What is the motivation for the three parameter gamma distribution and the resulting structure of its density?

What is the meaning of the location, scale and shape parameters here?

  • 1
    $\begingroup$ Which three parameter gamma? I've seen more than one. Do you mean the one that's simply a shifted two parameter gamma? $\endgroup$ – Glen_b Oct 18 '13 at 19:16
  • $\begingroup$ The meaning of "location parameter" and "scale parameter" is independent of the distribution. Also, what do you mean by "structure of its density"? $\endgroup$ – jbowman Oct 19 '13 at 0:00
  • $\begingroup$ It refers to the probability density function $\endgroup$ – Vani Oct 19 '13 at 4:42
  • 2
    $\begingroup$ @Carl That must be very confusing for physicists when they want to talk about a function that represents actual mass-density. I can understand a statistician dropping the adjective, but for a physicist it would seem to be necessary to keep it, since they might regularly need to refer to more than one kind of density. $\endgroup$ – Glen_b Dec 19 '16 at 0:28
  • 3
    $\begingroup$ I wouldn't call a pdf a probability function. It's a density function, but since more than one thing can have density, we need to be able to express what it's a density of (and that's probability). The only think I'd normally call a probability function is the function that represents P(X=x) for a discrete random variable. $\endgroup$ – Glen_b Dec 19 '16 at 0:55
  1. The three parameter gamma distribution is needed only when you need to shift the distribution itself.

  2. In the two-parameter gamma distribution, you could read the shape parameter as a proxy of the most probable value of the distribution, and the scale parameter of how "long" is its tail.

    The mean of the distribution is given exactly by the product of the shape and the scale parameters.

    If you need to shift the distribution, that's where you use the three-parameters gamma distribution. In this instance, the mean of the distribution is simply $\text{mean}=\text{location}+\text{shape}\cdot \text{scale}$.

| cite | improve this answer | |

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.