How To Solve An 1-parameter Equation Using Python (scipy/numpy?)

I hope you have some useful tip for me to approach the following task: I wrote some simple python snippet to plot probability density functions. In my particular case, let them rep

Solution 1:

In general, it sounds like you need the scalar root-finding functions: http://docs.scipy.org/doc/scipy/reference/optimize.html

But as others have pointed out, it seems like there is an analytical solution.

Solution 2:

Since you have a nice closed-form equation, you can solve it with SymPy.

I plugged in values for mu and sigma and entered this into Sympy Gamma:

 solve(1.0 / ( sqrt(2*pi) *(3**0.5) ) * exp( -0.5 * ( (x-10)/(3**0.5) )**2 ) /  (1.0 / ( sqrt(2*pi) *(2**0.5) ) * exp( -0.5 * ( (x-20)/(2**0.5) )**2 ))-1,x)

The result: 15.4554936768195