Maximize Multi-parameter summation with python

Question

I am trying to fit a wind data set v=v1,.....,vm using a two component mixture weibull distribution.

I found a paper suggesting to use the Maximum Likelihood method and in particular to maximize the following equation:

Omega, a1, a2, b1 and b2 are the parameters I want to change in order to maximize the function and v=v1,.....,vm is a series of known wind speeds.

I have been trying to use the SciPy minimization algorithm but without success.

Here is what I have so far:

def minimizer_function(v,omega,a1,b1,a2,b2):
   return np.reciprocal(np.sum((omega*(a1/b1)*((v/b1)**(a1-1))*(np.exp(-((v/b1)**a1)))+(1-omega)*(a2/b2)*((v/b2)**(a2-1))*(np.exp(-((v/b2)**a2))))))

x0 = np.array([0.5,1.0,1.0,1.0,1.0])
res = optimization.minimize(minimizer_function, x0, method='nelder-mead',options={'xtol': 1e-8, 'disp': True})

However I keep on getting the following error:

minimizer_function() missing 5 required positional arguments: 'omega', 'a1', 'b1', 'a2', and 'b2'

I am pretty sure I am missing something.

Warren Weckesser · Accepted Answer · 2017-02-27 17:26:38Z

1

The scipy minimizers expect the variables to be stored in a single one-dimensional array. In your case, the objective function should be something like minimizer_function(x, v), where x is an array of five elements containing omega, a1, b1, a2 and b2. That is, something like

def minimizer_function(x, v):
   omega, a1, b1, a2, b2 = x
   return np.reciprocal(np.sum((omega*(a1/b1)*((v/b1)**(a1-1))*(np.exp(-((v/b1)**a1)))+(1-omega)*(a2/b2)*((v/b2)**(a2-1))*(np.exp(-((v/b2)**a2))))))

The call to minimize would be something like

x0 = np.array([0.5,1.0,1.0,1.0,1.0])
res = optimization.minimize(minimizer_function, x0, args=(v,), method='nelder-mead',options={'xtol': 1e-8, 'disp': True})

answered Feb 27, 2017 at 17:26

Warren Weckesser

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2 Comments

user7630935 Over a year ago

Hi Warren, thank you very much for looking into this. It runs now, the values look very strange but I am probably still missing something

user7630935 Over a year ago

Any suggestion on how to maximize the function? At present I am minimizing the reciprocal of the abs of the function

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