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Applied and theoretical statistics: e.g. statistical inference, regression, time series, multivariate analysis, data analysis, Markov chain Monte Carlo, design of experiments.
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Analogues of Kac-Bernstein characterisation theorem for non-normal distributions
Let $X,Y$ be two independent random variables.
The Kac-Bernstein theorem states that if $X+Y,X-Y$ are also independent, then $X,Y$ are Normal.
Are there analogues of this theorem for non-normal, conti …