평가를 위한 Kolmogorov-Smirnov 수정통계량, <응용통계연구>, 21, 1065-1075

3.
Anderson, T. W. (1962). On the distribution of the two-sample Cramer-von mises criterion, The Annals of Mathematical Statistics, 33, 1148-1159

4.
Azzalini, A. (1985). A class of distributions which includes the normal ones, Scandinavian Journal of Statistics, 12, 171-178

5.
Barton, D. E. and Mallows, C. L. (1965). Some aspects of the random sequence, The Annals of Mathmatical Statistics, 36, 236-260

6.
Buccianti, A. (2005). Meaning of the $\lambda$ parameter of skew-normal and log-skew normal distributions in fluid geochemistry, CODAWORK, 19-21

7.
Burr, E. J. (1964). Small-sample distributions of the two-sample Cramer-von Mises' W $^{2}$ and Watson's U$^{2}$, The Annals of Mathematical Statistics, 35, 1091-1098

8.
Chang, F. C.. Gupta, A. K. and Huang, W. J. (2005). Some Skew-Symmetric Models, Random Operatots and Stochastic Equations, 10, 133-140

9.
Daniel, W. W. (1990). Applied Nonparametric Statistics, 2nd ed., PWS-Kent, Boston

10.
Darling, D. A. (1957). The Kolmogorov-Smirnov, Cramer-von Mises Tests, The Annals of Mathmatical Statistics, 28, 823-838

11.
Fisz, M. (1960). On a Result by M. Rosenblatt Concerning the Von Mises-mirnov Test, The Annals of Mathematical Statistics, 31, 427-429

12.
Genton, M. G. (2005). Discussion of 'The skew-normal distribution and related multivariate families' by A. Azzalini, Scandinavian Journal of Statistics, 32, 189-198

13.
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

14.
Hajek, J., Sidak, Z. and Sen, P. K. (1998). Theory of Rank Tests, 2nd ed., Academic Press, New York

15.
Henze, N. A. (1986). A probabilistic representation of the 'Skewed-normal' distribution, Scandinavian Journal of Statistics, 13, 271-275

16.
Joseph, M. P. (2005). A PD validation framework for Basel 11 internal rating-Based systems, Credit Scoring and Credit Control, IX

17.
Pearson, E. S. (1963). Comparison of tests for randomness of points on a line, Biometrika, 50, 315-325

18.
Pettitt, A. N. (1976). A two-sample Anderson-Darling rank statistic, Biometrika, 63, 161-168

19.
Scholz, F. W. and Stephens, M. A. (1987). K-sample Anderson-Darling tests, Journal of the American Statistical Association, 82, 918-924

20.
Smirnov, N. V. (1939). On the estimation of the discrepancy between empirical curves of distribution for two independent sample, Bulletin Moscow University, 2, 3-16

21.
Stephens, M. A. (1965). Significance points for the two-sample statistic U$^{2}$$_{M,N}$, Biometrika, 52, 661-663

22.
Stephens, M. A. (1970). Use of the Kolmogorov-Smirnov, Cramer-von Mises and related statistics without extensive tables, Journal of the Royal Statistical Society. Series B(Methodological), 32, 115-122

23.
Stephens, M. A. (1974). EDF statistics for goodness of fit and some comparisons, Journal of the American Statistical Association, 69, 730-737

24.
Stephens, M. A. (1976). Asymptotic results for goodness-of-fit statistics with unknown parameters, The Annals of Statistics, 4, 357-369

25.
Stephens, M. A. (1978). On the W test for exponentiality with origin known, Technometrics, 20, 33-35

26.
Tasche, D. (2006). Validation of internal rating system and PD estimates, Working paper, http://arxiv.org/physics/0606071v 1

27.
Watson, G. S. (1961). Goodness-of-fit tests on a circle, Biometrika, 48, 109-114

28.
Watson, G. S. (1962). Goodness-of-fit tests on a circle 11, Biometrika, 49, 57-63