lab4

function MC_LR_4_KHMELEV


 %_______________________________ЗАДАНИЕ I______________________________________

  a_ = -0.7; b_ = 7.3; % по условию
  printf('\n-------------\n  TASK NUMBER 1\n');

  X = sort(oneOfArrays('ud-2'));
  N = length(X);

  for j = 1:N
    F(j) = f(X(j));
    FNx(j) = Fn(j, 'x');
    FNx0(j) = Fn(j, '0');
  endfor
  [Dn, j] = max(max( abs(FNx - F), abs(FNx0 - F) ));

  x_ = X(j); % x_ - это x*,   X[] - это выборка, состоящая из элементов x от 1 до N
  DnN = Dn*sqrt(N);

  printf('\n------\nTABLE 1:\n a = %i\n b = %i\n N = %i\n Dn = %i\n Dn√N = %i\n x* = %i\n F(x*) = %i\n Fn(x*) = %i\n Fn(x*-0) = %i\n------\n\n', a_, b_, N, Dn, myround(DnN, 5), x_, myround(f(x_), 5), myround(Fn(j, 'x*'), 5), myround(Fn(j, '0'), 5));


  % график эмпирической функции распределения и график функции распределения равномерного закона на отрезке [a , b]:
  v = 0.1; % шаг по вертикали
  h = 1; % шаг по горизонтали

  high = 1 + v;
  left = fix(a_); right = fix(b_);
  low = 0 - v;
  xticks = [left:h:right];
  yticks = [low:v:high];

  figure('Name','EDF & uniform distribution');
  plot(X, FNx, 'b', X, F, 'g'); % FNx - точки эмпирической функции, F - точки функции равномерного закона
   title('blue - EDF; green - cumulative distribution function'), grid on
  set(gca,'xtick', xticks);
  set(gca,'ytick', yticks);
  xlim([left, right]);
  ylim([left, high]);

  % Проверка гипотезы о соответствии выборки равномерному распределению
  a = 0.05; % уровень значимости

    % первый способ:
    printf('Hypothesis'' check,\nthe first method:\n');
    ka = K(a);
    if DnN <= ka
      printf('Dn√N = %i; ka = %i, %i<=%i  =>  Gipoteza mozhet byt prinyata;\n', DnN, ka, DnN, ka);
    else
      printf('Dn√N = %i; ka = %i, %i>%i  =>  Gipoteza nie mozhet byt prinyata;\n', DnN, ka, DnN, ka);
    endif

    % второй способ:
    printf('\nthe second method:\n');
    pval = kolmogorov_smirnov_test(X, "unif", a_, b_);

    if pval >= a
      printf('pval = %i; a = %i, %i>=%i  =>  Gipoteza mozhet byt prinyata\n', myround(pval, 5), a, myround(pval, 5), a);
    else
      printf('pval = %i; a = %i, %i<%i  =>  Gipoteza nie mozhet byt prinyata.\n', myround(pval, 5), a, myround(pval, 5), a);
    endif


 %_______________________________ЗАДАНИЕ II_____________________________________

  printf('\n\n-------------\n  TASK NUMBER 2\n');

  Y = sort(oneOfArrays('ud-3'));
  M = length(Y);

  FNy = []; % Fn(y(k))
  FMy = []; % Fm(y(k))
  FMy0 = []; % Fm(y(k) - 0)

  for k = 1:M
    for j = 2:N-1
      if X(j) <= Y(k) && Y(k) < X(j+1)
        FNy(k) = Fn(j, 'y');
      endif
    endfor
    if Y(k) < X(1)
      FNy(k) = 0;
    elseif Y(k) >= X(N)
      FNy(k) = 1;
    endif

    FMy(k) = Fm(k, 'y');
    FMy0(k) = Fm(k, '0');
  endfor

  FMx = []; %Fm(x(j))
  for j = 1:N
    for k = 2:M-1
      if Y(k) <= X(j) && X(j) < Y(k+1)
        FMx(j) = Fm(k, 'x');
      endif
    endfor
    if X(j) < Y(1)
      FMx(j) = 0;
    elseif X(j) >= Y(M)
      FMx(j) = 1;
    endif
  endfor

  x_ = 0; % x*
  [xmax, j] = max(max( abs(FNx - FMx), abs(FNx0 - FMx) ));
  [ymax, k] = max(max( abs(FNy - FMy), abs(FNy - FMy0) ));

  if xmax > ymax
    Dnm = xmax;
    x_ = X(j);
    jk = j;
  else
    Dnm = ymax;
    x_ = Y(k);
    jk = k;
  endif

