# Create two distributions. One is a Normal distribution. The second is non-Normal.
# Run  normality tests are used to determine if a data set is well-modeled by a normal distribution,
# and to compute how likely it is for normally distributed.
# Calculate:  Normality tests using Anderson-Darling. You can also do , Cramer-Von Mises, D'Agostino-Pearson, Jarque Bera, Kolmogorov-Lilliefors, Shapiro-Francia, Shapiro-Wilk.
# This example calculates the p-value using R.B. D'Augostino and M.A. Stephens, Eds., 1986, Goodness-of-Fit Techniques, Marcel Dekker.


from java.awt import Color
from java.util import Random
from jhplot  import * 
from math import *

c1 = HPlotJa("Canvas")
c1.setGTitle("Normality tests")
c1.setAutoRange()
c1.visible()

h1 = H1D("Histo1",40, -3, 3.0)
h1.setColor(Color.blue)
h2 = H1D("Histo2",40, -3, 3.0)
r = Random()

data1=[]
data2=[]
for i in range(1000):
       r1=r.nextGaussian()
       h1.fill(r1)      
       data1.append(r1)
       r2=2*r.nextDouble() 
       h2.fill(r2)        
       data2.append(r2)
h1.setErrAll(1)
h2.setErrAll(0)
c1.draw(h1)
c1.draw(h2)

import math

def pvalue(AD):
  if (AD>0.6): return math.exp(1.2937-5.709*AD+0.0186*(AD*AD)) 
  if (AD>0.34 and AD<0.6): return math.exp(0.9177-4.279*AD-1.38*(AD*AD))
  if (0.2>AD and AD<=0.34): return 1-math.exp(-8.318 + 42.796*AD- 59.938*(AD*AD))
  if AD<0.2: 1-math.exp(-13.436 + 101.14*AD- 223.73*(AD*AD))
  return 0

from jdistlib.disttest import NormalityTest

w1=NormalityTest.anderson_darling_statistic(data1)
w2=NormalityTest.anderson_darling_statistic(data2)
print "anderson_darling for Gaussian=",w1
print "anderson_darling_statistic for Non-Gaussian=",w2

print "p-value for Gaussian=",pvalue(w1)
print "p-value for Non-Gaussian=",pvalue(w2)