GOODNESS-OF-FIT TESTS FOR THE EXPONENTIAL AND THE NORMAL DISTRIBUTION BASED ON THE INTEGRATED DISTRIBUTION FUNCTION

BERNHARD KLAR

Institut für Mathematische Stochastik, Universität Karlsruhe, Englerstr. 2, 76128 Karlsruhe, Germany

(Received December 14, 1998; revised November 8, 1999)

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.

Key words and phrases: Goodness-of-fit test, integrated distribution function, exponential distribution, normal distribution.