  Knm = Dnm*sqrt(N*M/(N+M));

  printf('\n------\nTABLE 2:\n N = %i\n M = %i\n Dnm = %i\n Knm = %i\n x* = %i\n Fn(x*) = %i\n Fn(x*-0) = %i\n Fm(x*) = %i\n Fm(x*-0) = %i\n------\n\n', N, M, myround(Dnm, 5), myround(Knm, 5), x_, myround(Fn(jk, 'x*'), 5), myround(Fn(jk, '0'), 5), myround(Fm(jk, 'x*'), 5), myround(Fm(jk, '0'), 5));


  % графики эмпирических функций наших выборок:
  figure('Name','EDFs');
  plot(X, FNx, 'b', Y, FMy, 'r');
   title('blue - EDF of ud-2; red - EDF of ud-3'), grid on
  set(gca,'xtick', xticks); % xticks и yticks указаны в задании I
  set(gca,'ytick', yticks);
  xlim([left, right]); % так же как и left и right
  ylim([left, high]);


  % Проверка гипотезы о соответствии выборки равномерному распределению
  a = 0.02; % уровень значимости

    % первый способ:
    printf('Hypothesis'' check,\nthe first method:\n');
    ka = K(a);
    if Knm <= ka
      printf('Dn√N = %i; ka = %i, %i<=%i  =>  Gipoteza mozhet byt prinyata;\n', DnN, ka, DnN, ka);
    else
      printf('Dn√N = %i; ka = %i, %i>%i  =>  Gipoteza nie mozhet byt prinyata;\n', DnN, ka, DnN, ka);
    endif

    % второй способ:
    printf('\nthe second method:\n');
    pval = kolmogorov_smirnov_test_2(X, Y);

    if pval >= a
      printf('pval = %i; a = %i, %i>=%i  =>  Gipoteza mozhet byt prinyata\n', myround(pval, 5), a, myround(pval, 5), a);
    else
      printf('pval = %i; a = %i, %i<%i  =>  Gipoteza nie mozhet byt prinyata.\n', myround(pval, 5), a, myround(pval, 5), a);
    endif


 %______________________________________________________________________________

 %%%%%%% ФУНКЦИИ, ВКЛЮЧЕННЫЕ В ОСНОВНУЮ ФУНКЦИЮ %%%%%%%

  function Fn = Fn(j, param) % Fn(x(j) - 0)
    Fn = 0;

    if param == '0'
      Fn = (j - 1)/N;
    else
      Fn = j/N;
    endif

  endfunction


  function Fm = Fm(k, param) % Fm(y(k) - 0)
    Fm = 0;

    if param == '0'
      Fm = (k - 1)/M;
    else
      Fm = k/M;
    endif

  endfunction


  function F = f(x)
    F = 0;

    if x < a_
      F = 0;
      return
    elseif x > b_
      F = 1;
      return
    endif

    F = (x-a_)/(b_-a_);

  endfunction


  function ka = K(a) % критические значения распределения Колмогорова
    ka = 0;

    switch a % уровни значимости

      case 0.01
        ka = 1.63;
      case 0.02
        ka = 1.57;
      case 0.05
        ka = 1.36;
      case 0.1
        ka = 1.22;
      case 0.2
        ka = 1.07;

    endswitch
  endfunction

 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
end


function R = myround(x, k) % округление до 5 знаков после запятой
  R = 0;

  R = round(x*10^k)/10^k;

