Exponential Distribution definition, formula with applications



Exponential distribution bt statisticalaid.com

 

Exponential Distribution

A continuous random variable X is said to have an exponential distribution with parameter θ if its probability density fumction is defined as,



where, θ is the only parameter of the distribution and θ>0. Exponential distribution is continuous probability distribution and it has memoryless property like geometric distribution.



exponential distribution curve


Characteristics of Exponential Distribution

  • Exponential distribution has only one parameter ‘λ’.
  • Mean of exponential distribution (variate) is 1/λ.
  • Variance of exponential distribution (variate) is 1/λ2
  • Moments of all order exists in exponential dis­tribution.
  • Characteristic function of exponential distribu­tion is .
  • Moment generating function of exponential distribution is .
  • Median of exponential distribution is also 1/λ.
  • The measure of skewness β1= 4.
  • Measure of kurtosis, β2= 6. These measures show that exponential distribution is positive skewed and leptokurtic.
  • If the value of  λ=1; mean= variance, if  λ<1; mean<variance and if  λ>1; mean>variance.
  • It also process the memoryless property just like geometric distribution.


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