Comments on: Random inequalities IX: new tech report http://www.johndcook.com/blog/2009/11/20/random-inequalities-ix/ The blog of John D. Cook Sat, 11 Feb 2012 01:10:06 -0500 http://wordpress.org/?v=2.8.4 hourly 1 By: New tech reports — The Endeavour http://www.johndcook.com/blog/2009/11/20/random-inequalities-ix/comment-page-1/#comment-105298 New tech reports — The Endeavour Mon, 26 Sep 2011 14:32:11 +0000 http://www.johndcook.com/blog/?p=3752#comment-105298 [...] are some other tech reports and blog posts on random inequalities. ? [...] [...] are some other tech reports and blog posts on random inequalities. ? [...]

]]> By: A support one-liner — The Endeavour http://www.johndcook.com/blog/2009/11/20/random-inequalities-ix/comment-page-1/#comment-71500 A support one-liner — The Endeavour Tue, 15 Mar 2011 16:11:50 +0000 http://www.johndcook.com/blog/?p=3752#comment-71500 [...] Calculator software Blog posts on random inequalities ? [...] [...] Calculator software Blog posts on random inequalities ? [...]

]]> By: Tweets that mention Random inequalities IX: new tech report — The Endeavour -- Topsy.com http://www.johndcook.com/blog/2009/11/20/random-inequalities-ix/comment-page-1/#comment-57633 Tweets that mention Random inequalities IX: new tech report — The Endeavour -- Topsy.com Tue, 28 Dec 2010 19:39:10 +0000 http://www.johndcook.com/blog/?p=3752#comment-57633 [...] This post was mentioned on Twitter by George Ghoussoubi. George Ghoussoubi said: RT @ProbFact: Computing P(X > Y) for independent random variables http://bit.ly/6E158Q [...] [...] This post was mentioned on Twitter by George Ghoussoubi. George Ghoussoubi said: RT @ProbFact: Computing P(X > Y) for independent random variables http://bit.ly/6E158Q [...]

]]> By: John http://www.johndcook.com/blog/2009/11/20/random-inequalities-ix/comment-page-1/#comment-27666 John Sat, 21 Nov 2009 15:02:54 +0000 http://www.johndcook.com/blog/?p=3752#comment-27666 If (X, Y) is bivariate normal, then P(X > Y) is just the probability above the line x = y. By rotating the coordinates, this reduces to computing P(W < 0) where (W, Z) is bivariate normal. The folded normal tech report has a reference to a paper by Alan Genz that explains how to compute such probabilities numerically. If (X, Y) is bivariate normal, then P(X > Y) is just the probability above the line x = y. By rotating the coordinates, this reduces to computing P(W < 0) where (W, Z) is bivariate normal. The folded normal tech report has a reference to a paper by Alan Genz that explains how to compute such probabilities numerically.

]]> By: Gregor Gorjanc http://www.johndcook.com/blog/2009/11/20/random-inequalities-ix/comment-page-1/#comment-27661 Gregor Gorjanc Sat, 21 Nov 2009 13:17:06 +0000 http://www.johndcook.com/blog/?p=3752#comment-27661 But <a href="http://www.bepress.com/cgi/viewcontent.cgi?article=1052&context=mdandersonbiostat" rel="nofollow">there</a> the correlation between U and V rises due to sums, U=X+Y and V=X-Y, while X and Y are assumed uncorrelated. I am talking about P(X > Y), where P(X,Y) ~ Normal(\mu, \Sigma) with "general" \mu and \Sigma. But there the correlation between U and V rises due to sums, U=X+Y and V=X-Y, while X and Y are assumed uncorrelated. I am talking about P(X > Y), where P(X,Y) ~ Normal(\mu, \Sigma) with “general” \mu and \Sigma.

]]> By: John http://www.johndcook.com/blog/2009/11/20/random-inequalities-ix/comment-page-1/#comment-27606 John Fri, 20 Nov 2009 20:32:46 +0000 http://www.johndcook.com/blog/?p=3752#comment-27606 Gregor, I talk briefly about the bivariate normal in my tech report on folded normals. For correlated normals, you can compute P(X > Y) in closed form, but you can reduce it to a well-known form. I give a link to a paper on how to solve the numerical problem. Gregor, I talk briefly about the bivariate normal in my tech report on folded normals. For correlated normals, you can compute P(X > Y) in closed form, but you can reduce it to a well-known form. I give a link to a paper on how to solve the numerical problem.

]]> By: Gregor Gorjanc http://www.johndcook.com/blog/2009/11/20/random-inequalities-ix/comment-page-1/#comment-27595 Gregor Gorjanc Fri, 20 Nov 2009 17:19:37 +0000 http://www.johndcook.com/blog/?p=3752#comment-27595 Have you looked for bivariate normal distribution of X and Y? That would be a usefull result! Have you looked for bivariate normal distribution of X and Y? That would be a usefull result!

]]> By: John http://www.johndcook.com/blog/2009/11/20/random-inequalities-ix/comment-page-1/#comment-27578 John Fri, 20 Nov 2009 15:04:18 +0000 http://www.johndcook.com/blog/?p=3752#comment-27578 Thanks. For custom distributions, you can always simulate. But numerical integration may be much faster. I give some general techniques for numerically evaluating random inequalities in the first section of <a href="http://www.bepress.com/mdandersonbiostat/paper46/" rel="nofollow">this report</a>. Thanks. For custom distributions, you can always simulate. But numerical integration may be much faster. I give some general techniques for numerically evaluating random inequalities in the first section of this report.

]]> By: Daniel Lemire http://www.johndcook.com/blog/2009/11/20/random-inequalities-ix/comment-page-1/#comment-27577 Daniel Lemire Fri, 20 Nov 2009 15:00:18 +0000 http://www.johndcook.com/blog/?p=3752#comment-27577 Cool. I'll know where to look if I need such inequalities! (Alas, in my research, I always end up with unknown or custom distributions.) Cool. I’ll know where to look if I need such inequalities!

(Alas, in my research, I always end up with unknown or custom distributions.)

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