getGammaFromCI {bootComb} R Documentation

## Find the best-fit gamma distribution for a given confidence interval.

### Description

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

### Usage

```getGammaFromCI(qLow, qUpp, alpha = 0.05, initPars = c(1, 1), 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 (shape & rate) to start the optimisation; defaults to c(1,1). `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 shape and rate for the best-fit gamma distribution (`shape` and `rate` as in `rgamma`, `dgamma`, `pgamma`, `qgamma`).

### See Also

`identifyGammaPars`, `optim`, `dgamma`

### Examples

```n<-getGammaFromCI(qLow=0.82,qUpp=5.14)
print(n\$pars) # the fitted parameter values (shape & rate)
n\$r(10) # 10 random values from the fitted gamma distribution
n\$d(6) # the probability density at x=6 for the gamma distribution
n\$p(2) # the cumulative density at x=2 for the fitted gamma distribution
n\$q(c(0.25,0.5,0.75)) # the 25th, 50th (median) and 75th percentiles of the fitted distribution
x<-seq(0,8,length=1e3)
y<-n\$d(x)
plot(x,y,type="l",xlab="",ylab="density") # density plot for the fitted gamma distribution

```

[Package bootComb version 1.0.1 Index]