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I'm not sure if this is exactly what you want, but there's a book called Practical Statistics for Astronomers by J.V. Wall and C.R. Jenkins that might fit the bill. According to the Cambridge University Press website (the book is a part of Cambridge Observing Handbooks for Research Astronomers): Astronomy needs statistical methods to interpret data, but ...


The Maxwell-Boltzmann distribution and the Boltzmann distributions are probability distributions, i.e. functions $\rho(\vec x,\vec v)$ of velocity and position of a particle, that say what is the probability density that the velocity and position belong to the small cube around the given value of them. The Boltzmann distribution is the more general one, $\...


To me, using the distance to measure 2 dimensional data is dubious, especially if the events are near to the reconstructed position (supposed 0 distance). Say if the events form a circle (the circle is perfect gaussian). The distribution will not be anymore gaussian since the blue area (in the drawing) will be lesser than the yellow:


As explained in the comments, for a given MC event, the errors $\delta x$ and $\delta y$ for the two reconstruction methods A1 and A2 are uncorrelated. Therefore, no extra information is gained by using both reconstructions. We should just use the better one. Now, what does "better" mean. As stated in the OP, for both reconstructions, the distributions of $\...

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