bayess (version 1.6)

solbeta: Recursive resolution of beta prior calibration

Description

In the capture-recapture experiment of Chapter 5, the prior information is represented by a prior expectation and prior confidence intervals. This function derives the corresponding beta \(B(\alpha,\beta)\) prior distribution by a divide-and-conquer scheme.

Usage

solbeta(a, b, c, prec = 10^(-3))

Value

alpha

first coefficient of the beta distribution

beta

second coefficient of the beta distribution

Arguments

a

lower bound of the prior 95%~confidence interval

b

upper bound of the prior 95%~confidence interval

c

mean of the prior distribution

prec

maximal precision on the beta coefficient \(\alpha\)

Details

Since the mean \(\mu\) of the beta distribution is known, there is a single free parameter \(\alpha\) to determine, since \(\beta=\alpha(1-\mu)/\mu\). The function solbeta searches for the corresponding value of \(\alpha\), starting with a precision of \(1\) and stopping at the requested precision prec.

See Also

probet

Examples

solbeta(.1,.5,.3,10^(-4))