JohnsonDistribution (version 0.24)

zJohnsonDistribution: Johnson variable (Y) to standard normal (Z) transformation

Description

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

Usage

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

Value

Corresponding vector of standard normal variables.

Details

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

References

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

See Also

yJohnsonDistribution, FitJohnsonDistribution

Examples

#
#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)