getNormFromCI {bootComb} R Documentation

## Find the best-fit normal / Gaussian distribution for a given confidence interval.

### Description

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

### Usage

```getNormFromCI(qLow, qUpp, alpha = 0.05, initPars = c(0, 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 (mean & sd) to start the optimisation; defaults to c(0,1). `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 mean and standard deviation for the best-fit normal distribution (`mean` and `sd` as in `rnorm`, `dnorm`, `pnorm`, `qnorm`).

### See Also

`identifyNormPars`, `optim`, `dnorm`

### Examples

```n<-getNormFromCI(qLow=1.08,qUpp=8.92)
print(n\$pars) # the fitted parameter values (mean & sd)
n\$r(10) # 10 random values from the fitted normal distribution
n\$d(6) # the probability density at x=6 for the normal distribution
n\$p(4.25) # the cumulative density at x=4.25 for the fitted normal distribution
n\$q(c(0.25,0.5,0.75)) # the 25th, 50th (median) and 75th percentiles of the fitted distribution
x<-seq(0,10,length=1e3)
y<-n\$d(x)
plot(x,y,type="l",xlab="",ylab="density") # density plot for the fitted normal distribution

```

[Package bootComb version 1.0.1 Index]