Tests for the Exponential Distribution Using Kolmogorov-Type Statistics

Abstract

A critical examination is made of the relative merits of two techniques for testing for the exponential distribution, involving transformations of the original observations to random variables uniformly distributed on the null hypothesis.

Some Exact Tests for Normality in the Presence of Unknown Parameters

“…1. INTRODUCTION THIS paper is based on a result of Kotlarski (1966) and is very close in spirit to our former papers, Seshadri et al (1969) and Seshadri (1970, 1971). The basic idea contained in all these papers is the elimination of unknown parameters in the normal, gamma and the exponential distributions by means of suitable (measurable) transformations on a given set of observations such that the transformed random variables obey known probability distributions with known parameters under the given null hypothesis.…”

An overview of tests for exponentiality

“…One such distribution is the beta distribu- Seshadri, cs$rg;, and Stephens (1969) show that for complete samples this property characterizes the one parameter exponential distribution. They also compare the power properties of several omnibus tests of uniformity when applied to the transformed data.…”

Testing Exponentiality Based on Kullback-Leibler Information

“…Finkelstein and Schafer (1971) concluded that their statistic was better than Lilliefors's statistic and equivalent to Van-Soest's statistic in terms of power. Seshadri et al (1969) considered Kolmogorov-Smirnov tests and the Van-Soest test and examined the relative merits of the two techniques, involving transformations of the original observations. Frecho and Ringer (1972) compared several test statistics due to Epstein (1960), Hartley's (1950)test and the F-test given by Gnedenko et al (1969).…”