# rdist90ci_exact: 90%-confidence interval based univariate random number... In decisionSupport: Quantitative Support of Decision Making under Uncertainty

## Description

This function generates random numbers for a set of univariate parametric distributions from given 90% confidence interval. Internally, this is achieved by exact, i.e. analytic, calculation of the parameters for the individual distribution from the given 90% confidence interval.

## Usage

 `1` ```rdist90ci_exact(distribution, n, lower, upper) ```

## Arguments

 `distribution` `character`; A character string that defines the univariate distribution to be randomly sampled. For possible options cf. section Details. `n` Number of generated observations. `lower` `numeric`; lower bound of the 90% confidence interval. `upper` `numeric`; upper bound of the 90% confidence interval.

## Details

The following table shows the available distributions and their identification (option: `distribution`) as a character string:

 `distribution` Distribution Name Requirements `"const"` Deterministic case `lower == upper` `"norm"` Normal `lower < upper` `"lnorm"` Log Normal `0 < lower < upper` `"unif"` Uniform `lower < upper`

#### Parameter formulae

We use the notation: l`=lower` and u=`upper`; Φ is the cumulative distribution function of the standard normal distribution and Φ^(-1) its inverse, which is the quantile function of the standard normal distribution.

`distribution="norm":`

The formulae for μ and σ, viz. the mean and standard deviation, respectively, of the normal distribution are μ=(l+u)/2 and σ=(μ - l)/Φ^(-1)(0.95).

`distribution="unif":`

For the minimum a and maximum b of the uniform distribution U([a,b]) it holds that a = l - 0.05 (u - l) and b = u + 0.05 (u - l).

`distribution="lnorm":`

The density of the log normal distribution is f(x)=1/((2 π)^(1/2)σ x) exp(-1/2(((ln(x)-μ)/σ)^2)) for x > 0 and f(x) = 0 otherwise. Its parameters are determined by the confidence interval via μ = (ln(l)+ln(u))/2 and σ = (μ-ln(l))/Φ^(-1)(0.95) . Note the correspondence to the formula for the normal distribution.

## Value

A numeric vector of length `n` with the sampled values according to the chosen distribution.

In case of `distribution="const"`, viz. the deterministic case, the function returns: `rep(lower, n).`

## Examples

 ``` 1 2 3 4 5 6 7 8 9 10 11``` ```# Generate uniformly distributed random numbers: lower=3 upper=6 hist(r<-rdist90ci_exact(distribution="unif", n=10000, lower=lower, upper=upper),breaks=100) print(quantile(x=r, probs=c(0.05,0.95))) print(summary(r)) # Generate log normal distributed random numbers: hist(r<-rdist90ci_exact(distribution="lnorm", n=10000, lower=lower, upper=upper),breaks=100) print(quantile(x=r, probs=c(0.05,0.95))) print(summary(r)) ```

decisionSupport documentation built on Nov. 28, 2017, 1:04 a.m.