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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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Distribution of the sum of the $m$ smallest values in a sample of size $n$

Let $\mathbf X = [X_1, X_2, \ldots, X_n]^\mbox{T}$ be a vector random variable drawn from a known distribution with CDF $F(x)$. The CDF for the minimum value in $\mathbf X$ is clearly $P[\min_{i=1\ld …
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