Abstract
We study two new omnibus goodness of fit tests for exponentiality, each based on a characterization of the exponential distribution via the mean residual life function. The limiting null distributions of the tests statistics are the same as the limiting null distributions of the Kolmogorov-Smirnov and Cramér-von Mises statistics proposed when testing the simple hypothesis that the distribution of the sample variables is uniform on the interval [0, 1].
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ASCHER, S. (1990). A Survey of tests for exponentiality.Commun. Statist.-Theory Meth.,19 1811–1825.
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.
CSÖRGÖ, M. (1972). On the problem of replacing composite hypotheses by equivalent simple ones (a characterization approach to goodness of fit).Progress in statistics (European Meeting of Statisticians, Budapest, 1972),Vol. I, 159–180. Colloq. Math. Soc. Janos Bolyai, Vol. 9, North-Holland, Amsterdam, 1974.
D’AGOSTINO, R.B. and STEPHENS, M.A. (1986).Goodness-of-fit techniques. Marcel Dekker, New York and Basel.
DOKSUM, K.A. and YANDELL, B.S. (1984),Tests for exponentiality. In: Handbook of Statistics Vol. 4, North-Holland, 579–612.
DE WET, T. and RANDLES, R.H. (1987). On the effect of substituting parameter estimators in limiting χ2,U andV statistics.Ann. Statist.,15 398–412.
EL AROUI, M.-A. (1996). Un test préquentiel d’adéquation pour la loi exponentielle.C. R. Acad. Sci., Paris, Ser. I. 323 1069–1072.
GUPTA, R.D. and RICHARDS, D. St. P. (1997). Invariance properties of some classical tests of exponentiality.J. Statist. Plann. Inference.63 203–213.
GWANYAMA, P.W. (1997). Equivalence of two definitions of a Poisson process; and some modifications of Kolmogorov-Smirnov test for the exponential distribution.Int. J. Math. Edu. Sci. Technol.,28 545–551.
KLEFSJOE, B. and WESTBERG, U. (1996). Efficiency calculations of some tests for exponentiality by using TTT-transforms.Arab. J. Math. Sci.,2 129–149.
NIKITIN, Ya. Yu. (1996). Bahadur efficiency of a test of exponentiality based on a loss-of-memory type functional equation.J. Nonparam. Statist.,6 13–26.
O’REILLY, F.J. and STEPHENS, M.A. (1982). Characterizations and goodness of fit tests.J. Roy. Statist. Soc. Ser. B. 44 353–360.
PEARSON, E.S. and HARTLEY, H.O. (1972).Biometrika Tables for Statisticians, Volume 2. Cambridge University Press, Cambridge.
SESHADRI, V, CSÖRGŐ, M. and STEPHENS, M.A. (1969). Tests for the exponential distribution using Kolmogorov-type statistics.J. Roy. Statist. Soc. B.31 499–509.
SPURRIER, J.D. (1984). An overview of tests for exponentialityCommun. Statist. Theory Meth. 13 1635–165.
STEPHENS, M.A. (1976). Asymptotic results for goodness-of-fit statistics with unknown parameters.Ann. Statist. 4 357–369.
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Work supported by the Deutsche Forschungsgemeinschaft
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Baringhaus, L., Henze, N. Tests of fit for exponentiality based on a characterization via the mean residual life function. Statistical Papers 41, 225–236 (2000). https://doi.org/10.1007/BF02926105
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DOI: https://doi.org/10.1007/BF02926105
Key words and phrases
- Exponential distribution
- Cramér-von Mises statistic
- Kolmogorov-Smirnov statistic
- mean residual life function