Skew-t Distribution

Description

Density function, distribution function and random number generation for the skew-t (ST) distribution. Functions copied from sn CRAN library v0.4.18 for argument name compatibility with st.mle function from the same version.

Usage

dst(x, location = 0, scale = 1, shape = 0, df = Inf, dp = NULL, log = FALSE)
pst(x, location = 0, scale = 1, shape = 0, df = Inf, dp = NULL, ...)
qst(p, location = 0, scale = 1, shape = 0, df = Inf, tol = 1e-06, dp = NULL, ...)
rst(n = 1, location = 0, scale = 1, shape = 0, df = Inf, dp = NULL)

Arguments

Value

Density (dst), probability (pst), quantiles (qst) and random sample (rst) from the skew-t distribution with given location, scale, shape and df parameters.

Details

Typical usages are

dst(x, location=0, scale=1, shape=0, df=Inf, log=FALSE)
dst(x, dp=, log=FALSE)
pst(x, location=0, scale=1, shape=0, df=Inf, ...)
pst(x, dp=, log=FALSE)
qst(p, location=0, scale=1, shape=0, df=Inf, tol=1e-8, ...)
qst(x, dp=, log=FALSE)
rst(n=1, location=0, scale=1, shape=0, df=Inf)
rst(x, dp=, log=FALSE)

Background

The family of skew-t distributions is an extension of the Student's t family, via the introduction of a shape parameter which regulates skewness; when shape=0, the skew-t distribution reduces to the usual Student's t distribution. When df=Inf, it reduces to the skew-normal distribution. A multivariate version of the distribution exists. See the reference below for additional information.

References

Azzalini, A. and Capitanio, A. (2003). Distributions generated by perturbation of symmetry with emphasis on a multivariate skew-t distribution. J.Roy. Statist. Soc. B 65, 367–389.

See Also

st.mle

Examples

pdf <- dst(seq(-4,4,by=0.1), shape=3, df=5)
rnd <- rst(100, 5, 2, -5, 8)
q <- qst(c(0.25,0.5,0.75), shape=3, df=5)
stopifnot(identical(all.equal(pst(q, shape=3, df=5), c(0.25,0.5,0.75)), TRUE))

Results

R version 3.3.1 (2016-06-21) -- "Bug in Your Hair"
Copyright (C) 2016 The R Foundation for Statistical Computing
Platform: x86_64-pc-linux-gnu (64-bit)

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Type 'license()' or 'licence()' for distribution details.

R is a collaborative project with many contributors.
Type 'contributors()' for more information and
'citation()' on how to cite R or R packages in publications.

Type 'demo()' for some demos, 'help()' for on-line help, or
'help.start()' for an HTML browser interface to help.
Type 'q()' to quit R.

> library(doppelgangR)
Loading required package: Biobase
Loading required package: BiocGenerics
Loading required package: parallel

Attaching package: 'BiocGenerics'

The following objects are masked from 'package:parallel':

    clusterApply, clusterApplyLB, clusterCall, clusterEvalQ,
    clusterExport, clusterMap, parApply, parCapply, parLapply,
    parLapplyLB, parRapply, parSapply, parSapplyLB

The following objects are masked from 'package:stats':

    IQR, mad, xtabs

The following objects are masked from 'package:base':

    Filter, Find, Map, Position, Reduce, anyDuplicated, append,
    as.data.frame, cbind, colnames, do.call, duplicated, eval, evalq,
    get, grep, grepl, intersect, is.unsorted, lapply, lengths, mapply,
    match, mget, order, paste, pmax, pmax.int, pmin, pmin.int, rank,
    rbind, rownames, sapply, setdiff, sort, table, tapply, union,
    unique, unsplit

Welcome to Bioconductor

    Vignettes contain introductory material; view with
    'browseVignettes()'. To cite Bioconductor, see
    'citation("Biobase")', and for packages 'citation("pkgname")'.

Loading required package: BiocParallel
> png(filename="/home/ddbj/snapshot/RGM3/R_BC/result/doppelgangR/dst.Rd_%03d_medium.png", width=480, height=480)
> ### Name: dst
> ### Title: Skew-t Distribution
> ### Aliases: dst pst qst rst
> ### Keywords: distribution
> 
> ### ** Examples
> 
> pdf <- dst(seq(-4,4,by=0.1), shape=3, df=5)
> rnd <- rst(100, 5, 2, -5, 8)
> q <- qst(c(0.25,0.5,0.75), shape=3, df=5)
> stopifnot(identical(all.equal(pst(q, shape=3, df=5), c(0.25,0.5,0.75)), TRUE))
> 
> 
> 
> 
> 
> dev.off()
null device 
          1 
>