20.2 Pareto type 2 distribution
20.2.1 Probability density function
If \(\mu \in \mathbb{R}\), \(\lambda \in \mathbb{R}^+\), and \(\alpha \in \mathbb{R}^+\), then for \(y \geq \mu\), \[ \mathrm{Pareto\_Type\_2}(y|\mu,\lambda,\alpha) = \ \frac{\alpha}{\lambda} \, \left( 1+\frac{y-\mu}{\lambda} \right)^{-(\alpha+1)} \! . \]
Note that the Lomax distribution is a Pareto Type 2 distribution with \(\mu=0\).
20.2.2 Sampling statement
y ~ pareto_type_2(mu, lambda, alpha)
Increment target log probability density with pareto_type_2_lupdf(y | mu, lambda, alpha).
Available since 2.5
20.2.3 Stan functions
real pareto_type_2_lpdf(reals y | reals mu, reals lambda, reals alpha)
The log of the Pareto Type 2 density of y given location mu, scale
lambda, and shape alpha
Available since 2.18
real pareto_type_2_lupdf(reals y | reals mu, reals lambda, reals alpha)
The log of the Pareto Type 2 density of y given location mu, scale
lambda, and shape alpha dropping constant additive terms
Available since 2.25
real pareto_type_2_cdf(reals y, reals mu, reals lambda, reals alpha)
The Pareto Type 2 cumulative distribution function of y given location
mu, scale lambda, and shape alpha
Available since 2.5
real pareto_type_2_lcdf(reals y | reals mu, reals lambda, reals alpha)
The log of the Pareto Type 2 cumulative distribution function of y
given location mu, scale lambda, and shape alpha
Available since 2.18
real pareto_type_2_lccdf(reals y | reals mu, reals lambda, reals alpha)
The log of the Pareto Type 2 complementary cumulative distribution
function of y given location mu, scale lambda, and shape alpha
Available since 2.18
R pareto_type_2_rng(reals mu, reals lambda, reals alpha)
Generate a Pareto Type 2 variate with location mu, scale lambda, and
shape alpha; may only be used in transformed data and generated quantities blocks.
For a description of argument and return types, see section
vectorized PRNG functions.
Available since 2.18