How to find sequence from set of values

I have set of probability values arranged in ascending order, p1<p2<p3<...<pM.

Now I want to assign set of numbers in the same manner in which probabilities are increasing. It means I want to find out values of n1,n2,n3...nM such that it follows same trend in which probability values are increasing. Also I have constraint that n1+n2+n3+...nM = L(Some known positive value)

I have two ideas in my find 1. With given probabilities, I can find function using Chebyshev aproximation/some other approximation, then I will find values of n1,n2,..nM satisfying the function.

Is there any other way, we can find out the values such as Geometric Progression and so on..

Please suggest me some idea how can do it? Any suggestion, comment is appreciable.

• I don't know what "I don't want that $n_1,n_2,\dots$ follows exactly with increase in probabilities" means. You can let $n_i=p_iL/P$, where $P=p_1+p_2+\cdots+p_M$. Jan 30, 2014 at 19:45

Why not multiply all the $p$'s by $\frac L{\sum_i p_i}?$ I have no idea what you mean by using Chebyshev approximation. You can certainly make a geometric progression with the desired sum.