Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

What is the name and application of this probability distribution

  1. Mar 1, 2012 #1
    Hi.

    In my homework I've encountered a discrete probability distribution of this form:

    [tex]f(k,\lambda)=N \frac{\lambda^k}{k!}[/tex]

    [tex]k[/tex] is the variable, and [tex]\lambda[/tex] is a parameter. I'm curious what is this distribution - what's its name and where can it be applied. I will be grateful for, for example, redirecting me to the proper wikipedia article. Thanks!
     
  2. jcsd
  3. Mar 1, 2012 #2

    micromass

    User Avatar
    Staff Emeritus
    Science Advisor
    Education Advisor
    2016 Award

  4. Mar 1, 2012 #3
    Are you sure you copied the formula correctly? The Poisson distribution is defined by:

    [itex] f(k;\lambda) = \frac{\lambda ^{k} e^{-\lambda}}{k!}[/itex]

    where [itex] \lambda [/itex] is the rate parameter (expected number of events per unit time), and k is the number of events observed.

    In evaluating Poisson noise the question becomes [itex]P(k=N_t)[/itex] but your formula still doesn't look right since it lacks the exponential term.
     
    Last edited by a moderator: Mar 2, 2012
  5. Mar 2, 2012 #4
    I think the number N here is used as a normlization factor.

     
  6. Mar 2, 2012 #5

    chiro

    User Avatar
    Science Advisor

    [EDIT]: After reading the wiki page, yes the value depends on lambda not k.

    Can't believe I've used this pdf so many times and forgotten it!
     
    Last edited: Mar 2, 2012
  7. Mar 2, 2012 #6
    Thank you all for responding. Yes, the number N stand for the normalization constant, and in the wikipedia article posted by micromass the exponent is exactly the normalization:
    [tex]e^{-\lambda},[/tex]

    so i does not vary with k.
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook




Similar Discussions: What is the name and application of this probability distribution
Loading...