# distIneqMassartPlot: Massart Inequality Plot Function In DistributionUtils: Distribution Utilities

## Description

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

## Usage

 ```1 2``` ```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 [email protected], Xinxing Li [email protected]

## References

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

## Examples

 ```1 2 3 4 5 6 7 8 9``` ```## Not run: ### Not run because of timing requirements of CRAN ### The Massart Inequality plot for standard Normal Distribution distIneqMassartPlot() ### The Massart Inequality plot for Gamma Distribution distIneqMassartPlot("gamma", shape = 1) ## End(Not run) ```

DistributionUtils documentation built on May 2, 2019, 4:46 p.m.