Uniform Distribution as the Limiting Form of a Density Function

Abstract

The uniform distribution, denoted by U(x;A,B)=1/(B-A) if 0<A<x<B<∞ and zero otherwise, is the simplest probability density functions of a continuous random variable X. For a continuous random variable X on the interval (0, 1), a three parameters density function, denoted by h(x;A,B,n), is constructed so that its limiting form is the uniform density function U(x;A,B) in which n→∞.