Haviside and Related Functions

Description

Functions which compute the Heaviside and related functions. These include the sign function, the delta function, the boxcar function, and the ramp function.

The functions are:

Usage

Heaviside(x, a = 0)
Sign(x, a = 0)
Delta(x, a = 0)
Boxcar(x, a = 0.5)
Ramp(x, a = 0)

Arguments

Details

The Heaviside step function Heaviside is 1 for x>a, 1/2 for x=a, and 0 for x<a.

The Sign function Sign is 1 for x>a, 0 for x=a, and -1 for x<a.

The delta function Delta is defined as: Delta(x) = d/dx H(x-a).

The boxcar function Boxcar is defined as: Boxcar(x) = H(x+a) - H(x-a).

The ramp function is defined as: Ramp(x)= (x-a)*H(x-a).

Value

returns the function values of the selected function.

Note

The Heaviside function is used in the implementation of the skew Normal, Student-t, and Generalized Error distributions, distributions functions which play an important role in modelling GARCH processes.

References

Weisstein W. (2004); http://mathworld.wolfram.com/HeavisideStepFunction.html, Mathworld.

See Also

GarchDistribution, GarchDistributionFits.

Examples

## Heaviside -
   x = sort(round(c(-1, -0.5, 0, 0.5, 1, 5*rnorm(5)), 2))
   h = Heaviside(x)
    
## Sign -
   s = Sign(x)
   
## Delta -
   d = Delta(x)
   
## Boxcar -
   Pi = Boxcar(x)

## Ramp - 
   r = Ramp(x)
   cbind(x = x, Step = h, Signum = s, Delta = d, Pi = Pi, R = r)