Note on discrete a-unimodality

An interpretation is given of ABOUAMMOH'S (1987) discrete analogue of the (one-dimensional) definition of a-unimodality by Olshen and Savage. The concepts are of some interest in the context of selfdecomposability.     

On the independence of integer and fractional parts

We use the independence of the integer and fractional parts of exponentially distributed random variables to obtain expressions for the order statistics from a geometric distribution. As our main result we show that a strong form of this independence characterizes the exponential distribution.     

A SIMPLE TEST FOR UNIFORMITY

Abstract A new and very simple test for uniformity is proposed. An exact formula for the distribution under H₀ of the corresponding test statistic is derived. This formula is only suitable for computer-oriented use. For other circumstances a table of critical values is given. The power of the test is compared with that of two well-known alternatives: the χ²-test and the Kolmogorov-Smirnov test.