Problem with simulation kernel density with python

Question

I want to get simulation observation with kernel Density, but I have the Following error type: TypeError: unsupported operand type(s) for +: 'float' and 'NoneType'

how to resolve it? This is the code that I use:

    from matplotlib.pyplot import *
    from math import *
    from array import *
    import numpy as np 
    from numpy.random import *
    from scipy.misc import *
    from scipy.stats import *
    from scipy import *
    from random import *


    N=1000
    n=30
    lamb=0.5
    X=lamb*tan(pi*(np.reshape(rand(n,1),n)-0.5)) #loi de Cauchy  
    x=1
    alpha=0.45

    def k_gaussien(x):
        sigma=1
        if(sigma<=0):
            return((1/(sigma*sqrt(2*pi)))*exp(-(x**2/(2*sigma**2))))

    def h(n,alpha):
        for i in range(1,n):   
            return (i**(1-alpha))

    def f_PR(x,X,alpha):
        global F;
        F = ones((n,1))
        h_n = h(n,alpha)
        for k in range(2,n):
            for i in  range(1,k):
                F[k] = F[k-1] + k_gaussien((x-X[i])*i**alpha)
            F[k] = F[k-1] * h_n
        return F

    # Almost sure convergence f_n(x)--> f(x) ps
    figure(figsize=(20,10))
    fPR=f_PR(x,X,alpha)
    T=linspace(1,n,n);
    plot(cumsum(fPR)/T)
    plot(T,(1/pi)*(lamb/(lamb**2 + y**2))*linspace(1,1,N),"r--",lw=3)#with Cauchy density
    grid(True)
    title("convergence presque sure",fontsize=20,color="blue")

    #Convergence in mean N(0,e2f(x))
    hist(fPR,bins=linspace(-10,10,50),normed=True)
    y=linspace(-10,10,100);
    v=(1/pi)*(lamb/(lamb**2 + y**2))
    plot(y,(1/sqrt(2*pi)*v)*exp ((-(y*y)/(2*v**2)))*linspace(1,1,n),'r--') #with cauchy density
    title("convergence asymptotique", fontsize=20,color="blue")

TypeError Traceback (most recent call last)

<ipython-input-76-13bc86608417> in <module>()
         38 # Almost sure convergence f_n(x)--> f(x) ps
         39 figure(figsize=(20,10))
    ---> 40 fPR=f_PR(x,X,alpha)
         41 T=linspace(1,n,n);
         42 plot(cumsum(fPR)/T)

    <ipython-input-76-13bc86608417> in f_PR(x, X, alpha)
         32     for k in range(2,n):
         33         for i in  range(1,k):
    ---> 34             F[k] = F[k-1] + k_gaussien((x-X[i])*i**alpha)
         35         F[k] = F[k-1] * h_n
         36     return F

TypeError: unsupported operand type(s) for +: 'float' and 'NoneType'

Hi, welcome to Stackoverflow. Please post the complete stacktrace. — quant
– quant, Commented Nov 11, 2018 at 11:02

user8408080 · Accepted Answer · 2018-11-11 13:31:56Z

0

It's in your definition:

def k_gaussien(x):
    sigma=1
    if(sigma<=0):
        return((1/(sigma*sqrt(2*pi)))*exp(-(x**2/(2*sigma**2))))

You hardcoded sigma=1, but your function only returns something if sigma<=0 which will never be the case. So k_gaussien((x-X[i])*i**alpha) will return None. Therefore F[k] = F[k-1] + k_gaussien((x-X[i])*i**alpha) tries to sum float and None types, which does not work.

answered Nov 11, 2018 at 13:31

user8408080

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