#include <iostream>
#include <string>
#include <iomanip>
#include <math.h>
#include <vector>
using namespace std;

void recursion();
void uniform();
void exponent();

int main()
{
	cout << "Recursion method:" << endl; //2nd work, 1st task
	recursion();
	//cout << endl << endl << "Uniform distribution:" << endl;
	//uniform();
	//cout << endl << endl << "Exponential distribution:" << endl; //2nd work, 2nd task
	//exponent();
	system("pause");
	return 0;
}

void recursion()
{
	double Mat, D, sigma, sum = 0, sumd = 0, sumd_buff;
	double Z[100], x[100];
	double x1[100], q;
	int n = 100;
	int Z_1 = 12345,
		Z0 = 97531,
		a0 = 1,
		a1 = 1,
		M = 5000;

	Z[0] = Z_1;
	Z[1] = Z0;
	for (int i = 2; i < n; i++)
		Z[i] = a0*Z[i - 2] + a1*Z[i - 1];

	cout << "x:" << endl;
	for (int i = 0; i < n; i++)
	{
		x[i] = fmod(Z[i], M);
		x1[i] = x[i] / M;
		cout << x1[i] << endl;
	}

	for (int i = 0; i < n; i++)
	{
		sum = sum + x1[i];
		sumd_buff = pow(x1[i], 2);
		sumd += sumd_buff;
	}
	Mat = sum / n;
	D = (sumd / n) - (pow(Mat, 2));
	sigma = sqrt(D);
	cout << "Mat = " << Mat << endl << "D = " << D << endl << "Sigma = " << sigma << endl;

	//-----------2nd work-----------//
	//интервалы
	double b = 0.9, t = 1.643, e1, e2, Id1, Id2, Im1, Im2, u4, us, u_buff, u_sum = 0, sigmaD;
	e1 = sigma * t;
	Id1 = Mat - e1;
	Id2 = Mat + e1;
	for (int i = 0; i < n; i++)
	{
		us = x1[i] - Mat;
		u_buff = pow(us, 4);
		u_sum += u_buff;
	}
	u4 = u_sum / n;
	sigmaD = sqrt((u4/n)-(((n-3)/(n*(n-1)))*pow(D,2)));
	e2 = sigmaD * t;
	Im1 = D - e2;
	Im2 = D + e2; \
	cout << endl << "Intervals:" << endl;
	cout << "Id = (" << Id1 << "; " << Id2 << ")" << endl;
	cout << "Im = (" << Im1 << "; " << Im2 << ")" << endl;

	//Пирсон
	double Xnabl = 0, Xkrit = 11.0705, min = x1[0], max = x1[0], h,  td;
	int k;
	for (int i = 0; i < n; i++)
	{
		if (x1[i] < min) min = x1[i];
		if (x1[i] > max) max = x1[i];
	}
	//cout << "Xmax = " << max << endl << "Xmin = " << min << endl;
	h = max - min;
	k = 1 + log2(n);
	td = h / k;
	//cout << "t = " << td << endl;
	vector<double> xi;
	for (int i = 0; i < k; i++)
		xi.push_back(min + i*td);
	xi.push_back(max);
	vector<int> mi;
	for (int i = 0; i < k; i++)
		mi.push_back(0);
	for (int i = 0; i < n; i++)
		for (int j = 0; j < k; j++)
		{
			if (x1[i] >= xi[j] && x1[i] <= xi[j + 1])
			{
				mi[j]++;
				break;
			}
		}
	double mi_;
	double summi, sumpow, sumnabl = 0;
	for (int i = 0; i < k; i++)
	{
		mi_ = (xi[i+1] - xi[i])*n;
		summi = mi[i] - mi_;
		sumpow = pow(summi, 2);
		sumnabl += sumpow;
	}
	Xnabl = sumnabl / mi_;
	cout << endl << "Pirson:" << endl << "Xkrit (0.05; 5) = " << Xkrit << endl << "Xnabl = " << Xnabl << endl;
	if (Xnabl < Xkrit) cout << "H0 is not rejected" << endl;
	else cout << "H0 is rejected" << endl;

	//вывод гистограммы (все рассчитывалось в Пирсоне)
	cout << endl << "Gistogramm:" << endl;
	cout << "Fg:" << endl;
	double Fg;
	for (int i = 0; i < k; i++)
	{
		Fg = mi[i] / (n*td);
		cout << Fg << endl;
	}
	cout << "xi:" << endl;
	for (int i = 0; i < k; i++)
	{
		cout << xi[i] << endl;
	}
}

void uniform()
{
	int n = 100;
	double r[100], x[100], Mat, D, sigmau, sum = 0, sumd_buff, sumd = 0, sigma;
	int b = rand(), a = rand() < b;
	cout << "a = " << a << ";" << setw(8) << "b = " << b << endl << "x:" << endl;
	for (int i = 0; i < n; i++)
	{
		r[i] = ((double)rand() / (RAND_MAX));
		x[i] = a + (b - a)*r[i];
		cout << x[i] << endl;
	}

	for (int i = 0; i < n; i++)
	{
		sum = sum + x[i];
		sumd_buff = pow(x[i], 2);
		sumd += sumd_buff;
	}
	Mat = sum / n;
	D = (sumd / n) - (pow(Mat, 2));
	sigmau = sqrt(D);
	cout << "Mat = " << Mat << endl << "D = " << D << endl << "Sigma = " << sigmau << endl;

