Gamma distribution Guide, Meaning , Facts, Information and Description

In probability theory and statistics, the gamma distribution is a continuous probability distribution. Its probability density function can be expressed in terms of the gamma function:

where k > 0 is the shape parameter and θ > 0 is the scale parameter of the gamma distribution.

The cumulative distribution function can be expressed in terms of the incomplete gamma function,

Let X be a random variable following a gamma distribution with parameters k and θ. Then X has the following properties:

; mode : for k ≥ 1 ; mean : ; variance : ; skewness : ; kurtosis :

If X₁ has a gamma distribution with parameters k₁ and θ, and X₂ has a gamma distribution with parameters k₂ and θ, then X₁ + X₂ has a gamma distribution with parameters k₁ + k₂ and θ.

If k is equal to 1, the gamma distribution is an exponential distribution with parameter θ. The sum of n exponential variables, all with the same parameter θ, is a gamma variable with parameters n and θ.

If k is an integer, the gamma distribution is an Erlang distribution (so named in honor of A. K. Erlang) and is the probability distribution of the waiting time of the kth "arrival" in a one-dimensional Poisson process with intensity 1/θ.

If k is a half-integer and θ = 2, then the gamma distribution is a chi-square distribution with 2 k degrees of freedom.

The gamma distributions are infinitely divisible probability distributions.

References

• R. V. Hogg and A. T. Craig. Introduction to Mathematical Statistics, 4th edition. New York: Macmillan, 1978. (See Section 3.3.)

This is an Article on Gamma distribution. Page Contains Information, Facts Details or Explanation Guide About Gamma distribution

	Web www.E-paranoids.com