find sigma for known normcdf parameters
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Hi,
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.
syms x mu sigma
p = 1/2 - erf((2^(1/2) * (mu - x)) / (2 * sigma)) / 2
solve(p,sigma)
Thanks in advance for your help,
Philippe
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Walter Roberson
on 11 Aug 2011
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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