SuppDists (version 1.1-9.8)

maxFratio: The maximum F-ratio distribution

Description

Density, distribution function, quantile function, random generator and summary function for the maximum F-ratio.

Usage

dmaxFratio(x, df, k, log=FALSE)
pmaxFratio(q, df, k, lower.tail=TRUE, log.p=FALSE)
qmaxFratio(p, df, k, lower.tail=TRUE, log.p=FALSE)
rmaxFratio(n, df, k)
smaxFratio(df, k)

Value

The output values conform to the output from other such functions in R. dmaxFratio() gives the density, pmaxFratio() the distribution function and qmaxFratio its inverse. rmaxFratio() generates random numbers. smaxFratio() produces a list containing parameters corresponding to the arguments -- mean, median, mode, variance, sd, third cental moment, fourth central moment, Pearson's skewness, skewness, and kurtosis.

Arguments

x,q

vector of non-negative quantities

p

vector of probabilities

n

number of values to generate. If n is a vector, length(n) values will be generated

df

vector non-negative, integer degrees of freedom

k

vector non-negative, integer number of mean squares

log, log.p

logical vector; if TRUE, probabilities p are given as log(p)

lower.tail

logical vector; if TRUE (default), probabilities are \(P[X <= x]\), otherwise, \(P[X > x]\)

Limitations

The literature contains no information on numerical procedures for this distribution, with the result that all calculations are slow.

Finding p from x should give results for almost any values of df and k -- of course absolutely enormous values will take a while.

Finding x from p is an iterative calculation dependent on a good starting guess. Such good guesses have been made for \(df \le 24\) and \(k \le 160\). NA will be returned if larger values are attempted.

Author

Bob Wheeler

Details

The maximum F-ratio is the ratio of the largest to the smallest of k independent mean squares, all with the same df. The usual use is to test for homogeneity of normal variances.

References

Hartley, H.O. (1950) The maximum F-ratio as a short cut test for heterogeneity of variance. Biometrika. 37. 308-312.

David, H.A. (1952). Upper 5 and 1% points of the maximum F-ratio. Biometrika. 38. 422-424.

Nelson, L.S. (1987). Upper 10%, 5% and 1% points of the maximum F-ratio, Jour. Qual. Tech. 19-3. 165-167.

Examples

pmaxFratio(4, 10, 10)
pmaxFratio(c(2.3, 4, 8.5), 10, 10)	## approximately 5% 50% and 95% 
qmaxFratio(p=.95,df=c(10,20), k=10)
smaxFratio(10, 10) ## Wait for this, it may take a while
plot(function(x)dmaxFratio(x, 10, 10),1,10)