getBetaFromCI {bootComb} R Documentation

## 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

```

[Package bootComb version 1.0.1 Index]