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From |
Joseph Coveney <jcoveney@bigplanet.com> |

To |
Statalist <statalist@hsphsun2.harvard.edu> |

Subject |
st: Stata's functions relating to the binomial distribution |

Date |
Thu, 04 Nov 2004 21:43:55 +0900 |

I have two questions related to Stata's functions relating to the binomial distribution: The first question relates to the functions -Binomial()- and -invbinomial()-: This direction is pretty good . . . . display Binomial(100, 50, invbinomial(100, 50, 0.5)) .5 . display Binomial(100, 50, invbinomial(100, 50, 0.999)) .99950217 But is there any way to improve accuracy in the following direction? Or is it that I'm not understanding these functions correctly? . display invbinomial(100, 50, Binomial(100, 50, 0.5)) .50996594 . display invbinomial(100, 50, Binomial(100, 50, 0.999)) .85115891 I've discovered that it works best to keep the probability under 0.5. Is that the key, then: work with 1 - P if P >= 0.5? . display invbinomial(100, 50, Binomial(100, 50, 0.0001)) .0001 The second question is about a function that I haven't found in the user's manuals, or online sources (-help functions-, -findit binomial-, search of StataCorp's FAQs with "binomial" as the search term): In R / S-Plus, there is a function called called "qbinomial()" / "qbinom()". If I understand it correctly, then it appears to return the number of successes, k, that just(?) satisfies the equation probability of observing at least k successes = Binomial(n, k, p), with k the only unknown. (I've used Stata's -Binomial()- function for the description.) The function is displayed at http://lib.stat.cmu.edu/S/discrete. Is there something similar in Stata? In -Binomial()-, k does not apparently need to be an integer, so I suppose that the equation could be solved with -ridder- or -bisect- . . . If I read the R / S-Plus function correctly, it seems to just plod through the numbers. Well, perhaps a third question: Has anyone considered implementing Blaker's binomial confidence interval in Stata, or is anyone aware of its acceptance in comparison to, say, the Blyth-Still-Casella interval, in particular for inverting it to obtain a P-value of the test p = p0? StatXact advocates the Blyth-Still-Casella interval for this (www.cytel.com/Library/Issue_seven/smallerPvalues-final.pdf), but Blaker's article indicates that it is unsuitable for this purpose, since its intervals aren't necessarily nested. Reference: H. Blaker, Confidence curves and improved exact confidence intervals for discrete distributions. _Canad J Statist_ 28:783-98, 2000. Google "blaker00confidence" for a preprint from CiteSeer, and see www.stat.ufl.edu/~aa/cda/R/one_sample/R1/index.html for corrected R / S-Plus code. Joseph Coveney * * 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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