Beta - tribution with = 2 and = 3. p.d.f. of Beta...

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Beta Distribution The beta distribution is used to model continuous data with values between 0 and 1. Typically, beta distributions are used to model proportions. The characteristics of the beta distribution are The parameters of the beta distribution are α > 0 and β > 0. Unlike the gamma distribution, these parameters do not have special names. With diFerent values of these parameters, the shape of the probability density curve can change signi±cantly. The probability density curve for a beta distribution is f ( y ) = y α - 1 (1 - y ) β - 1 B ( α,β ) 0 y 1 where B ( α,β ) = Γ( α )Γ( β ) Γ( α + β ) Under most circumstances, the distribution function F ( y ) for the beta distribution has no closed form solution. Therefore, in order to ±nd probabilities associated with the beta distri- bution, we must use tables or a statistical computer package. Here are graphs of the probability density function and distribution function of a Beta dis-
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Unformatted text preview: tribution with = 2 and = 3. p.d.f. of Beta Distribution with alpha = 2 and beta = 3 y f(y) 0.0 0.2 0.4 0.6 0.8 1.0 0.0 0.5 1.0 1.5 Distribution of Beta Distribution with alpha = 2 and beta = 3 y F(y) 0.0 0.2 0.4 0.6 0.8 1.0 0.2 0.4 0.6 0.8 The theoretical mean of the beta distribution is = E ( Y ) = + The variance of the beta distribution is 2 = V ( Y ) = ( + ) 2 ( + + 1) Working with the beta distribution in R. To nd the probability P ( Y y ) the command in R is pbeta(y,alpha,beta) 1 To fnd the value oF y so that P ( Y y ) = p the command in R is qbeta(p,alpha,beta) To generate observations From a beta distribution the command in R is rbeta(numobs,alpha,beta) where numobs is the number oF observations you would like to generate. 2...
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Beta - tribution with = 2 and = 3. p.d.f. of Beta...

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