fBasics (version 290.75)

Heaviside: 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: ll{ Heaviside Computes Heaviside unit step function, Sign Just another signum function, Delta Computes delta function, Boxcar Computes boxcar function, Ramp Computes ramp function. }

Usage

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

Arguments

a

a numeric value, the location of the break.

x

a numeric vector.

Value

• returns the function values of the selected function.

Details

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

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)