from scipy.optimize import leastsq from scipy.optimize import curve_fit import matplotlib.pyplot as plt import numpy as np #time intervals t= np.linspace(1.0, 10.0, num=10) # sales vector sales=np.array([840,1470,2110,4000, 7590, 10950, 10530, 9470, 7790, 5890]) # cumulatice sales c_sales=np.cumsum(sales) # initial variables(M, P & Q) vars = [60630, 0.03,0.38] # residual (error) function def residual(vars, t, sales): M = vars[0] P = vars[1] Q = vars[2] Bass = M * (((P+Q)**2/P)*np.exp(-(P+Q)*t))/(1+(Q/P)*np.exp(-(P+Q)*t))**2 return (Bass - (sales)) # non linear least square fitting varfinal,success = leastsq(residual, vars, args=(t, sales)) # estimated coefficients m = varfinal[0] p = varfinal[1] q = varfinal[2] print(varfinal) #sales plot (pdf) #time interpolation tp=(np.linspace(1.0, 100.0, num=100))/10 cofactor= np.exp(-(p+q) * tp) sales_pdf= m* (((p+q)**2/p)*cofactor)/(1+(q/p)*cofactor)**2 plt.plot(tp, sales_pdf,t,sales) plt.title('Sales pdf') plt.legend(['Fit', 'True']) plt.show() # Cumulative sales (cdf) sales_cdf= m*(1-cofactor)/(1+(q/p)*cofactor) plt.plot(tp, sales_cdf,t,c_sales) plt.title('Sales cdf') plt.legend(['Fit', 'True']) plt.show()