问题描述
G'day，
我正在尝试通过以下公式为2个随机变量(X1，X2)计算双变量正态分布的较低尾部概率:
I am trying to compute the lower tail probability for the bivariate Normal distribution given by the following formula for 2 random variables (X1, X2):
其中X1 = -1.23，X2 = -2.75，rho = 0.65.我很好奇如何解决这个问题?第一项只是计算，但您将如何攻击积分?有人可以向我提供一些代码或提示吗，或者有可能解决方案? X是对数正态分布随机变量.
Where X1 = -1.23, X2 = -2.75 and rho = 0.65. I am very curious how to solve this problem?The first term it's just calculations but how would you attack the integrals?Can someone provide me with some code or hints or if it's possible a solution? X's are log normal distributed random variables.
此外；如何将其扩展到多个维度.如果我们说我们有一个变量X_3 = -1.78.你会怎么攻击?
Furthermore; how would extend it to multiple dimensions. If we say we have a variable X_3 = -1.78. How would you attack that?
推荐答案
您可以将mvncdf函数用作此处.对于您的情况，您可以编写:
You can use mvncdf function as here in documentation. For your case you can write:
p = mvncdf([X1, X2], [0, 0], [1 rho; rho 1]);
基于rho的sigma是[1 rho; rho 1]，正如您所说的平均值是[0, 0].如果要对此一概而论，只需将X的尺寸增加到[X1, X2, X3]，将其尺寸增大到[0, 0, 0]，然后定义新的sigma(3x3矩阵)即可.
The sigma base on rho is [1 rho; rho 1] and as you said mean is [0, 0]. If you want to generalize this one, just you need to increase the dimension of X to [X1, X2, X3], mean to [0, 0, 0], and define your new sigma (a 3x3 matrix).
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