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

```[1] 0.6397473 0.8835478 0.9565551 0.9816775 0.9915000
```

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