Uniform Distribution definition, formula and applications


 
uniform distribution by statisticalaid.com

Uniform Distribution

There are various continuous probability distributions such as uniform distribution, normal distribution, exponential distribution, gamma distribution, beta distribution, weibul distribution, cauchy distribution ect. Uniform distribution is a univariate continuous probability distribution with two parameter a and b.
A continuous random variable x is said to have a uniform distribution if the probability function is defined by-


where, a and b are the two parameters of the distribution such that -∞<=a<=b<=∞.

uniform distribution curve


Properties of uniform distribution

There are some impotant properties of uniform distribution-
  • The mean of uniform distribution is  
  • The median of uniform distribution is .
  • The variance of uniform distribution is  (b-a)∧2/12.
  • The mode of uniform distribution is  any value of.
  • The skewness of uniform distribution is 0.
  • The kurtosis of uniform distribution is .

Special characteristics of Uniform distribution

Some special characteristics of uniform distribution are given below-
  • The probability of this distribution is same for equal intervals in any part of the distribution.
  • The probability of uniform distribution depends on the length of the intervals, not on its position.
  • The pdf of the uniform distribution over the interval [0,1] is defined by f(x)=1.
  • Moreover, uniform distribution can be defined in a infinite number of ways.


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