Results 1 to 5 of 5

Math Help - comparing two covariances of concave functions

  1. #1
    Newbie
    Joined
    Jul 2010
    Posts
    6

    comparing two covariances of concave functions

    Hello,

    I have two increasing concave functions f and g where f is more concave than g.
    Let x be a random variable.
    Does f more concave than g imply that Cov(x,f(x))>=Cov(x,g(x))?
    I would say yes, but I am not sure...

    Many thanks for your help!
    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 jazz123 View Post
    Hello,

    I have two increasing concave functions f and g where f is more concave than g.
    Let x be a random variable.
    Does f more concave than g imply that Cov(x,f(x))>=Cov(x,g(x))?
    I would say yes, but I am not sure...

    Many thanks for your help!
    Depends what you mean by more concave?

    Simplest example would be a couple of quadratics and X ~U(0,1), or consider what happens when the two functions are very close to being linear.

    CB
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Newbie
    Joined
    Jul 2010
    Posts
    6
    Thanks a lot so far. You are right, I was not very precise. f more concave than g means that f''(x)<g''(x)<0 for every x. (I assume that f and g are two times continuously differentiable on their domain). Moreover, f(x) equals -g'(x). Do you mean with your example of a linear function that we care more about the slope of the functions that is if f'(x)>g'(x) or in other words if -g''(x)>g'(x)?
    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 jazz123 View Post
    Thanks a lot so far. You are right, I was not very precise. f more concave than g means that f''(x)<g''(x)<0 for every x. (I assume that f and g are two times continuously differentiable on their domain). Moreover, f(x) equals -g'(x). Do you mean with your example of a linear function that we care more about the slope of the functions that is if f'(x)>g'(x) or in other words if -g''(x)>g'(x)?
    Your introduction of the extra condition that f(x)=g'(x) changes the question completely. In its original form your suggestion was false.

    Please try posting the exact question.

    CB
    Follow Math Help Forum on Facebook and Google+

  5. #5
    Newbie
    Joined
    Jul 2010
    Posts
    6
    I have two increasing concave functions f and g.
    properties:
    g is three times continously differentiable.
    f(x)=-g'(x)
    -g'''(x)< g''(x)< 0 ----> f''(x)<g''(x)
    -g''(x)>g'(x)> 0 ----> f'(x)>g'(x)
    x is a random variable.

    Is the following statement true (for any distribution of x):
    Cov(x,f(x))>=Cov(x,g(x)) ?
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Comparing growth of functions
    Posted in the Discrete Math Forum
    Replies: 3
    Last Post: October 14th 2010, 03:25 AM
  2. Replies: 1
    Last Post: August 24th 2010, 07:06 AM
  3. Concave functions...Help please!
    Posted in the Calculus Forum
    Replies: 0
    Last Post: October 18th 2009, 01:35 PM
  4. comparing graphs of functions
    Posted in the Pre-Calculus Forum
    Replies: 14
    Last Post: September 22nd 2009, 09:36 PM
  5. [SOLVED] comparing polar functions and graphs
    Posted in the Calculus Forum
    Replies: 1
    Last Post: June 14th 2009, 03:31 PM

Search Tags


/mathhelpforum @mathhelpforum