Fit sigmoid function ("S" shape curve) to data using Python

Question

I'm trying to fit a sigmoid function to some data I have but I keep getting:ValueError: Unable to determine number of fit parameters.

My data looks like this:

My code is:

from scipy.optimize import curve_fit

def sigmoid(x):
    return (1/(1+np.exp(-x)))

popt, pcov = curve_fit(sigmoid, xdata, ydata, method='dogbox')

Then I get:

---------------------------------------------------------------------------
ValueError                                Traceback (most recent call last)
<ipython-input-5-78540a3a23df> in <module>
      2     return (1/(1+np.exp(-x)))
      3 
----> 4 popt, pcov = curve_fit(sigmoid, xdata, ydata, method='dogbox')

~\Anaconda3\lib\site-packages\scipy\optimize\minpack.py in curve_fit(f, xdata, ydata, p0, sigma, absolute_sigma, check_finite, bounds, method, jac, **kwargs)
    685         args, varargs, varkw, defaults = _getargspec(f)
    686         if len(args) < 2:
--> 687             raise ValueError("Unable to determine number of fit parameters.")
    688         n = len(args) - 1
    689     else:

ValueError: Unable to determine number of fit parameters.

I'm not sure why this does not work, it seems like a trivial action--> fit a curve to some point. The desired curve would look like this:

Sorry for the graphics.. I did it in PowerPoint...

How can I find the best sigmoid ("S" shape) curve?

UPDATE

Thanks to @Brenlla I've changed my code to:

def sigmoid(k,x,x0):
    return (1 / (1 + np.exp(-k*(x-x0))))

popt, pcov = curve_fit(sigmoid, xdata, ydata, method='dogbox')

Now I do not get an error, but the curve is not as desired:

x = np.linspace(0, 1600, 1000)
y = sigmoid(x, *popt)

plt.plot(xdata, ydata, 'o', label='data')
plt.plot(x,y, label='fit')
plt.ylim(0, 1.3)
plt.legend(loc='best')

and the result is:

How can I improve it so it will fit the data better?

UPDATE2

The code is now:

def sigmoid(x, L,x0, k, b):
    y = L / (1 + np.exp(-k*(x-x0)))+b

But the result is still...

Answer 1

After great help from @Brenlla the code was modified to:

def sigmoid(x, L ,x0, k, b):
    y = L / (1 + np.exp(-k*(x-x0))) + b
    return (y)

p0 = [max(ydata), np.median(xdata),1,min(ydata)] # this is an mandatory initial guess

popt, pcov = curve_fit(sigmoid, xdata, ydata,p0, method='dogbox')

The parameters optimized are L, x0, k, b, who are initially assigned in p0, the point the optimization starts from.

• L is responsible for scaling the output range from [0,1] to [0,L]
• b adds bias to the output and changes its range from [0,L] to [b,L+b]
• k is responsible for scaling the input, which remains in (-inf,inf)
• x0 is the point in the middle of the Sigmoid, i.e. the point where Sigmoid should originally output the value 1/2 [since if x=x0, we get 1/(1+exp(0)) = 1/2].

And the result: