fBasics (version 3011.87)

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:

Heaviside

Computes Heaviside unit step function,

Sign

Just another signum function,

Delta

Computes delta function,

Boxcar

Computes boxcar 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)