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Conditional Optimization
*To*: mathgroup at smc.vnet.net
*Subject*: [mg80910] Conditional Optimization
*From*: John <jwa0 at lehigh.edu>
*Date*: Wed, 5 Sep 2007 02:55:35 -0400 (EDT)
Problem:
Find the largest value of n for which BetaRegularized[1-p0,n-c,c
+1]>=1-alpha.
Find the smallest value of n for which BetaRegularized[1-p1,n-c,c
+1]<=beta.
0<p0<p1<1, 0<alpha<1, 0<beta<1, c is a positive integer.
Values of p0, p1, alpha, beta and c are specified.
Since BetaRegularized[1-p0, n-c,c+1] decreases as n increases, the
required value of n satisfies the equation, BetaRegularized[1-p0,n-c,c
+1]=1-alpha.
Since BetaRegularized[1-p1, n-c,c+1] decreases as n increases, the
required value of n satisfies
the equation, BetaRegularized[1-p1,n-c,c+1]=beta.
My attempts to use Solve to find the required values of n were
unsuccessful. Hints or suggestions would be appreciated.
John
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