Discrete scan statistics are used for testing the null hypothesis that the observations are identically distributed against a clustering alternative that specifies an increased incidence of observations in a connected subregion of the circle. To implement the testing procedures based on the scan...

Scan statistics have been extensively used in many areas of science to analyze the occurrence of observed clusters of events in time or space. Since the scan statistics are based on the highly dependent consecutive subsequences of observed data, accurate probability inequalities for their...

This article investigates the accuracy of approximations for distributions of two-dimensional discrete scan statistics. A product-type approximation, a Bonferroni-type inequality, two Poisson approximations and a compound Poisson approximation are studied. A simulation study is presented to...

In this article we introduce a maximum scan score-type statistic for testing the null hypothesis that the observations are iid according to a specified distribution, against an alternative that the observations cluster within a window of unknown length. This statistic is a variable window scan...

In this article, multiple scan statistics of variable window sizes are derived for independent and identically distributed 0-1 Bernoulli trials. Both one and two dimensional, as well as, conditional and unconditional cases are treated. The advantage in using multiple scan statistics, as opposed...

New simultaneous prediction intervals for multiple forecasts from ARIMA models based on the Bonferroni-type and the product-type inequalities are introduced. These prediction intervals are compared with the marginal prediction intervals used in forecasting.