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The gamma distribution is a two-parameter family of continuous probability distributions. Name three special cases of the gamma distribution and briefly describe each one.
The gamma distribution is a two-parameter family of continuous probability distributions. Name three special cases of the gamma distribution and briefly describe each one.
The special cases of the gamma distribution are the exponential distribution, Erlang distribution, and chi-squared distribution. The exponential distribution is often used to model the time until an event occurs, the Erlang distribution is the sum of k independent exponentially distributed random variables, and the chi-squared distribution is the sum of the squares of k independent standard normal random variables.
What are the two equivalent parameterizations of the gamma distribution, and how are they related?
What are the two equivalent parameterizations of the gamma distribution, and how are they related?
The two equivalent parameterizations of the gamma distribution are: 1. With a shape parameter $k$ and a scale parameter $\theta$. 2. With a shape parameter $\alpha = k$ and an inverse scale parameter $\beta = 1/\theta$, called a rate parameter. These are related by the equations $\alpha = k$ and $\beta = 1/\theta$.
What are the constraints on the parameters in both forms of the gamma distribution?
What are the constraints on the parameters in both forms of the gamma distribution?
In both forms of the gamma distribution, both parameters are constrained to be positive real numbers.
