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From |
"FEIVESON, ALAN H. (AL) (JSC-SD) (NASA)" <alan.h.feiveson@nasa.gov> |

To |
"'statalist@hsphsun2.harvard.edu'" <statalist@hsphsun2.harvard.edu> |

Subject |
st: RE: integrals - correction! |

Date |
Fri, 22 Nov 2002 12:57:38 -0600 |

Dear Statalist: Sorry - Please disregard my last message on this - I took the integration on y to be over -oo to +oo. However, for fixed x, the partial integral over y for fixed x is just the probability that Y< 0.56 |X=x, where X and Y are the random variables whose joint distribution is f(x,y). Since the conditional distribution of Y|X is also a normal with adjusted mean and variance (e.g. see T.W. Anderson -An Introduction to Multivariuate Statistical Analysis - Wiley), you can express P(Y < 0.56) in terms of the cumulative normal function PHI ("norm" in Stata). Thus after integration by y, you are left with something like x*PHI( (x-a)/b) to integrate with respect to x. You could do this numerically, but you might be able to get this integral in closed form also, by integrating by parts twice. First differentiate the PHI and integrate x, leaving an integral of the form x*x*f( (x-a)/b) ) where f(x) is the normal density. Then differentiate x and integrate x*f( (x-a)/b) ) . The latter is a perfect differential. Al Feiveson -----Original Message----- From: Clara [mailto:bldvegac@xa.bs.ehu.es] Sent: Friday, November 22, 2002 10:26 AM To: statalist@hsphsun2.harvard.edu Subject: st: integrals hi, I need to solve a double integral. This integral does not have an analytic solution, then i need to do this numerically. There are someone that know how can i do this in stata?? I need to integral: x*f(x,y)dxdy where f(x,y) is a bivariate normal density function. the integration intervals are: [-infinity, 0.56] thanks, clara * * For searches and help try: * http://www.stata.com/support/faqs/res/findit.html * http://www.stata.com/support/statalist/faq * http://www.ats.ucla.edu/stat/stata/ * * For searches and help try: * http://www.stata.com/support/faqs/res/findit.html * http://www.stata.com/support/statalist/faq * http://www.ats.ucla.edu/stat/stata/

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