fBasics (version 4021.92)

Heaviside: Heaviside 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:

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)

Value

returns the function values of the selected function.

Arguments

a

a numeric value, the location of the break.

x

a numeric vector.

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).

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)