PTL: Polynomial-Tail Laplace

In LCA: Localised Co-Dependency Analysis

Description

Probability density and distribution functions for Polynomial-Tail Laplace distribution

Usage

dPTL(x,alpha,beta,gamma)
pPTL(q,alpha,beta,gamma)

Arguments

x,q	Numeric vector of quantiles
alpha	Linear tail adjustment coefficient for PTL distribution
beta	Exponential decay term for PTL distribution, similar to beta parameter in Laplace distribution
gamma	Polynomial tail adjustment coefficient for PTL distribution

Details

The PTL distribution has density

f(x) = ≤ft\{\begin{array}{cc} 0 & x < -2\\ \displaystyle \frac{α(\frac{x^2}{2}+2x+2) + β(e^{\frac{x}{β}}-e^{\frac{-2}{β}}) + γ(\frac{x^3}{3}+4x+\frac{16}{3})}{4α + 2β(1-e^{\frac{-2}{β}}) + \frac{32γ}{3}} & -2 ≤q x ≤q 0\\ \displaystyle \frac{α(2x-\frac{x^2}{2}-2) + β(e^{\frac{-2}{β}}-e^{\frac{x}{β}}) + γ(4x-\frac{x^3}{3}-\frac{16}{3})}{4α + 2β(1-e^{\frac{-2}{β}}) + \frac{32γ}{3}} & 0 < x ≤q 2\\ 1 & x > 2 \end{array}\right.

Value

dnorm gives the density, pnorm gives the distribution function.

The length of the result is the maximum of the lengths of the numerical parameters for the other functions. The numerical parameters are recycled to the length of the result.

Author(s)

Ed Curry [e-mail]

LCA documentation built on May 2, 2019, 8:26 a.m.