从两个变量创建和采样联合分布

Question

I have a question that's been bothering me.

I have a pandas dataframe with two columns corresponding to a and b coefficients which depend on each row (they are not independent):

            a          b
0   13.967158   2.370449
1   12.375649   2.199846
2   12.005615   2.268646
3   12.030142   1.542835
4   12.119529   1.570510
... ... ...
63  12.215212   1.677631
64  12.221597   1.483855
65  12.758342   2.311847
66  11.712199   2.505323
67  12.393513   1.402272

These can be plotted as:

From this, I need to generate random samples from the joint distribution of a and b variables, but I'm not sure how to do it. I tried generating random samples from a normal distribution for each one of these variables, using np.random.normal(mean_variable, sd_variable, 1000) . However, after creating these values, I'm not sure how to join them. Any ideas in this regard would be very useful. Regards

Answer 1

You need the function that samples a multivariate normal distribution. This function requires a 1D array of the means and a 2D array of covariances, both of which are readily calculated from your dataframe:

numpy.random.multivariate_normal(df.mean(), df.cov())
#array([11.69993186,  1.64400885])