       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], 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

```

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