Results 1 to 4 of 4

Math Help - Cumulative distribution function help!

  1. #1
    Newbie
    Joined
    Mar 2009
    Posts
    22

    Cumulative distribution function help!

    Hey, I'm new here. I'm stuck with this problem. Will post what I've tried to do. Hopefully someone can provide hints to help me out. Thanks.

    If Z is a standard normal random variable, and Y = -ln (1-cdf(Z)), what is the distribution of the random variable Y. (note: cdf is cumulative distribution function)

    Here's what I've done:
    cdf(y) = P ( Y < y) = P (-ln(1-cdf(Z))<y) = ... = P ( cdf (Z) < 1 - e^-y ) -> stuck..

    my approach is to find cdf of y and then differentiate it to get pdf of y, which is what's required.
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Grand Panjandrum
    Joined
    Nov 2005
    From
    someplace
    Posts
    14,972
    Thanks
    4
    Quote Originally Posted by knighty View Post
    Hey, I'm new here. I'm stuck with this problem. Will post what I've tried to do. Hopefully someone can provide hints to help me out. Thanks.

    If Z is a standard normal random variable, and Y = -ln (1-cdf(Z)), what is the distribution of the random variable Y. (note: cdf is cumulative distribution function)

    Here's what I've done:
    cdf(y) = P ( Y < y) = P (-ln(1-cdf(Z))<y) = ... = P ( cdf (Z) < 1 - e^-y ) -> stuck..

    my approach is to find cdf of y and then differentiate it to get pdf of y, which is what's required.
    If you don't know this prove it, otherwise just use it:

    \text{cdf}(Z) \sim U(0,1)

    so:

    1-\text{cdf}(Z) \sim U(0,1)

    CB
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Newbie
    Joined
    Mar 2009
    Posts
    22
    Quote Originally Posted by CaptainBlack View Post
    If you don't know this prove it, otherwise just use it:

    \text{cdf}(Z) \sim U(0,1)

    so:

    1-\text{cdf}(Z) \sim U(0,1)

    CB
    why is the cdf of Z a uniform distribution?
    Follow Math Help Forum on Facebook and Google+

  4. #4
    Grand Panjandrum
    Joined
    Nov 2005
    From
    someplace
    Posts
    14,972
    Thanks
    4
    Quote Originally Posted by knighty View Post
    why is the cdf of Z a uniform distribution?
    let f(Z)=cdf(Z) then as f is strictly increasing it is invertable and so:

     <br />
p(cdf(Z)<a)=p(f(Z)<a)=p(Z<f^{-1}(a))<br />

    but p(Z<f^{-1}(a))=f(f^{-1}(a))=a

    So if X=cdf(Z) then p(X<a)=a which is the cdf of the uniform distribution U(0,1).

    CB
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Cumulative distribution function
    Posted in the Advanced Statistics Forum
    Replies: 4
    Last Post: April 17th 2011, 02:20 AM
  2. cumulative distribution function
    Posted in the Statistics Forum
    Replies: 12
    Last Post: October 11th 2010, 03:23 PM
  3. cumulative distribution function using a gamma distribution
    Posted in the Advanced Statistics Forum
    Replies: 0
    Last Post: September 11th 2010, 10:05 AM
  4. Cumulative distribution function
    Posted in the Statistics Forum
    Replies: 2
    Last Post: May 19th 2009, 01:42 AM
  5. Cumulative distribution function of binomial distribution
    Posted in the Advanced Statistics Forum
    Replies: 2
    Last Post: October 31st 2008, 03:34 PM

Search Tags


/mathhelpforum @mathhelpforum