Re: Re: Calculate n in binomial distribution
- To: mathgroup at smc.vnet.net
- Subject: [mg101601] Re: [mg101581] Re: Calculate n in binomial distribution
- From: Bob Hanlon <hanlonr at cox.net>
- Date: Fri, 10 Jul 2009 23:23:28 -0400 (EDT)
- Reply-to: hanlonr at cox.net
As a general rule, never mix exact and inexact and expect exact results
Minimize[Rationalize[(x - 6.1)^2], x, Integers]
{1/100, {x -> 6}}
Minimize[Rationalize[(x - 6.)^2], x, Integers]
{0, {x -> 6}}
Bob Hanlon
---- dh <dh at metrohm.com> wrote:
=============
Hi Peter,
I think there is a bug in Minimize for the Integer domain. Consider:
Minimize[(x - 6.1)^2, x, Integers] giving: {1.21, {x -> 5}}
Minimize[(x - 6.)^2, x, Integers] giving: {1., {x -> 5}}
Minimize[(x - 6)^2, x, Integers] giving: {0, {x -> 6}}
Minimize seems to have problems mixing integers and reals. I think you
should report this to Wolfram.
Daniel
Peter Breitfeld 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.
>