Results 1 to 4 of 4

Math Help - correlations about half normal distributions

  1. #1
    Newbie
    Joined
    Jan 2013
    From
    Pittsburgh
    Posts
    2

    correlations about half normal distributions

    Hi all:

    I want to bound the following quantity:

    f(n)=\mathbf{E}_{h_1,\ldots,h_n,y_1,\ldots,y_n}[sign(\sum_{i}h_iy_i) \prod_{i}y_i]

    where h_1,\ldots,h_n are independent half normal random variables, and y_1,\ldots,y_n are uniformly random {-1,1}.


    For n even, f(n) is 0.

    By some experiment simulation we can show that for n =4k+1, f(n)>0 ; and for n = 4k+3, f(n)<0.

    My questions is can we give lower bounds for the absolute value of the quantity? i.e, can we show that |f(n)|> something inverse exponential of n?

    Or even easier, can we show that for n odd, f(n) is not 0?

    Thanks
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor
    Joined
    Sep 2012
    From
    Australia
    Posts
    4,173
    Thanks
    765

    Re: correlations about half normal distributions

    Hey GerrardWu.

    Have you tried using some kind of analysis theorem on the integral of the y_i's?

    Something like this:

    Absolute convergence - Wikipedia, the free encyclopedia

    But instead you consider a sum of logarithms and then the exponential of that sum.
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Newbie
    Joined
    Jan 2013
    From
    Pittsburgh
    Posts
    2

    Re: correlations about half normal distributions

    Hi chiro:

    Thank you very much for you quick reply, I don't quite understand what you mean by the integral of the y_i's, as here y_i are discrete random variable, which is 1 or -1 with equal probability.

    Quote Originally Posted by chiro View Post
    Hey GerrardWu.

    Have you tried using some kind of analysis theorem on the integral of the y_i's?

    Something like this:

    Absolute convergence - Wikipedia, the free encyclopedia

    But instead you consider a sum of logarithms and then the exponential of that sum.
    Follow Math Help Forum on Facebook and Google+

  4. #4
    MHF Contributor
    Joined
    Sep 2012
    From
    Australia
    Posts
    4,173
    Thanks
    765

    Re: correlations about half normal distributions

    Sorry I confused the y_i's with the h_i's.

    Basically you can look at the expectation term of the products by consider the nth integral of 1/2^n dV where dV is over n integrals.

    I'm ignoring the sign term since you want to look at the magnitude.

    Have you tried looking at E[Multiply all Y_I]?
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. normal distributions
    Posted in the Statistics Forum
    Replies: 6
    Last Post: July 19th 2011, 05:50 AM
  2. Normal Distributions
    Posted in the Algebra Forum
    Replies: 1
    Last Post: May 27th 2011, 01:35 PM
  3. Normal distributions
    Posted in the Advanced Statistics Forum
    Replies: 1
    Last Post: March 24th 2009, 02:39 PM
  4. Sum of normal distributions
    Posted in the Advanced Statistics Forum
    Replies: 7
    Last Post: April 10th 2008, 11:54 AM
  5. Normal distributions
    Posted in the Advanced Statistics Forum
    Replies: 0
    Last Post: March 31st 2007, 08:42 PM

Search Tags


/mathhelpforum @mathhelpforum