Gamma Density Function

A Gamma Density Function is a probability density function from a gamma distribution family.

• • …
• Example(s):
  • [math]\displaystyle{ \gamma(k=7.5, \theta=0.5) }[/math].
  • a Chi-Square Function.
  • …
• Counter-Example(s):
  • a Beta Probability Function.
• See: Binomial Density Function, Shape Parameter.

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References

• https://upload.wikimedia.org/wikipedia/commons/thumb/e/e6/Gamma_distribution_pdf.svg/325px-Gamma_distribution_pdf.svg.png
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2006

• (Dubnicka, 2006g) ⇒ Suzanne R. Dubnicka. (2006). “Special Continuous Distributions - Handout 7." Kansas State University, Introduction to Probability and Statistics I, STAT 510 - Fall 2006.
  • THE GAMMA FUNCTION: The gamma function is a function of t, defined for all k > 0 as ...
  • TERMINOLOGY : A random variable X is said to have a gamma distribution with parameters k > 0 and > 0 if its pdf is given by fX(x) =
    • …
    • 0, otherwise.
  • TERMINOLOGY : In the Gamma(k, ) family, when k = /2, for any integer , and = 1/2, we call the resulting distribution a 2 distribution with degrees of freedom. If X has a 2 distribution with degrees of freedom, we write X ∼ 2().

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