limma (version 3.22.7)

fitFDist: Moment Estimation of Scaled F-Distribution

Description

Moment estimation of the parameters of a scaled F-distribution given one of the degrees of freedom. This function is called internally by eBayes and squeezeVar and is not usually called directly by a user.

Usage

fitFDist(x, df1, covariate=NULL)
fitFDistRobustly(x, df1, covariate=NULL, winsor.tail.p=c(0.05,0.1), trace=FALSE)

Arguments

x

numeric vector or array of positive values representing a sample from a scaled F-distribution.

df1

the first degrees of freedom of the F-distribution. Can be a single value, or else a vector of the same length as x.

covariate

if non-NULL, the estimated scale value will depend on this numeric covariate.

winsor.tail.p

numeric vector of length 1 or 2, giving left and right tail proportions of x to Winsorize.

trace

logical value indicating whether a trace of the iteration progress should be printed.

Value

A list containing the components

scale

scale factor for F-distribution. A vector if covariate is non-NULL, otherwise a scalar.

df2

the second degrees of freedom of the F-distribution.

Details

fitFDist implements an algorithm proposed by Smyth (2004). It estimates scale and df2 under the assumption that x is distributed as scale times an F-distributed random variable on df1 and df2 degrees of freedom. The parameters are estimated using the method of moments, specifically from the mean and variance of the x values on the log-scale.

fitFDistRobustly is similar to fitFDist except that it computes the moments of the Winsorized values of x, making it robust against left and right outliers. Larger values for winsor.tail.p produce more robustness but less efficiency. The robust method is described by Phipson (2013).

References

Smyth, G. K. (2004). Linear models and empirical Bayes methods for assessing differential expression in microarray experiments. Statistical Applications in Genetics and Molecular Biology, 3, No. 1, Article 3. http://www.statsci.org/smyth/pubs/ebayes.pdf

Phipson, B. (2013). Empirical Bayes modelling of expression profiles and their associations. PhD Thesis. University of Melbourne, Australia. http://repository.unimelb.edu.au/10187/17614

Phipson, B., and Smyth, G. K. (2013). Robust empirical Bayes estimation protetcts against hyper-variable genes and improves power to detect differential expression in RNA-seq data. Bioinformatics Division, Walter and Eliza Hall Institute of Medical Research, Australia

See Also

This function is called by squeezeVar, and hence by ebayes and eBayes.

This function calls trigammaInverse.

Examples

x <- rf(100,df1=8,df2=16)
fitFDist(x,df1=8)