Question

有没有人知道是否有现有的代码来计算矢量限制和相关性的cdf？内置选项mvncdf不允许rho在行上变化。

编辑：

一个有效的例子是对每行x使用相同的mu和V，即

x = rand(10,2);
mu = [0 0];
sig = [1 .5; .5 1];

mvncdf(x,mu,sig);

但是，没有办法为x的每一行输入不同的mu和sig。

Answer 1

如果有人需要这个，这里是一个完全矢量化的版本。在非常高的相关性下不对其精确度进行修改，但对于rho <0.9应该没有问题。

function p = bvnl( dh, dk, r )
%BVNL
%  A function for computing bivariate normal probabilities.
%  bvnl calculates the probability that x < dh and y < dk. 
%    parameters  
%      dh 1st upper integration limit
%      dk 2nd upper integration limit
%      r   correlation coefficient
%  Example:
%    p = bvnl( 3, 1, .35 )
%

% Original author Alan Genz, modified to be vectorized.

      p = bvnu( -dh, -dk, r );
%
%   end bvnl
%
function p = bvnu( dh, dk, r )
%BVNU
%  A function for computing bivariate normal probabilities.
%  bvnu calculates the probability that x > dh and y > dk. 
%    parameters  
%      dh 1st lower integration limit
%      dk 2nd lower integration limit
%      r   correlation coefficient
%  Example: p = bvnu( -3, -1, .35 )
%  Note: to compute the probability that x < dh and y < dk, 
%        use bvnu( -dh, -dk, r ). 
%

  if dh ==  inf | dk ==  inf, 
      p = 0;
  elseif dh == -inf, 
      if dk == -inf, 
          p = 1; 
      else
          p = phid(-dk);
      end
  elseif dk == -inf, 
      p = phid(-dh);
  elseif r == 0, 
      p = phid(-dh)*phid(-dk);  
  else
      tp = 2*pi; 
      h = dh; 
      k = dk;
      hk = h.*k; 
      bvn = 0; 
    if abs(r) < 0.3      % Gauss Legendre points and weights, n =  6
      w(1:3) = [0.1713244923791705 0.3607615730481384 0.4679139345726904];
      x(1:3) = [0.9324695142031522 0.6612093864662647 0.2386191860831970];
    elseif abs(r) < 0.75 % Gauss Legendre points and weights, n = 12
      w(1:3) = [.04717533638651177 0.1069393259953183 0.1600783285433464];
      w(4:6) = [0.2031674267230659 0.2334925365383547 0.2491470458134029];
      x(1:3) = [0.9815606342467191 0.9041172563704750 0.7699026741943050];
      x(4:6) = [0.5873179542866171 0.3678314989981802 0.1252334085114692];
    else                 % Gauss Legendre points and weights, n = 20
      w(1:3) = [.01761400713915212 .04060142980038694 .06267204833410906];
      w(4:6) = [.08327674157670475 0.1019301198172404 0.1181945319615184];
      w(7:9) = [0.1316886384491766 0.1420961093183821 0.1491729864726037];
      w(10) =   0.1527533871307259;
      x(1:3) = [0.9931285991850949 0.9639719272779138 0.9122344282513259];
      x(4:6) = [0.8391169718222188 0.7463319064601508 0.6360536807265150];
      x(7:9) = [0.5108670019508271 0.3737060887154196 0.2277858511416451];
      x(10) =   0.07652652113349733;
    end, w = [w  w]; x = [1-x 1+x]; 

    hs = ( h.*h + k.*k )/2; 
    asr = asin(r)/2;  
    sn = sin(asr*x); 
    bvn = exp(bsxfun(@minus,bsxfun(@times,sn,hk),hs)./(1-sn.^2))*w';
    bvn = bvn.*asr./tp + phid(-h).*phid(-k);  

    p = max( 0, min( 1, bvn ) );
  end
%
%   end bvnu
%
function p = phid(z), p = erfc( -z/sqrt(2) )/2; % Normal cdf
%
% end phid
%

Matlab矢量化双变量标准正常CDF

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