Knowing p, x and mu I would like to find the corresponding sigma for p = normcdf(x,mu,sigma). I tried with the symbolic toolbox using the following code but it failed.
That can be rearranged so that the essential part is solving an equation of the form erf(t)=r for t. Unfortunately I have not found a useful analytic method of solving that.
It appears that there is a real solution if and only if p is in the range 0 to 1; however, if mu = x then any non-zero sigma satisfies the equation.
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