# zJohnsonDistribution: Johnson variable (Y) to standard normal (Z) transformation In JohnsonDistribution: Johnson Distribution

## Description

A Johnson distribution variable with specified parameters is transformed to a unit normal variable and can be used to compute percentiles.

## Usage

 `1` ```zJohnsonDistribution(s, ITYPE, GAMMA, DELTA, XLAM, XI) ```

## Arguments

 `s` value of Johnson distribution variable. May be vector `ITYPE` is 1, SL; 2 for SU, 3 for SB and 4 for Normal `GAMMA` parameter in Johnson distribution `DELTA` parameter in Johnson distribution `XLAM` parameter in Johnson distribution `XI` parameter in Johnson distribution

## Details

Our function provides an interface to the Fortran algorithm AS 100 (Hill, 1976).

## Value

Corresponding vector of standard normal variables.

## Note

The input parameters ITYPE, GAMMA, DELTA, XLAM, XI must all be scalars. An error is given if they are not.

## Author(s)

A. I. McLeod and Leanna King

## References

I. D. Hill, Algorithm AS 100. Normal-Johnson and Johnson-normal transformations, Appl. Statist.,25, No. 2, 190-192 (1976).

`yJohnsonDistribution`, `FitJohnsonDistribution`

## Examples

 ``` 1 2 3 4 5 6 7 8 9 10 11 12 13``` ```# #Example: find the percentage points for an SL distribution # with mean 1, standard deviation 1, skewness 3 # corresponding to observed values 1, 2, 3, 4, 5 ans <- FitJohnsonDistribution(1, 1, 3, -1) GAMMA <- ans["GAMMA"] DELTA <- ans["DELTA"] XLAM <- ans["XLAM"] XI <- ans["XI"] ITYPE <- 1 y <- 1:5 Z <- zJohnsonDistribution(y, ITYPE, GAMMA, DELTA, XLAM, XI) pnorm(Z) ```

### Example output

``` 0.6397473 0.8835478 0.9565551 0.9816775 0.9915000
```

JohnsonDistribution documentation built on May 29, 2017, 1:38 p.m.