original_hist_fit

import numpy as np
import matplotlib.pyplot as plt
import seaborn as sns
from scipy.stats.kde import gaussian_kde
import math
import scipy

def survivalFunction():

    data = np.random.normal(7,1,100) #Random data

    p = sns.kdeplot(data, shade=False, lw = 3)
    x,y = p.get_lines()[0].get_data()
    cdf = scipy.integrate.cumtrapz(y, x, initial=0)


    plt.hist(data, 50, normed = 1, facecolor='b',alpha = 0.3)

    interp = scipy.interpolate.interp1d(x, y, kind="cubic")

    def ret_func(x):
        try:
          return interp(x)
        except ValueError:
          return 0

    return ret_func


def surpriseFunction(mu,variance):

    hStates = np.linspace(0,20,100)
    sigma = math.sqrt(variance)

    plt.plot(hStates, scipy.stats.norm.pdf(hStates, mu, sigma))


    def ret_func(x):
      return scipy.stats.norm.pdf(x, mu, sigma)

    return ret_func




random_dist = survivalFunction()

def gaussian_fit(inp):
  mu, sigma = inp

  def f(x):
    return scipy.stats.norm.pdf(x, mu, sigma) * random_dist(x)

  return -scipy.integrate.romberg(f, 0, 20)


mean, variance = scipy.optimize.fmin(gaussian_fit, [5,1])
print mean, variance

surpriseFunction(mean, variance)