Gamma distribution
Gamma distribution is a two-parameter family of continuous probability distributions. It is frequently used in both the natural and social sciences as a simple model of the times to events in a Poisson process.
Definition
The gamma distribution can be parameterized in terms of a shape parameter α = k and an inverse scale parameter β = 1/θ, called a rate parameter., the symbol Γ(n) is the gamma function and is defined as (n−1)! :
The variable X is said to be gamma-distributed with the shape k and the scale θ.
Properties
Probability density function
The probability density function (pdf) of the gamma distribution shows the likelihood of a random variable X, given the parameters α and β.
Cumulative distribution function
The cumulative distribution function (cdf) of a random variable X gamma-distributed is the probability that X will take a value less than or equal to x.
Characteristic function
The characteristic function of a gamma-distributed random variable X with parameters α and β is derived by taking the inverse Fourier transform of the characteristic function.
Applications
The gamma distribution has been used to model various types of processes in the fields of life testing, reliability engineering, queuing theory, biology, medical sciences, hydrology, and many others.
See also
References
This article is a probability-related stub. You can help WikiMD by expanding it!
Gamma_distribution
Gamma PDF 252
Gamma CDF 252
Gamma PDF 3D
Gamma PDF 3D by k
Gamma PDF 3D by Theta
Gamma PDF 3D by x
Gamma distribution median bounds
Gamma distribution median Lyon bounds
Gamma distribution median loglog bounds
Gamma KL 3D
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