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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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Order statistics (e.g., minimum) of infinite collection of chi-square variates?
It might be best to look at the hazard function, since the hazard function of min of independent variates is the sum of individual hazard functions.
Hence the hazard function of your distribution is …