# Macdonald: Compute the Macdonald density function for a specified... In hwwntest: Tests of White Noise using Wavelets

## Description

Compute the Macdonald density function for a specified parameter value `m` at a vector of `x` values.

## Usage

 `1` ```Macdonald(x, m) ```

## Arguments

 `x` The `x` ordinates that you want to evaluate the density at. A vector of real numbers. `m` The parameter of the Macdonald's density

## Details

This function computes the Macdonald probability density function for parameter `m` and values at which to evaluate the density supplied in `x`. The mean and variance of this density is zero and one respectively.

The density

## Author(s)

Delyan Savchev and Guy Nason

## References

Nason, G.P. and Savchev, D. (2014) White noise testing using wavelets. Stat, 3, 351-362. http://dx.doi.org/10.1002/sta4.69

## See Also

`compute.rejection`, `hwwn.test`

## Examples

 ``` 1 2 3 4 5 6 7 8 9 10``` ```# # Work out density at x=0, 0.5 and 1 for the m=1 Macdonald density # Macdonald(x=c(0,0.5,1), m=2) # 0.3535534 0.2975933 0.2075131 # # Check that the density integrates to one, e.g. for m=3 # integrate(Macdonald, lower=-20, upper=20, m=3) #1 with absolute error < 4.7e-07 ```

hwwntest documentation built on May 2, 2019, 6:39 a.m.