kstats-distributions/org.oremif.kstats.distributions/ParetoDistribution

ParetoDistribution

class ParetoDistribution(val shape: Double = 1.0, val scale: Double = 1.0) : ContinuousDistribution(source)

The Pareto Type I distribution, defined by its shape (α) and scale (xm) parameters.

The Pareto distribution is a heavy-tailed, right-skewed continuous distribution originally used to model the distribution of wealth. It is widely used in actuarial science, reliability engineering, and modeling phenomena that follow power laws. The distribution has support on [scale, +∞).

Example:

val dist = ParetoDistribution(shape = 2.0, scale = 1.0)
dist.pdf(1.0)       // 2.0 (peak density at the scale)
dist.cdf(2.0)       // 0.75
dist.quantile(0.5)  // 1.4142... (√2)

Constructors

ParetoDistribution

constructor(shape: Double = 1.0, scale: Double = 1.0)

Types

object Companion

Properties

open override val entropy: Double

The Shannon entropy of this distribution in nats. Equal to ln(xm/α) + 1/α + 1.

open override val kurtosis: Double

The excess (Fisher) kurtosis of this distribution. Defined only for α > 4.

open override val mean: Double

The mean of this distribution. Equal to α*xm/(α-1) if α > 1, else +∞.

val scale: Double

the minimum value / location (xm). Must be positive. Defaults to 1.0.

val shape: Double

the tail index (α). Must be positive. Defaults to 1.0.

open override val skewness: Double

The skewness of this distribution. Defined only for α > 3.

open override val variance: Double

The variance of this distribution. Equal to xm²·α / ((α-1)²·(α-2)) if α > 2, else +∞.

Functions

open override fun cdf(x: Double): Double

Returns the cumulative distribution function value at x for this Pareto distribution.

open override fun logPdf(x: Double): Double

Returns the natural logarithm of the probability density at x for this Pareto distribution.

open override fun pdf(x: Double): Double

Returns the probability density at x for this Pareto distribution.

open override fun quantile(p: Double): Double

Returns the quantile (inverse CDF) for the given probability p.

open override fun sample(random: Random): Double

Draws a single random value from this Pareto distribution using inverse CDF sampling.

open override fun sf(x: Double): Double

Returns the survival function value at x for this Pareto distribution.