endfunction


function arr = oneOfArrays(a) % выдача массива
  arr = []; %вариант 17

    if a == 'ud-2'
        arr = [ -0.39944, 6.75288, 3.31944, -0.48104, 2.61992, 5.96608, 5.66712, 4.99512, 3.20880, 3.06232, 2.20880, -0.11496, 4.19288, 7.12520, 3.03560, -0.56360, 0.43696, 4.32168, 0.81152, -0.06968, -0.61544, 5.30408, 3.98192, 0.07384, 1.54960, 4.06720, 0.45048, 2.57456, 7.04328, 1.64072, 2.83576, 2.44760, 4.22840, 6.32536, 0.18424, 0.95256, 4.69024, 5.25800, 1.66920, 3.89008, 4.64128, 0.43728, 3.15824, 0.35560, 2.09704, 7.03984, 7.13752, 0.83640, 2.63864, -0.62744, 6.64240, 1.05056, 1.45264, 6.26824, 5.71104, 2.18056, -0.18240, 4.26096, 3.40840, 1.65960, 3.66640, 4.17248, 1.61944, 0.45624, 5.40328, 5.01400, 4.35712, -0.52176, 0.55720, 1.09208, -0.35032, 2.42904, 1.67488, 6.21360, 6.42264, -0.56240, 1.92344, 1.76880, 0.38584, 2.94968, 4.02616, 5.09936, 6.16928, 0.13368, 6.87656, 3.73112, 4.09616, 0.58224, 7.07080, 2.60096, 4.55792, 4.91496, 4.02120, 1.55648, 0.38624, 0.09968, 5.12928, 5.38552, -0.14792, 3.30696, 5.98192, 5.84112, 3.79000, 7.28200, 2.92104, -0.12168, 6.14240, 3.45272, 0.21008, 3.28312, 3.36880, 0.87608, 1.14888, 4.54560, 5.97800, 0.07280, 4.23640, -0.25800, 2.65880, -0.38464, 5.64496, -0.00864, 1.15808, -0.50472, 0.92080, 2.99072, 1.41280, 3.70256, 0.43632, 4.90456, 1.51096, 7.21520, 3.36024, 3.51312, 4.10872, 3.53424, 4.57088, 1.60248, 1.51760, 6.46240, 5.62552, 1.93408, 2.88712, 0.59824, 3.36392, 6.77608, 4.60576, 6.11392, 2.80656, 3.53128, 2.81800, 1.56672, 2.97120, 4.60296, 4.93376, 4.05208, 6.54216, 1.67656, -0.04072, 6.37000, 4.02336, 1.32976, 4.99040, 3.11976, 5.62544, 3.48656, 2.31432, 1.71704, 4.66264, 4.10344, 2.15032, 5.22112, -0.69224, 2.71608, 7.20856, 5.63312, 0.65536, 0.12864, 4.88544, 1.27200, 2.84016, 7.24824, 3.16328, 2.26544, 6.39216, 0.01832, 5.36344, 5.97456, 2.63144, 4.16824, 3.62856, -0.02200, 3.99360, 5.43744, 2.90744, 1.01976, 5.27976, -0.10112, 1.18800, 6.06552, 2.56688, 2.88288, 1.66056, 1.90168, 6.26872, 1.58360, 4.89144, 1.95688, 5.61112, 6.07032, 7.17096, 5.30800, 3.07528, 0.77632, 5.78792, 5.25768, 3.28296, 2.67496, -0.15960, 4.46120, 2.02616, 1.37648, 2.91520, 0.65480, -0.39344 ];
  elseif a == 'ud-3'
        arr = [ 6.31552, 4.11264, 6.56736, -0.48704, 0.43344, 0.60616, 0.90928, 5.76784, 6.62000 6.50536, -0.06320, 4.48152, 1.29048, 0.01656, 3.42600, 4.59536, 4.95592, 2.11648 1.07640, 5.57536, 1.45536, 6.79088, 6.59208, 0.37488, 2.33232, 1.90840, 1.17848 0.49480, 6.47288, 6.96040, 6.07528, 5.53096, 2.33072, 3.07584, 1.08968, 2.48720 6.33360, 1.14640, 1.17712, 4.08704, 5.41472, 1.88368, 3.61904, 6.86976, 2.24624 3.85440, 3.68752, 3.78248, 6.53288, 3.31800, 5.03600, 2.00872, 5.79824, 3.23256 5.09064, 2.22064, 5.92912, 3.36816, 0.60736, 4.61112, 4.09192, 6.24808, 6.29184 6.97784, 7.19656, 1.95384, -0.42848, 4.97408, 4.11192, 4.33032, 5.09344, 0.28168 5.15720, 1.85880, 0.67072, 2.46776, 0.52416, -0.23392, 2.25904, 1.72624, 7.20104 0.10808, 5.30144, 3.00144, 4.38832, 7.01656, 3.00272, 0.46944, 1.89472, 6.84232 -0.51504, 7.13128, 0.48152, 3.97552, 0.25880, -0.33232, 7.15312, 4.35944, 3.67256 2.06088, 2.43432, 2.87704, 1.84080, 0.22936, 3.69592, 1.20304, 0.15944, 3.86696 2.31088, 6.51296, 1.91040, 0.71304, -0.39056, 1.02632, 3.53840, 1.14864, 1.59424 1.21120, 6.30400, 3.31000, 4.15016, 0.44560, 4.75040, 1.24392, 1.93936, 4.10968 5.69208, 2.26176, 0.72632, 5.15096, 5.14464, -0.04216, 6.96768, 1.65728, 6.93440 1.84528, 2.96392, 1.27104, 6.26928, 1.59512, 5.68664, -0.35936, 2.78648, 1.15728 0.42272, 0.85120, 6.88056, 4.27968, 0.44752, 6.06968, 0.91632, 2.80912, 5.19872 5.39200, 6.13736, 6.26920, 3.72552, 5.78648, 4.01912, 0.06312, 5.04096, 6.52192 5.62768, -0.37712, 0.49000, 2.67504, 5.74976, 3.87840, 3.95752, 4.07392, 4.96000 1.08176, 5.18920, 3.07328, 5.69696, 2.26976, 5.53432, 1.39512, 0.16264, 3.91384 ];
  endif

endfunction