Special Case of Distribution Parametrization
- A binomial (n, p) random variable with n = 1, is a Bernoulli (p) random variable.
- A negative binomial distribution with r = 1 is a geometric distribution.
- A gamma distribution with shape parameter α = 1 and scale parameter β is an exponential (β) distribution.
- A gamma (α, β) random variable with α = ν/2 and β = 2, is a chi-squared random variable with ν degrees of freedom.
- A chi-squared distribution with 2 degrees of freedom is an exponential distribution with mean 2 and vice versa.
- A Weibull (1, β) random variable is an exponential random variable with mean β.
- A beta random variable with parameters α = β = 1 is a uniform random variable.
- A beta-binomial (n, 1, 1) random variable is a discrete uniform random variable over the values 0 ... n.
- A random variable with a t distribution with one degree of freedom is a Cauchy(0,1) random variable.
Read more about this topic: Relationships Among Probability Distributions
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