This module provides the following distributions for JAGS:
PARETO TYPE I: dpar1(alpha, sigma)
$$
p(x) = \alpha \sigma^{\alpha} x^{-\left(\alpha+1 \right)}
$$
$$\alpha > 0, \sigma > 0, x > \sigma$$
PARETO TYPE II: dpar2(alpha, sigma, mu)
$$
p(x) = \frac{\alpha}{\sigma} \left( \frac{\alpha + x - \mu}{\sigma}\right)^{-\left(\alpha+1\right)}
$$
$$\alpha > 0, \sigma > 0, x > \mu$$
PARETO TYPE III: dpar3(sigma, mu, gamma)
$$
p(x) = \frac{\frac{x-\mu}{\sigma}^{\frac{1}{\gamma}-1} \left(\frac{x-\mu}{\sigma}^{\frac{1}{\gamma}} +1\right)^{-2}}{\gamma \sigma}
$$
$$\sigma > 0, \gamma > 0, x > \mu$$
PARETO TYPE IV: dpar4(alpha, sigma, mu, gamma)
$$
p(x) = \frac{\alpha \frac{x-\mu}{\sigma}^{\frac{1}{\gamma}-1} \left(\frac{x-\mu}{\sigma}^{\frac{1}{\gamma}} +1\right)^{-\left(\alpha+1\right)}}{\gamma \sigma}
$$
$$\alpha > 0, \sigma > 0, \gamma > 0, x > \mu$$
LOMAX: dlomax(alpha, sigma)
$$
p(x) = \frac{\alpha}{\sigma} \left(1 + \frac{x}{\sigma}\right)^{-\left(\alpha+1\right)}
$$
$$\alpha > 0, \sigma > 0, x > 0$$
GENERALISED PARETO: dgenpar(sigma, mu, xi)
$$
p(x) = \frac{1}{\sigma} \left(1 + \xi \left(\frac{x-\mu}{\sigma}\right)\right)^{-\left(\frac{1}{\xi}+1\right)}
$$
For \(\xi=0\):
$$
p(x) = \frac{1}{\sigma} e^{\frac{-\left(x-\mu\right)}{\sigma}}
$$
$$\sigma > 0, x > \mu$$
DUMOUCHEL: dmouch(sigma)
$$
p(x) = \frac{\sigma}{\left(x+\sigma\right)^2}
$$
$$\sigma > 0, x > 0$$
HALF CAUCHY: dhalfcauchy(sigma)
$$
p(x) = \frac{2 \sigma}{\pi \left(x^2+\sigma^2\right)}
$$
$$\sigma > 0, x > 0$$
For an easier to read version of these PDF equations, see the userguide vignette.