On a Class of Unimodal Distributions
نویسنده
چکیده
A distribution function F(x) is said to be unimodal [l, p. 157] if there exists at least one value x = a such that F(x) is convex for xa. The point x = a is called the vertex of the distribution. In particular, if F(x) is absolutely continuous, then the corresponding probability density function p(x) = F'{x) is nondecreasing for xa. In the present paper we shall establish the unimodality of a class of distribution functions which were studied by Linnik in [2]. He has shown that for any real a in the interval 0<a = 2 the function
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تاریخ انتشار 2010