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From |
Jeph Herrin <junk@spandrel.net> |

To |
statalist@hsphsun2.harvard.edu |

Subject |
Re: st: how to find the integral for a portion of a normal distribution. |

Date |
Tue, 04 May 2010 14:49:59 -0400 |

So you want to integrate xf(x), so to speak; let's try to integrate using centiliters (cls): drawnorm x , means(2.02) sds(1.75) n(100000) clear gen cl=round(x,0.01) // integrate over centiliters bys cl: gen cls=_N*cl/100000 // expected cls in this cl egen liters=sum(cls*(x<=1)/100) // total liters over x < = 1 liter // the 100 is cl->l factor replace liters=liters*10 // 10 cows! sum liters hth, Jeph Buzz Burhans wrote:

Let me try again, I am sorry I am so dense here. Suppose I have an intervention applied to cows with a demonstrated mean milk yield response of +2.05 liters, sd 1.74. Suppose I am interested a 1 liter cut point. I know how to find the proportion of responses at or below the 1 liter response; and the proportion of responses at or above the one liter response. This is what you are doing here, or it can be done with a z score. My question is, if the response is normally distributed, given n cows, how many total liters were included or accumulated in the only responses below 1 liter, and how many total liters were accumulated in only the responses at or above 1 liter. (Negative responses are possible). My interest is in the total liters, not the fraction of the total population either above or below the cutpoint. This is not the same as the proportion of responders in either category; it is the total accumulated response above and below my cut point. I am off to a meeting, so thanks for any further responses - I won't be able to see them until this evening. BuzzBuzz Burhans, Ph.D.Dairy-Tech Group So. Albany, VT / Twin Falls ID Phone: 802-755-6842 Cell: 208-320-0829 Fax VT: 802-755-6842 Fax ID: 208-735-1289 Email: buzzb3@earthlink.net -----Original Message----- From: owner-statalist@hsphsun2.harvard.edu [mailto:owner-statalist@hsphsun2.harvard.edu] On Behalf Of Jeph Herrin Sent: Tuesday, May 04, 2010 10:15 AM To: statalist@hsphsun2.harvard.edu Subject: Re: st: how to find the integral for a portion of a normal distribution. The total area under any normal curve is always 1, so you just need to count obs: drawnorm x , means(2.02) sds(1.75) n(100000) clear gen byte lessthan1=x<=1 sum lessthan1 The mean value of -lessthan1- is the area under the curve to the left of 1. hth, Jeph Buzz Burhans wrote:My weak math skills are showing up here -For demonstration purposes, I have generated a set of 100,000 observations with a normal distribution, mean 2.02, SD 1.74 and visualized this dataandthe portion of observations above 1 with a histogram drawnorm x , means(2.02) sds(1.75) n(100,000) clear hist, xline(1) I also computed the proportion of the observations <=1 from the Z score. What I don't know how to do in Stata is find the integral for theproportions of the distribution above and below 1.How can I determine those two integrals in Stata? ThanksBuzz Burhans, Ph.D.Dairy-Tech Group So. Albany, VT / Twin Falls ID Phone: 802-755-6842 Cell: 208-320-0829 Fax VT: 802-755-6842 Fax ID: 208-735-1289 Email: buzzb3@earthlink.net * * For searches and help try: * http://www.stata.com/help.cgi?search * http://www.stata.com/support/statalist/faq * http://www.ats.ucla.edu/stat/stata/* * For searches and help try: * http://www.stata.com/help.cgi?search * http://www.stata.com/support/statalist/faq * http://www.ats.ucla.edu/stat/stata/ * * For searches and help try: * http://www.stata.com/help.cgi?search * http://www.stata.com/support/statalist/faq * http://www.ats.ucla.edu/stat/stata/

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**References**:**RE: st: how to find the integral for a portion of a normal distribution.***From:*"Buzz Burhans" <buzzb3@earthlink.net>

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