Compute the Macdonald density function for a specified parameter value m at a vector of x values.
Compute the Macdonald density function for a specified parameter value m at a vector of x values.
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.
Returns
The density
References
Nason, G.P. and Savchev, D. (2014) White noise testing using wavelets. Stat, 3 , 351-362. tools:::Rd_expr_doi("10.1002/sta4.69")
Author(s)
Delyan Savchev and Guy Nason
See Also
compute.rejection, hwwn.test
Examples
## 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)#[1] 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