import matplotlib.pyplot as plt
import random
import math
import scipy.stats as sc
MO = 0
PV = 0.1

def gen(n):
    arr = [random.triangular(a,b) for i in range(2**n)]
    return arr

def cnt(arr,x,y):
    k = 0
    for i in range(len(arr)):
        if x <= arr[i] < y:
            k+=1
    return k

def FR(x):
    fr = (x - a)/(b - a)
    return fr

def cm(arr,k):
    cmk = 0
    for i in range(len(arr)):
       cmk += (arr[i] - MO)**k
    cmk/= len(arr)
    return cmk

def hist(arr,f,a,b):
    n = 100
    step = (b-a)/n
    x = a
    y = a+step
    k = 1
    harr = []
    while k<n:
        harr.append(cnt(arr,x,y)/(len(arr)*step))
        k+=1
        x=y
        y=x+step
    harr.append(cnt(arr, x, b) / (len(arr) * step))
    x = a
    y = a + step
    plt.figure(f)
    for i in range(len(harr)):
        plt.plot([x,x,y,y],[0,harr[i],harr[i],0],color = 'blue')
        x = y
        y = x + step

def ing(arr,f):
    step = 1/len(arr)
    y = a + step
    n = (b-a) * len(arr)
    iarr = [0]
    x = [0]
    for i in range(n):
        iarr.append(cnt(arr,a,y)/len(arr))
        x.append(y)
        y+=step
    plt.figure(f)
    plt.plot(x,iarr)
    fx = [i for i in range(11)]
    fy = [FR(i) for i in range(11)]
    plt.plot(fx,fy)

def ka(arr):
    k = cm(arr,3)/(cm(arr,2)**(3/2))
    return k

def ke(arr):
    k = cm(arr,4)/(cm(arr,2)**(4/2))
    return k

def kplot(arr,f):
    plt.figure(f)
    plt.plot(ka(arr),ke(arr),'ro')
    plt.plot(0, 1.8, 'bs')
    plt.axis([-0.2,4,10,1])

def eh(arr):
    n = 1 + math.log2(len(arr))
    step = (b-a)/n
    x = a
    y = a+step
    k = 1
    harr = []
    xh = []
    while k<n:
        harr.append(cnt(arr,x,y)/(len(arr)*step))
        k+=1
        xh.append((x+y)/2)
        x=y
        y=x+step
    harr.append(cnt(arr, x, b) / (len(arr) * step))
    xh.append((x+y)/2)
    e = 0
    trg = sc.triang(scale=40, c=0.5, loc=-20)
    for i in range(len(harr)):
        e += (1 - harr[i]/trg.pdf(xh[i]))**2
    e = e*0.025
    return e

def ec(arr):
    step = 1/len(arr)
    y = a + step
    n = (b-a) * len(arr)
    iarr = [0]
    x = [0]
    for i in range(n):
        iarr.append(cnt(arr,a,y)/len(arr))
        x.append(y)
        y+=step
    k = 0
    i = 0
    while 1:
        if iarr[k] == 1:
            i = k
            break
        k+=1
    e = iarr[i] - FR(x[i])
    return(e)

"""""
arr = gen(9)
hist(arr,1)
ing(arr,2)
kplot(arr,3)
print(ec(arr))
plt.figure(4)
e1 = []
x = []
for i in range(10):
    e1.append(ec(gen(i+1)))
    x.append(2**(i+1))
plt.xscale('log',basex = 2)
plt.plot(x,e1)
plt.figure(5)
e2 = []
x2 = []
for i in range(10):
    e2.append(eh(gen(i+1)))
    x2.append(2**(i+1))
plt.xscale('log',basex = 2)
plt.plot(x2,e2)
plt.show()
"""""