The Pareto distribution is parameterized by a scale and a concentration parameter.

tfd_pareto(
concentration,
scale = 1,
validate_args = FALSE,
allow_nan_stats = TRUE,
name = "Pareto"
)

## Arguments

concentration Floating point tensor. Must contain only positive values. Floating point tensor, equivalent to mode. scale also restricts the domain of this distribution to be in [scale, inf). Must contain only positive values. Default value: 1. Logical, default FALSE. When TRUE distribution parameters are checked for validity despite possibly degrading runtime performance. When FALSE invalid inputs may silently render incorrect outputs. Default value: FALSE. Logical, default TRUE. When TRUE, statistics (e.g., mean, mode, variance) use the value NaN to indicate the result is undefined. When FALSE, an exception is raised if one or more of the statistic's batch members are undefined. name prefixed to Ops created by this class.

## Value

a distribution instance.

## Details

Mathematical Details

The probability density function (pdf) is,

pdf(x; alpha, scale, x >= scale) = alpha * scale ** alpha / x ** (alpha + 1)
#'
where concentration = alpha.

Note that scale acts as a scaling parameter, since
Pareto(c, scale).pdf(x) == Pareto(c, 1.).pdf(x / scale).
The support of the distribution is defined on [scale, infinity)`.