	//------------2nd work---------//
	double t = 1.643, e1, e2, Id1, Id2, Im1, Im2, u4, us, u_buff, u_sum = 0, sigmaD;
	e1 = sigmau * t;
	Id1 = Mat - e1;
	Id2 = Mat + e1;
	for (int i = 0; i < n; i++)
	{
		us = x[i] - Mat;
		u_buff = pow(us, 4);
		u_sum += u_buff;
	}
	u4 = u_sum / n;
	sigmaD = sqrt((u4 / n) - (((n - 3) / (n*(n - 1)))*pow(D, 2)));
	e2 = sigmaD * t;
	Im1 = D - e2;
	Im2 = D + e2;
	cout << "Id = (" << Id1 << "; " << Id2 << ")" << endl;
	cout << "Im = (" << Im1 << "; " << Im2 << ")" << endl;
}

void exponent()
{
	int n = 100;
	double r[100], x[100], Mat, D, sigmau, sum = 0, sumd_buff, sumd = 0, sigma;;
	double jl = 0.8;
	cout << "x:" << endl;
	for (int i = 0; i < n; i++)
	{
		r[i] = ((double)rand() / (RAND_MAX));
		x[i] = (-1 / jl) * log(r[i]);
		cout << x[i] << endl;
	}

	for (int i = 0; i < n; i++)
	{
		sum = sum + x[i];
		sumd_buff = pow(x[i], 2);
		sumd += sumd_buff;
	}
	Mat = sum / n;
	D = (sumd / n) - (pow(Mat, 2));
	sigmau = sqrt(D);
	cout << "Mat = " << Mat << endl << "D = " << D << endl << "Sigma = " << sigmau << endl;

	//-----------2nd work----------//
	//интервалы
	double b = 0.9, t = 1.643, e1, e2, Id1, Id2, Im1, Im2, u4, us, u_buff, u_sum = 0, sigmaD;
	e1 = sigmau * t;
	Id1 = Mat - e1;
	Id2 = Mat + e1;
	for (int i = 0; i < n; i++)
	{
		us = x[i] - Mat;
		u_buff = pow(us, 4);
		u_sum += u_buff;
	}
	u4 = u_sum / n;
	sigmaD = sqrt((u4 / n) - (((n - 3) / (n*(n - 1)))*pow(D, 2)));
	e2 = sigmaD * t;
	Im1 = D - e2;
	Im2 = D + e2;
	cout << endl << "Intervals:" << endl;
	cout << "Id = (" << Id1 << "; " << Id2 << ")" << endl;
	cout << "Im = (" << Im1 << "; " << Im2 << ")" << endl;

	//пирсон
	double Xnabl = 0, Xkrit = 12.5916, min = x[0], max = x[0], h, td;
	int k;
	for (int i = 0; i < n; i++)
	{
		if (x[i] < min) min = x[i];
		if (x[i] > max) max = x[i];
	}
	//cout << "Xmax = " << max << endl << "Xmin = " << min << endl;
	h = max - min;
	k = 1 + log2(n);
	td = h / k;
	//cout << "t = " << td << endl;
	vector<double> xi;
	for (int i = 0; i < k; i++)
		xi.push_back(min + i*td);
	xi.push_back(max);
	vector<int> mi;
	for (int i = 0; i < k; i++)
		mi.push_back(0);
	for (int i = 0; i < n; i++)
		for (int j = 0; j < k; j++)
		{
			if (x[i] >= xi[j] && x[i] <= xi[j + 1])
			{
				mi[j]++;
				break;
			}
		}
	double mi_;
	vector<double> f;
	for (int i = 0; i < k+1; i++)
		f.push_back(1 - pow(2.72, (-jl*xi[i])));
	for (int i = 0; i < k; i++)
	{
		mi_ = (f[i+1]-f[i])*n;
		Xnabl += pow(mi[i] - mi_, 2) / mi_;
	}
	cout << endl << "Pirson:" << endl << "Xkrit (0.05; 6) = " << Xkrit << endl << "Xnabl = " << Xnabl << endl;
	if (Xnabl < Xkrit) cout << "H0 is not rejected" << endl;
	else cout << "H0 is rejected" << endl;

	//вывод гистограммы (все рассчитывалось в Пирсоне)
	cout << endl << "Gistogramm:" << endl;
	cout << "Fg:" << endl;
	double Fg;
	for (int i = 0; i < k; i++)
	{
		Fg = mi[i] / (n*td);
		cout << Fg << endl;
	}
	cout << "xi:" << endl;
	for (int i = 0; i < k; i++)
	{
		cout << xi[i] << endl;
	}
}