R/pareto.R

In BayesForge: Bayesian Inference using 'numpyro' and 'XLA'

#' @title Samples from a Pareto distribution.
#' @description
#' The **Pareto distribution**, named after economist Vilfredo Pareto, is a **power-law** probability distribution used to describe phenomena with "rich-get-richer" or "heavy-tail" properties - for example, income distribution, city sizes, or wealth concentration.
#'It is characterized by:
#'  * a **scale parameter** \deqn{  x_m > 0 } (the minimum possible value), and
#'  * a **shape parameter** \deqn{  \alpha > 0 } (which controls the tail heaviness).
#'A random variable \deqn{ X \sim \text{Pareto}(\alpha, x_m) } takes values \deqn{  x \ge x_m }.
#'
#' @param scale A numeric vector or single number representing the scale parameter of the Pareto distribution. Must be positive.
#' @param alpha A numeric vector or single number representing the shape parameter of the Pareto distribution. Must be positive.
#' @param shape A numeric vector. When \code{sample=FALSE} (model building), this is used with `.expand(shape)` to set the distribution's batch shape. When \code{sample=TRUE} (direct sampling), this is used as `sample_shape` to draw a raw JAX array of the given shape.
#' @param event An integer representing the number of batch dimensions to reinterpret as event dimensions (used in model building).
#' @param mask A logical vector. Optional boolean array to mask observations.
#' @param create_obj A logical value. If `TRUE`, returns the raw BI distribution object instead of creating a sample site. This is essential for building complex distributions like `MixtureSameFamily`.
#' @param validate_args Logical: Whether to validate parameter values.  Defaults to `reticulate::py_none()`.
#' @param sample A logical value that controls the function's behavior. If `TRUE`,
#'   the function will directly draw samples from the distribution. If `FALSE`,
#'   it will create a random variable within a model. Defaults to `FALSE`.
#' @param seed An integer used to set the random seed for reproducibility when
#'   `sample = TRUE`. This argument has no effect when `sample = FALSE`, as
#'   randomness is handled by the model's inference engine. Defaults to 0.
#' @param obs A numeric vector or array of observed values. If provided, the
#'   random variable is conditioned on these values. If `NULL`, the variable is
#'   treated as a latent (unobserved) variable. Defaults to `NULL`.
#' @param name A character string representing the name of the random variable
#'   within a model. This is used to uniquely identify the variable. Defaults to 'x'.
#' @param to_jax Boolean. Indicates whether to return a JAX array or not.
#'
#' @return
#'  - When \code{sample=FALSE}, a BI Pareto distribution object (for model building).
#'
#'  - When \code{sample=TRUE}, a JAX array of samples drawn from the Pareto distribution (for direct sampling).
#'
#'  - When \code{create_obj=TRUE}, the raw BI distribution object (for advanced use cases).
#'
#' @seealso \url{https://num.pyro.ai/en/stable/distributions.html#pareto}
#'
#' @examples
#' \donttest{
#' library(BayesForge)
#' m=importBF(platform='cpu')
#' bf.dist.pareto(scale = c(0.2, 0.5, 0.8), alpha = c(-1.0, 0.5, 1.0), sample = TRUE)
#' }
#' @export
bf.dist.pareto=function(scale, alpha, validate_args=py_none(), name='x', obs=py_none(), mask=py_none(), sample=FALSE, seed = py_none(), shape=c(), event=0, create_obj=FALSE, to_jax = TRUE) {
     shape=do.call(tuple, as.list(as.integer(shape)))
     if (!.BF_env$.py$is_none(seed)){seed=as.integer(seed);}
     .BF_env$.bf_instance$dist$pareto(
       scale = .BF_env$jnp$array(scale),
       alpha = .BF_env$jnp$array(alpha),
       validate_args= validate_args,  name= name,  obs= obs,  mask= mask,  sample= sample,  seed= seed,  shape= shape,  event= event,  create_obj= create_obj,   to_jax = to_jax)
}