Page 51 - MATLAB Recipes for Earth Sciences

42 3 Univariate Statistics

Uniform Distribution

A uniform distribution or rectangular distribution is a distribution that
has constant probability (Fig. 3.4). The corresponding probability density
function is

where the random variable x has any of N possible values. The cumulative
distribution is

The probability density function is normalized to unity

i.e., the sum of probabilities is one. Therefore, the maximum value of the
cumulative distribution is one as well.

Probability Density Cumulative Distribution
Function Function
0.2 1.2
f(x)=1/6 1
0.15
0.8
f(x) 0.1 f(x) 0.6

0.4
0.05
0.2

0 0
1 2 3 4 5 6 0 1 2 3 4 5 6
x x
a b

Fig. 3.4 a Probability density function f(x) and b cumulative distribution function F(x)
of a uniform distribution with N=6. The 6 discrete values of the variable x have the same
probability 1/6.