The Exponential Power Distribution¶
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gsl_ran_exppow(a, b)¶
This function returns a random variate from exponential power distribution with scale parameter
aand exponentb. The distribution is,\[p(x) dx = {1 \over 2 a \Gamma(1+1/b)} \exp(-|x/a|^b) dx\]for \(x \geq 0\). For \(b = 1\) this reduces to the Laplace distribution. For \(b = 2\) it has the same form as a Gaussian distribution, but with \(a = \sqrt{2} \sigma\).
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gsl_ran_exppow_pdf(x, a, b)¶
This function computes the probability density \(p(x)\) at \(x\) for an exponential power distribution with scale parameter
aand exponentb, using the formula given above.
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gsl_ran_exppow_P(x, a, b)¶
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gsl_ran_exppow_Q(x, a, b)¶
These functions compute the cumulative distribution functions \(P(x), Q(x)\) for the exponential power distribution with parameters
aandb.