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Creating samples from a well-specified population using a probabilistic method and/or producing random numbers from a specified distribution. As this tag is ambiguous, please consider [survey-sampling] for the former and [monte-carlo] or [simulation] for the latter. For questions regarding creating random samples from known distributions, please consider using the [random-generation] tag.

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Piecewise continuous power law distribution sampling

I am trying to sample a piecewise power law distribution: $$ \ f(x) = \begin{cases} a_1x^{-\alpha_1} & \text{if } x_1 \leq x \leq \tilde{x} \newline a_2x^{-\alpha_2} & \text{if } \tilde{x} \leq x …
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