= Power-law distribution
{title2=$p_X(x)=Cx^{-\beta}$}
A <power-law distribution> uses a <power law> for a <probability mass function> or a <probability density> on a specified range. For a continuous model with $p_X(x)=Cx^{-\beta}$ on $x\geq x_{\min}>0$ and zero below it, the total <integral> is finite exactly when $\beta>1$. Normalization then requires $C=(\beta-1)x_{\min}^{\beta-1}$, giving a <Pareto distribution> with shape parameter $\alpha=\beta-1$. Discrete models instead normalize a <sum>. The support and normalizing coefficient are part of the model, and a <power law> for its <tail probability> uses a different exponent from its <probability density>.
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