Re: Calculate n in binomial distribution

*To*: mathgroup at smc.vnet.net*Subject*: [mg101243] Re: [mg101212] Calculate n in binomial distribution*From*: Bob Hanlon <hanlonr at cox.net>*Date*: Sat, 27 Jun 2009 06:06:59 -0400 (EDT)*Reply-to*: hanlonr at cox.net

cf[n_, p_, k_] = CDF[BinomialDistribution[n, p], k]; You mean the smallest n such that cf[n, 0.2, 7] < 0.3 or the largest n such that cf[n, 0.2, 7] > 0.3 For largest n such that cf[n, 0.2, 7] > 0.3 Floor[n /. FindRoot[cf[n, 0.2, 7] == 0.3, {n, 40}]] 44 For smallest n such that cf[n, 0.2, 7] < 0.3 Ceiling[n /. FindRoot[cf[n, 0.2, 7] == 0.3, {n, 40}]] 45 cf[#, 0.2, 7] & /@ {44, 45} {0.322925,0.297457} Bob Hanlon ---- Peter Breitfeld <phbrf at t-online.de> wrote: ============= Suppose I have the following distribution: cf[n_,p_,k_]=CDF[BinomialDistribution[n,p],k] Now I want to calculate n so that the biggest n such that e.g. cf[n,0.2,7]<0.3 I made a ListPlot ListPlot[Abs[cf[#,0.2,7]-0.3]&/@Range[60]], where I see, that a value of about n=46 gives an approximation nearest to 0.3 To get this value of n I tried Minimize[{Abs[cf[n,0.2,7]-0.3],n>7},n,Integers] Out: {0.699765, {n->11}} which is obviously wrong. Why? Is it, because Abs isn't differentiable at the peak? I tried other ways too, like Reduce NMinimize, FindMinimum, but no success. -- _________________________________________________________________ Peter Breitfeld, Bad Saulgau, Germany -- http://www.pBreitfeld.de