mixtureBeta: Calculate parameters of a composite beta distribution arising...
In tmcd82070/EoAR: Evidence of Absence Regression (EoAR)

Description Usage Arguments Details Value Examples

Assuming n beta distributions, each with parameters a and b, this routine computes the A and B of an overall beta distribution when the n distributions are mixed. Mixing parameters (fractions) can be specified as weights.

1	mixtureBeta(Ba, Bb, w = NULL)

`Ba`	A vector containing the alpha parameter for all beta distributions.
`Bb`	A vector containing the beta parameter for all beta distributions.
`w`	A vector indicating the relative weight for each beta distribution in the mixture distribution. The default is `NULL`, in which case weights are all equal.

The assumption is that each beta distribution is independent of every other, and that they are combined into a composite mixture beta distribution. This routine uses mixture distribution theory to calculate a mean and a variance. The mean and variance are then used in a method of moments approach to calculate the parameters for the composite beta distribution.

A data frame (containing 1 row) with the beta mixture parameter estimates and summary statistics. The compoents (columns) of the returned data frame are:

alpha = alpha parameter of the composite beta distribution,
beta = beta parameter of the composite beta distribution,
mean = mean of the composite beta distribution (alpha/(alpha+beta)),
variance = variance of the composite beta (alpha*beta)/((alpha+beta)^2*(alpha+beta+1)),
lower2.5 = 2.5-th quantile of the composite beta distribution
upper97.5 = 97.5-th quantile of the coomposite beta distribution.

## alpha parameter for the beta distribution
(alpha <- c(100.5,100.5,100.5,235.4,235.4))
## beta parameter for the beta distribution
(beta <- c(234.5,234.5,234.5,2708,2708))
## alpha and beta are assumed to be in the same order

mixtureBeta(Ba=alpha,Bb=beta) ## equal weights

weight <- 1:5

mixtureBeta(Ba=alpha,Bb=beta,w=weight) ## unequal weights