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Steven Ascher

Bio: Steven Ascher is an academic researcher. The author has an hindex of 1, co-authored 1 publications receiving 88 citations.

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TL;DR: A wide selection of tests for exponentiality is discussed and compared in this article, where power computations, using simulations, were done for each procedure, and the score test presented in Cox and Oakes (1984) appears to be the best if one does not have a particular alternative in mind.
Abstract: A wide selection of tests for exponentiality is discussed and compared. Power computations, using simulations, were done for each procedure. Certain tests (e.g. Gnedenko (1969), Lin and Mudholkar (1980), Harris (1376), Cox and Oakes (1384), and Deshpande (1983)) performed well for alternative distributions with non-monotonic hazard rates, while others (e.g. Deshpande (1983), Gail and Gastwirth (1978), Kolmogorov-Smirnov (LillViefors (1969)), Hahn and Shapiro (1967), Hollander and Proschan (1972), and Cox and Oakes (1984)) fared well for monotonic hazard rates. Of all the procedures compared, the score test presented in Cox and Oakes (1984) appears to be the best if one does not have a particular alternative in mind.

94 citations


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682 citations

Journal ArticleDOI
01 Feb 2005-Metrika
TL;DR: In this paper, a wide selection of classical and recent tests for exponentiality are discussed and compared and a new goodness-of-fit test utilizing a novel characterization of the exponential distribution through its characteristic function is proposed.
Abstract: A wide selection of classical and recent tests for exponentiality are discussed and compared. The classical procedures include the statistics of Kolmogorov-Smirnov and Cramer-von Mises, a statistic based on spacings, and a method involving the score function. Among the most recent approaches emphasized are methods based on the empirical Laplace transform and the empirical characteristic function, a method based on entropy as well as tests of the Kolmogorov-Smirnov and Cramer-von Mises type that utilize a characterization of exponentiality via the mean residual life function. We also propose a new goodness-of-fit test utilizing a novel characterization of the exponential distribution through its characteristic function. The finite-sample performance of the tests is investigated in an extensive simulation study.

127 citations

Journal ArticleDOI
TL;DR: In this paper, the Weibull renewal process is proposed as an alternative to the simple (homogeneous) Poisson process, where the interevent times are independent and distributed identically.
Abstract: Recently, a special nonhomogeneous Poisson process known as the Weibull process has been proposed by C-H. Ho for fitting historical volcanic eruptions. Revisiting this model, we learn that it possesses some undesirable features which make it an unsatisfactory tool in this context. We then consider the entire question of a nonstationary model in the light of availability and completeness of data. In our view, a nonstationary model is unnecessary and perhaps undesirable. We propose the Weibull renewal process as an alternative to the simple (homogeneous) Poisson process. For a renewal process the interevent times are independent and distributed identically with distribution function F where, in the Weibull renewal process, F has the Weibull distribution, which has the exponential as a special situation. Testing for a Weibull distribution can be achieved by testing for exponentiality of the data under a simple transformation. Another alternative considered is the lognormal distribution for F. Whereas the homogeneous Poisson process represents purely random (memoryless) occurrences, the lognormal distribution corresponds to periodic behavior and the Weibull distribution encompasses both periodicity and clustering, which aids us in characterizing the volcano. Data from the same volcanoes considered by Ho were analyzed again and we determined there is no reason to reject the hypothesis of Weibull interevent times although the lognormal interevent times were not supported. Prediction intervals for the next event are compared with Ho's nonhomogeneous model and the Weibull renewal process seems to produce more plausible results.

89 citations

Journal ArticleDOI
TL;DR: For general composite hypotheses, consistency of the data-driven Neyman's test holds at essentially any alternative as discussed by the authors, but the number of components in the smooth test statistic should be chosen well; otherwise, considerable loss of power may occur.
Abstract: In recent years several authors have recommended smooth tests for testing goodness of fit. However, the number of components in the smooth test statistic should be chosen well; otherwise, considerable loss of power may occur. Schwarz's selection rule provides one such good choice. Earlier results on simple null hypotheses are extended here to composite hypotheses, which tend to be of more practical interest. For general composite hypotheses, consistency of the data-driven smooth tests holds at essentially any alternative. Monte Carlo experiments on testing exponentiality and normality show that the data-driven version of Neyman's test compares well to other, even specialized, tests over a wide range of alternatives.

86 citations

Journal ArticleDOI
TL;DR: In this article, the authors identify peaks and troughs in the inflation adjusted prices for 14 metals, using monthly average data from January 1947 through December 2007, and find many cases in which the duration of these phases are not purely random and have some degree of cyclicality.

86 citations