Goodness of Fit Statistics for the Exponential Distribution When the Data Are Grouped

Weighted Kolmogrov–Smirnov type tests for grouped Rayleigh data

“…Large values of each statistic provide evidence against the null hypothesis. The distributions of the above type of statistics are explored in Damianou and Kemp [8] and Gulati and Neus [9], they are rather complicated and do not exist in closed forms. Thus we use the bootstrap techniques Efron and Tibshirani [11]; Davison and Hinkley [12] to find the appropriate P-values.…”

“…The solution that maximizes the likelihood function exists if r 1 < n and r k < n, otherwise no acceptable solution exists Kulldorff [10]. Following Gulati and Neus [9], define the following quantities at the inspection times…”

“…Damianou and Kemp [8] consider a subclass of the Kolmogrov-Smirnov type statistics which utilizes the distances between the empirical and the hypothesized distribution functions at all data points and obtained more powerful tests than the Kolmogrov-Smirnov test for both discrete and continuous data. Gulati and Neus [9] developed weighted Kolmogrov-Smirnov type statistics for the case of grouped data from the exponential distribution with unknown mean and studied their power performance.…”

Chi-squared components for tests of fit and improved models for the grouped exponential distribution

“…A more thorough examination of the null grouped exponential hypothesis can be made by using the components of the X 2 statistic, successfully exploited in Best and Rayner (2003, 2005 to test for the Geometric, Poisson and Binomial distributions. It was thus thought worthwhile to examine this components of X 2 approach to test for the grouped exponential distribution, recently considered by Spinelli (2001) and Gulati and Neus (2001). Extra complications in the grouped exponential case are that the MME and MLE no longer coincide and iterative methods are needed to find both of these estimators.…”

On the Power Performance of Test Statistics for the Generalized Rayleigh Interval Grouped Data

“…Many other researchers studied the asymptotic distributions of some of these statistics as in Schmid [11] and Pettitt and Stephens [12]. Modifications, critical values and powers of these statistics are also considered for some distributions with grouped data as in Conover [13], Reidwyl [14], Maag [15], Damianou and Kemp [16], Gulati and Neus [17], Richard and Lockhart [18], and Ampai and Kanisa [19].…”