pJohnson: The Johnson distributions
In Haplin: Analyzing Case-Parent Triad and/or Case-Control Data with SNP Haplotypes

pJohnson

R Documentation

The Johnson distributions

Description

Density of the Johnson distribution; adapted from the orphaned SuppDists package.

Usage

pJohnson(q, parms, lower.tail = TRUE, log.p = FALSE)

JohnsonFit(t, moment = "quant")

Arguments

`q`	vector of quantities.
`parms`	list or list of lists each containing output of `JohnsonFit`.
`lower.tail`	logical vector; if TRUE (default), probabilities are `P[X <= x]`, otherwise, `P[X > x]`.
`log.p`	logical vector; if TRUE, probabilities p are given as log(p).
`t`	observation vector, t=x.
`moment`	character scalar specifying t: for now only "quant".

Details

The Johnson system (Johnson 1949) is a very flexible system for describing statistical distributions. It is defined by

z=\gamma+\delta \log{f(u)}, u=(x-\xi)/\lambda

and where f( ) has four possible forms:

SL:	`f(u)=u` the log normal
SU:	`f(u)=u+\sqrt{1+u^2}` an unbounded distribution
SB:	`f(u)=u/(1-u)` a bounded distribution
SN:	`\exp(u)` the normal

Estimation of the Johnson parameters may be done from quantiles. The procedure of Wheeler (1980) is used. They may also be estimated from the moments. Applied Statistics algorithm 99, due to Hill, Hill, and Holder (1976) has been translated into C for this implementation.

Value

pJohnson() gives the distribution function. JohnsonFit() outputs a list containing the Johnson parameters (gamma, delta, xi, lambda, type), where type is one of the Johnson types: "SN", "SL", "SB", or "SU". JohnsonFit() does this using 5 order statistics when moment="quant".

Author(s)

Bob Wheeler

References

Hill, I.D., Hill, R., and Holder, R.L. (1976). Fitting Johnson curves by moments. Applied Statistics. AS99; Johnson, N.L. (1949). Systems of frequency curves generated by methods of translation. Biometrika, 36. 149-176; Wheeler, R.E. (1980). Quantile estimators of Johnson curve parameters. Biometrika. 67-3 725-728