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Last data update: 2014.03.03

R: Massart Inequality Plot Function

distIneqMassartPlot

R Documentation

Massart Inequality Plot Function

Description

Creates a Massart inequality plot for testing the empirical distribution and distribution function based on an inequality due to Massart (1990).

Usage

distIneqMassartPlot(densFn = "norm", param = NULL,
                    nSamp = 50, n = 100, ...)

Arguments

`densFn`	Character. The root name of the distribution to be tested.
`n`	Numeric. The size of the sample to be used.
`nSamp`	Numeric. The number of samples used to approximate the LHS probability of the inequality.
`param`	Numeric. A vector giving the parameter values for the distribution specified by `densFn`. If no `param` values are specified, then the default parameter values of each distribution are used instead.
`...`	Passes the parameters of the distribution other than specified by `param`.

Details

Massart (1990) gave a version of the Dvoretsky-Kiefer-Wolfowitz inequality with the best possible constant:

P(sup_x|F_n(x)-F(x)|> t) <= 2exp(-2nt^2)

where F_n is the empirical distribution function for a sample of n independent and identically distributed random variables with distribution function F. This inequality is true for all distribution functions, for all n and t.

The red curve in the plot shows the LHS probabilities and the black curve gives the RHS bound. The red curve should lie below the black curve in order that the empirical distribution represents a sample from the theoretical distribution.

Value

Returns NULL invisibly.

Author(s)

David Scott d.scott@auckland.ac.nz, Xinxing Li xli053@aucklanduni.ac.nz

References

Massart P. (1990) The tight constant in the Dvoretsky-Kiefer-Wolfovitz inequality. Ann. Probab., 18, 1269–1283.

Examples

### The Massart Inequality plot for standard Normal Distribution
distIneqMassartPlot()

### The Massart Inequality plot for Gamma Distribution
distIneqMassartPlot("gamma", shape = 1)

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)

R is free software and comes with ABSOLUTELY NO WARRANTY.
You are welcome to redistribute it under certain conditions.
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(DistributionUtils)
Loading required package: RUnit
> png(filename="/home/ddbj/snapshot/RGM3/R_CC/result/DistributionUtils/distIneqMassartPlot.Rd_%03d_medium.png", width=480, height=480)
> ### Name: distIneqMassartPlot
> ### Title: Massart Inequality Plot Function
> ### Aliases: distIneqMassartPlot
> ### Keywords: distribution univar
> 
> ### ** Examples
> 
> ### The Massart Inequality plot for standard Normal Distribution
> distIneqMassartPlot()
> 
> ### The Massart Inequality plot for Gamma Distribution
> distIneqMassartPlot("gamma", shape = 1)
> 
> 
> 
> 
> 
> dev.off()
null device 
          1 
>