Density of the Johnson distribution; adapted from the orphaned SuppDists package.
pJohnson(q, parms, lower.tail = TRUE, log.p = FALSE)JohnsonFit(t, moment = "quant")
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".
vector of quantities.
list or list of lists each containing output of JohnsonFit.
logical vector; if TRUE (default), probabilities are \(P[X <= x]\), otherwise, \(P[X > x]\).
logical vector; if TRUE, probabilities p are given as log(p).
observation vector, t=x.
character scalar specifying t: for now only "quant".
Bob Wheeler
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.
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