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# Gamma - distribution with α = 2 and β = 2 p.d.f of Gamma...

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Gamma Distribution The Gamma Distribution is used to model continuous data whose values are positive and have a probability histogram that is skewed to the right. Most of the data are near the origin, but some of the observations trail off to the larger numbers (to the right). The properties of the gamma distribution are The parameters for the gamma distribution are α > 0 and β > 0. The α parameter is referred to as the shape parameter and the β parameter is referred to as the scale parameter. The probability density function for the gamma distribution is f ( y ) = y α - 1 e - y/β β α Γ( α ) 0 y < where Γ( α ) = integraltext 0 y α - 1 e - y dy . In most circumstances, the distribution function F ( y ) does not have a closed form solution. Therefore, the probabilities for the gamma distribution must be obtained from tables or from a statistical software package. Here are graphs of the probability density function and distribution function of a Gamma

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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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Gamma - distribution with α = 2 and β = 2 p.d.f of Gamma...

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