uniform distribution

Uniform Distribution definition, formula and applications

Spread the love
  •  
  •  
  •  
  •  
  •  
  •  
  •  
  •  
  •  
  •  

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

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.
 

Leave a Reply

Your email address will not be published. Required fields are marked *

Releated

Probability Distributions in Statistics

Spread the love
  •  
  •  
  •  
  •  
  •  
  •  
  •  
  •  
  •  
  •  

Spread the love          In statistics, probability distributions are very important measure which related to the random variable and statistical data. Every data patern follows a probability distribution. Continuous data follow the continuous distribution and discrete data follow the discrete distributions. According to wikipedia, “In probability theory and statistics, a probability distribution is the mathematical function that […]

gamma distribution

Gamma Distribution definition, formula and applications

Spread the love
  •  
  •  
  •  
  •  
  •  
  •  
  •  
  •  
  •  
  •  

Spread the love          In probabilistic statistics, the gamma distribution is a two-parameter family of continuous probability distributions which is widely used in different sectors. The exponential distribution, Erlang distribution, and chi-square distribution are special cases of it. Gamma Distribution A continuous random variable X is said to have a generalised gamma distribution with parameter α and […]

exponential distribution

Exponential Distribution definition, formula with applications

Spread the love
  •  
  •  
  •  
  •  
  •  
  •  
  •  
  •  
  •  
  •  

Spread the love          In probabilistic statistics, the exponential distribution is the probability distribution of the time between events in a Poisson point process where events occur continuously and independently at a constant average rate. It is a special case of the gamma distribution.   Definition A continuous random variable X is said to have an exponential […]