- #1
codiloo
- 2
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Given a bivariate gaussian distribution,
I'm attempting to find the probability p for which
the ellipse of all points (x,y) for which P(X = x, Y= y) = p contains
a given % of the samples drawn from the distribution.
I want the 2d equivalent for the 1 dimensional case:
given a normal distribution N(0,1):
e.g interval between points with p = 0.24197072 contains 68.2% of all samples
e.g interval between points with p = 0.05399097 contains 95.4% of all samples
e.g interval between points with p = 0.00013383 contains 99.6% of all samples
in two dimensions these interval boundries become an ellipse and I'm interested in finding the p value corresponding to a given % (contained samples in contour ellipse with p) value in the 2 dimensional case.
Some extra info:
A matlab, python (using numpy, scipy?) numerical approximation is ok, I don't need an analytic formula.
Actually I just want to draw the ellipses containing 75%, 95%, 99% of the samples in python (using matlibplot) for a given gaussian distribution (varying mean & covariance). I know how to do this if I obtain p first (contour plots).
Thank you for reading my question and I hope you can help.
I'm attempting to find the probability p for which
the ellipse of all points (x,y) for which P(X = x, Y= y) = p contains
a given % of the samples drawn from the distribution.
I want the 2d equivalent for the 1 dimensional case:
given a normal distribution N(0,1):
e.g interval between points with p = 0.24197072 contains 68.2% of all samples
e.g interval between points with p = 0.05399097 contains 95.4% of all samples
e.g interval between points with p = 0.00013383 contains 99.6% of all samples
in two dimensions these interval boundries become an ellipse and I'm interested in finding the p value corresponding to a given % (contained samples in contour ellipse with p) value in the 2 dimensional case.
Some extra info:
A matlab, python (using numpy, scipy?) numerical approximation is ok, I don't need an analytic formula.
Actually I just want to draw the ellipses containing 75%, 95%, 99% of the samples in python (using matlibplot) for a given gaussian distribution (varying mean & covariance). I know how to do this if I obtain p first (contour plots).
Thank you for reading my question and I hope you can help.