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

This preview shows pages 1–2. Sign up to view the full content.

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-

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: tribution with α = 2 and β = 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 μ = E ( Y ) = α α + β • The variance of the beta distribution is σ 2 = V ( Y ) = αβ ( α + β ) 2 ( α + β + 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...
View Full Document

{[ snackBarMessage ]}

### Page1 / 2

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

This preview shows document pages 1 - 2. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online