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