getBetaFromCI {bootComb}

Find the best-fit beta distribution for a given confidence interval for a probability parameter.

Description

Finds the best-fit beta distribution for a given confidence interval for a probability parameter; returns the corresponding density, distribution, quantile and sampling functions.

Usage

getBetaFromCI(qLow, qUpp, alpha = 0.05, initPars = c(50, 50), maxiter = 1000)

Arguments

qLow

The observed lower quantile.

qUpp

The observed upper quantile.

alpha

The confidence level; i.e. the desired coverage is 1-alpha. Defaults to 0.05.

initPars

A vector of length 2 giving the initial parameter values to start the optimisation; defaults to c(50,50).

maxiter

Maximum number of iterations for optim. Defaults to 1e3. Set to higher values if convergence problems are reported.

Value

A list with 5 elements:

r

The sampling function.

d

The density function.

p

The distribution function.

q

The quantile function.

pars

A vector of length 2 giving the two shape parameters for the best-fit beta distribution (shape1 and shape2 as in rbeta, dbeta, pbeta, qbeta).

See Also

identifyBetaPars, optim, dbeta

Examples

b<-getBetaFromCI(qLow=0.1167,qUpp=0.1636,initPars=c(200,800))
print(b$pars) # the fitted parameter values
b$r(10) # 10 random values from the fitted beta distribution
b$d(0.15) # the probability density at x=0.15 for the fitted beta distribution
b$p(0.15) # the cumulative density at x=0.15 for the fitted beta distribution
b$q(c(0.25,0.5,0.75)) # the 25th, 50th (median) and 75th percentiles of the fitted distribution
x<-seq(0,1,length=1e3)
y<-b$d(x)
plot(x,y,type="l",xlab="",ylab="density") # density plot for the fitted beta distribution