We prove the following conjecture of Narayana: there are no nontrivial dominance reene-ments of the Smirnov two-sample test if and only if the two sample sizes are relatively prime. We also count the number of natural signiicance levels of the Smirnov two-sample test in terms of the sample sizes and relate this to the Narayana conjecture. In particular, Smirnov tests with relatively prime sampl...

Aims. This paper reports on a search for new classical nova candidates in the M81 galaxy based on archival, as well as recent, new images. Methods. We used images from 1999–2007 to search for optical transients in M81. The positions of the identified classical nova candidates were used to study their spatial distribution. Kolmogorov-Smirnov test (KS) and bottom-to-top (BTR) ratio diagnostic wer...

background: understanding of the incident electron energy and angular distributions from clinical electron accelerators (linacs) is important for dosimetry and treatment planning. the most important goals of this study were to evaluate the energy fluence and angular distributions of electron beams from a neptun 10pc linac using the monte carlo (mc) code. materials and methods: the linac electro...

The Kolmogorov-Smirnov (K-S) test is widely used as a goodness-of-fit test. This thesis consists of two parts to describe ways to improve the classical K-S test in both 1-dimensional and 2-dimensional data. The first part is about how to improve the accuracy of the classical K-S goodness-of-fit test in 1-dimensional data. We replace the p-values estimated by the asymptotic distribution with nea...

In this paper we propose an improvement of the Kolmogorov-Smirnov test for normality. In the current implementation of the Kolmogorov-Smirnov test, a sample is compared with a normal distribution where the sample mean and the sample variance are used as parameters of the distribution. We propose to select the mean and variance of the normal distribution that provide the closest fit to the data....