Natural logarithm of the probability density of the Pearson type VII distribution

The red curve shows the limiting density with infinite kurtosis; the blue curve shows the density with kurtosis equal to 2; the black curve shows the limiting (normal) density with zero kurtosis. The gray curves (between the blue and the black) show densities with kurtoses 1, 1/2, 1/4, 1/8, and 1/16.

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For further background and gnuplot source code, see Image:Pearson type VII distribution PDF.png.

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