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Statistics/Distributions/Uniform

Continuous Uniform DistributionEdit

Uniform
Probability density function
 
Using maximum convention
Cumulative distribution function
 
Notation  
Parameters  
Support  
PDF  
CDF  
Mean  
Median  
Mode any value in  
Variance  
Skewness 0
Ex. kurtosis  
Entropy  
MGF  
CF  

The (continuous) uniform distribution, as its name suggests, is a distribution with probability densities that are the same at each point in an interval. In casual terms, the uniform distribution shapes like a rectangle.

Mathematically speaking, the probability density function of the uniform distribution is defined as

 

 

And the cumulative distribution function is:

 

MeanEdit

We derive the mean as follows.

 

As the uniform distribution is 0 everywhere but [a, b] we can restrict ourselves that interval

 
 
 
 

VarianceEdit

We use the following formula for the variance.

 
 
 
 
 
 
 
 

External linksEdit