I Want to check whether a set of data points follow Poisson distribution or not. For this First I plot histogram using 10 bins and count values in each bin. Then I try to fit Poisson distribution using the following code. At the end my chisquare value is too large. I have gone through several examples in which chisquare value is reasonable to compare with chisquare distribution table. My input data x has normalized 256 values that I use to plot histogram. Since input data contains both positive and negative value. After normalizing I get reasonable shape of histogram as show in the attached figure. I'm really confused why chisquare value is too large? If I increase values from 256 to 1000 histogram shape still looks similar to Poisson distribution but chisqure value also shows a large increase. How can I fix this problem?
`x =np.array(flatten_list)
x = Ls_Store/Ls_Store.mean()
#Formula of Poisson distribution:
def Poisson_fit(mu,x):
return (((mu**x) * np.exp(-mu))/math.factorial(x))
fig = plt.figure()
ax = fig.add_subplot(111)
hist,bins,patches=plt.hist(x,bins=10,label='h=5.0')
print("bin_counts: ",hist)
#bin_count: [94. 64. 32. 30. 16. 11. 3. 1. 3. 1.]
x_ = np.arange(len(hist))
fx = np.multiply(x_,hist)
mu = np.sum(fx)/np.sum(hist)
print("mu: ",mu)
#mu: 1.5490196078431373
result=[]
for k in range(len(x_)):
result.append(Poisson_fit(mu,x_[k]))
result = np.array(result)
h = np.sum(hist)
#Counts in Poisson
m= h*result
#Implement Chisquare Test
f_obs =hist
f_exp= m
print("f_obs: ",f_obs)
print("f_exp: ",f_exp)
chisquare =[]
for h in range(len(f_obs)):
chisquare.append(((f_obs[h]-f_exp[h])**2)/f_exp[h])
chisquare = np.array(chisquare)
print(np.sum(chisquare))
#394.74825860641397`
