Risk theory Decision-making
under uncertainty

Description

A random variable has uniform distribution on an interval [a,b], if it is continuous, takes values only within [a,b], and its density function is constant on [a,b], and is equal to 0 outside this interval.

The picture below show graphs of a density function f (bound to the left axix) and a cumulative distribution function F (bound to the right axis) of the uniform distribution on [0,2].

Density function and CDF of the uniform distribution on [0,2]

Characteristics

Following table contains formulae for calculation of characteristics of a uniform distribution.

Density function
Distribution function
Expectation (a + b) / 2
Standard deviation (b - a) / 2
Variance (b - a)2 / 12
Asymmetry 0
Kurtosis -6/5

Simulation

Simulation of values of the random variable U with uniform distribution on [0,1] is available in most programming systems, e.g. function Rnd() in VBA and random in Pascal and Delphi.

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