Heaviside Function


by zli034
Tags: function, heaviside
zli034
zli034 is offline
#1
Sep20-11, 10:54 AM
P: 103
Hi all:

The Heaviside function multiples a random varaible, is that a probability density function?

This is my first time knowing about Heaviside, any tutorial and application of it?
Phys.Org News Partner Science news on Phys.org
Simplicity is key to co-operative robots
Chemical vapor deposition used to grow atomic layer materials on top of each other
Earliest ancestor of land herbivores discovered
MisterX
MisterX is offline
#2
Sep20-11, 11:51 AM
P: 532
The Heaviside function multiplied by a random variable (that may only have a real value) is not a probability density function. For a probability density function P of a random variable which may only have real values,

[itex]\int _{\infty}^{\infty} P(x)dx = 1[/itex]

whereas if H(x) is the Heaviside step function, and a is a real number

[itex]\int _{\infty}^{\infty} aH(x)dx \neq 1[/itex]
chiro
chiro is offline
#3
Sep21-11, 03:52 AM
P: 4,570
Quote Quote by zli034 View Post
Hi all:

The Heaviside function multiples a random varaible, is that a probability density function?

This is my first time knowing about Heaviside, any tutorial and application of it?
You need to normalize your pdf.

This kind of thing happens in Bayesian statistics. What happens is you have a prior and a likelihood and then you create the posterior from the prior and the likelihood.

One thing you should realize though is that if you want to use the Heaviside function as some kind of prior, you will need to normalize the posterior. What will happen is that for a probability to be normalized, if you have a likelihood that is normalized and a prior that is not (this will definitely nearly always be the case), then you need to find the total area of the un-normalized pdf and divide your posterior definition by this area.

In terms of interpreting what you are doing, it is basically the equivalent of defining a uniform prior in some (possibly collections of) interval(s).

So yeah, figuring out the total area of our new pdf (find the integral over the whole real line for your new pdf), and divide your pdf by that number and you will have a proper pdf.


Register to reply

Related Discussions
Integrate product of heaviside function and function of x Calculus 3
Integral of a function multiplied by a Heaviside step function Calculus & Beyond Homework 11
Is the square of Heaviside function equal to Heaviside? General Math 11
[SOLVED] Dirac delta function and Heaviside step function Advanced Physics Homework 2
Is the square of Heaviside function equal to Heaviside? Calculus & Beyond Homework 5