Abstract
This paper presents new omnibus tests for the exponential and the normal distribution which are based on the difference between the integrated distribution function Ψ(t) = ∫t ∞(1 - F(x)dx and its empirical counterpart. The procedures turn out to be serious competitors to classical tests for exponentiality and normality.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Araujo, A. and Giné, E. (1980). The Central Limit Theorem for Real and Banach Valued Random Variables, Wiley, New York.
Baringhaus, L. and Henze, N. (1991). A class of consistent tests for exponentiality based on the empirical Laplace transform, Ann. Inst. Statist. Math., 43, 551-564.
Baringhaus, L. and Henze, N. (1992). An adaptive omnibus test for exponentiality, Comm. Statist. Theory Methods, 21(4), 969-978.
Baringhaus, L., Danschke, R. and Henze, N. (1989). Recent and classical tests for normality—a comparative study, Comm. Statist. Simulation Comput., 18(1), 363-379.
Baringhaus, L., Gürtler, N. and Henze, N. (2000). Weighted integral test statistics and components of smooth tests of fit, Australian & New Zealand Journal of Statistics, 42, 179-192.
Billingsley, P. (1968). Convergence of Probability Measures, Wiley, New York
D'Agostino, R. and Stephens, M. (1986). Goodness-of-fit Techniques, Marcel Dekker, New York.
Gail, M. and Gastwirth, J. (1978). A scale-free goodness-of-fit test for the exponential distribution based on the Gini statistic, J. Roy. Statist. Soc. Ser. B, 40, 350-357.
Gastwirth, J. and Owens, M. (1977). On classical tests of normality, Biometrika, 64, 135-139.
Groeneveld, R. (1998). A class of quantile measures for kurtosis, Amer. Statist., 51(4), 325-329.
Henze, N. and Nikitin, Y. (1998). A new approach to goodness-of-fit testing based on the integrated empirical process (Preprint 98/18), University of Karlsruhe, Germany (to appear in J. Nonparametr. Statist.).
Klar, B. (1999). Goodness-of-fit tests for discrete models based on the integrated distribution function, Metrika, 49, 53-69.
Klefsjö, B. (1983). Testing exponentiality against HNBUE, Scand. J. Statist., 10, 65-75.
Lewis, P. (1965). Some results on tests for Poisson processes, Biometrika, 52, 67-77.
Müller, A. (1996). Ordering of risks: A comparative study via stop-loss transforms, Insurance Math. Econom., 17, 215-222.
Neuhaus, G. (1974). Asymptotic properties of the Cramér-von Mises statistic when parameters are estimated, Proceedings of the Prague Symposium on Asymptotic Statistics (Ed. J. Hájek), 257-297, Universita Karlova, Praha.
Pearson, E., D'Agostino, R. and Bowman, K. (1977). Tests for departure from normality: Comparison of powers, Biometrika, 64, 231-246.
Pollard, D. (1984). Convergence of Stochastic Processes, Springer, New York.
Widder, D. (1959). The Laplace transform, 5th ed., Princeton University Press, Princeton.
Author information
Authors and Affiliations
About this article
Cite this article
Klar, B. Goodness-Of-Fit Tests for the Exponential and the Normal Distribution Based on the Integrated Distribution Function. Annals of the Institute of Statistical Mathematics 53, 338–353 (2001). https://doi.org/10.1023/A:1012422823063
Issue Date:
DOI: https://doi.org/10.1023/A:1012422823063