From: <emir.toktar_at_gmail.com>

Date: Mon, 04 Aug 2008 23:55:18 -0300

}

R-help_at_r-project.org mailing list

https://stat.ethz.ch/mailman/listinfo/r-help PLEASE do read the posting guide http://www.R-project.org/posting-guide.html and provide commented, minimal, self-contained, reproducible code. Received on Tue 05 Aug 2008 - 03:01:55 GMT

Date: Mon, 04 Aug 2008 23:55:18 -0300

The objective is to obtain the smallest value of 'n' (sample size) satisfying both inequalities:

(1-alpha) <= pbinom(c, n, p1) && pbinom(c, n, p2) <= beta

I´m using Mathematica 6 but it is a Trial, so I would like use R intead (or better, I need it)!

/* function name "findOpt" and parameters... */

restriction = (1 - alpha) <= CDF[BinomialDistribution[sample_n, p1], c]

&& betha >= CDF[BinomialDistribution[sample_n, p2], c] && 0 < alpha < alphamax && 0 < betha < bethamax && 1 < sample_n <= lot_Size && 0 <= c < lot_size && p1 < p2 < p2max ; fcost = sample_n/lot_Size;

result = NMinimize[{fcost, restriction}, {sample_n, c, alpha, betha, p2max}, Method -> "NelderMead", AccuracyGoal -> 10];

/* Calling the function findOpt */

findOpt[p1=0.005, lot_size=1000, alphamax=0.05, bethamax =0.05, p2max =
0.04]

/* and I got the return of values of; minimal "n", "c", "alpha", "betha" and

the "p2" or (LTPD) were computed */ {0.514573, {alpha$74 -> 0.0218683,
sample_n$74 -> 155.231, betha$74 -> 0.05,
c$74 -> 2, p2$74 -> 0.04}}

Now, using R, I would define the "pbinom(c, n, prob)" given only the minimum and maximum values to "n" and "c" and limits to p1 and p2 probabilities (Consumer and Producer), similar on the example above.

I found some examples to optimize equations in R and some tips, but I not be able to define the sintaxe to use with that functions. Among the functions that could be used to resolve the problem presented, I found the function optim() that it is used for unconstrained optimization and the nlm() which is used for solving nonlinear unconstrained minimization problems. May I wrong, but the nlm() function would be appropriate to solve this problem, is it right?

Can I get a pointer to solve this problem using the nlm() function or where could I get some tips/example to help me, please?

// (1-alpha) <= pbinom(c, n, p1) && pbinom(c, n, p2) <= beta It was used "betha" parameter name to avoid the 'beta' function used in Mathematica...

findS <- function(p1='numeric', lot_size='numeric', alphamax='numeric',
bethamax ='numeric', p2max ='numeric')

{

(1 - alpha) <= pbinom(c, sample_n, p1) && betha >= pbinom(c, sample_n, p2)

&& 0 < alpha < alphamax && 0 < betha < bethamax && 1 < sample_n <= lot_Size && 0 <= c < lot_size && p1 < p2 < p2max ;

}

Parameters:

p1=0.005, lot_size=1000, alphamax=0.05, bethamax =0.05, p2max = 0.04 Minimize results should return/printing the following values: sample_n, (minimal sample size) c , (critical level of defectives) alpha , (producer's risk) betha , (consumer's risk) p2max (consumer's probability p2)

Could one help me understand how can desing the optimize nonlinear function using R for two binomials or point me some tips?

Thanks in advance.

EToktar

R-help_at_r-project.org mailing list

https://stat.ethz.ch/mailman/listinfo/r-help PLEASE do read the posting guide http://www.R-project.org/posting-guide.html and provide commented, minimal, self-contained, reproducible code. Received on Tue 05 Aug 2008 - 03:01:55 GMT

Archive maintained by Robert King, hosted by
the discipline of
statistics at the
University of Newcastle,
Australia.

Archive generated by hypermail 2.2.0, at Tue 05 Aug 2008 - 14:33:12 GMT.

*
Mailing list information is available at https://stat.ethz.ch/mailman/listinfo/r-help.
Please read the posting
guide before posting to the list.
*