You can do the following
sqrtllrh=fminsearch(@(sqrtllr)(cdf_func(sqrtllr.^)-h)^2,1);
llrh=sqrtllrh^2;
The explanation is as follows:
1) cdf_func as you defined it is monotonous increasing, and therefore it can be inverted. 2) However, it is not well defined for negative values. 3) The function fminsearch will look for the minimum of a function. 4) What I did then was to construct a function for which the minimum occurs at the value llr that you are looking for. That function is (cdf_func(llr)-h)^2. The minimum will occur at the point in which cdf_func(llr)=h and the function will give you the value of llr. 5) But, as I mentioned before, since your function does not handle negative values, and fminsearch does not know that, I instead used the function (cdf_func(sqrtllr^2)-h)^2, where sqrtllr is the square root of the value of llr. That guarantees that the function will always get positive values. 6) The last value inside the function is completely arbitrary and it is the starting point where fminsearch starts looking for the minimum. 7) After the function finishes, the value that you are looking for will be the square of what the function gives you as an answer.
Hope this helps.
