Re: Maximum of two correlated random variables
- From: hrubin@xxxxxxxxxxxxxxxxxxxx (Herman Rubin)
- Date: 23 Oct 2005 20:24:49 -0500
In article <15792750.1130111300730.JavaMail.jakarta@xxxxxxxxxxxxxxxxxxxxxx>,
Niraj Patel <niraj_wisconsin@xxxxxxxxx> wrote:
>I have the following problem:
>Let X and KY be two correlated random variables with correlation coefficient 'r'. Also given are first 3 raw moments m1_x, m2_x and m3_x of X and m1_y, m2_y and m3_y of Y. Is there any way one can compute the first 3 raw moments of random variable Z defined as:
>Z=max(X,Y)
>I know these can be computed if X and Y are gaussian using the analytical expressions given in
It cannot be done with this information, even or independent
random variables. The range of distributions with many more
moments is huge; the first 20 moments of the standard normal
distribution does not get P(X < 0) beteween 1/3 and 2/3.
In addition, there is no canonical meaning as to what correlated
random variables with given marginals are. In the normal case,
the assumption is that they are joint normal, which is far
stronger than that they are correlated and normal.
--
This address is for information only. I do not claim that these views
are those of the Statistics Department or of Purdue University.
Herman Rubin, Department of Statistics, Purdue University
hrubin@xxxxxxxxxxxxxxx Phone: (765)494-6054 FAX: (765)494-0558
.
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