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Unformatted text preview: distribution with α = 2 and β = 2. p.d.f. of Gamma Distribution with alpha = 2 and beta = 2 y f(y) 5 10 15 0.0 0.05 0.10 0.15 Distribution of Gamma Distribution with alpha = 2, beta = 2 y F(y) 5 10 15 0.2 0.4 0.6 0.8 1.0 • The theoretical mean of the gamma distribution is μ = E ( Y ) = αβ • The variance of the gamma distribution is σ 2 = V ( Y ) = αβ 2 Working with the gamma distribution in R. To ±nd the probability P ( Y ≤ y ) the command in R is pgamma(y, shape = alpha, scale = beta) 1 To fnd the value oF y such that P ( Y ≤ y ) = p the command in R is qgamma(p, shape = alpha, scale = beta) To generate observations From a gamma distribution the command in R is rgamma(numobs, shape = alpha, scale = beta) where numobs is the number oF observed values you would like to generate. 2...
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- Spring '08
- Probability, Probability theory