ll4: Log-Logistic Transformation (LL4-like)

In beezdemand: Behavioral Economic Easy Demand

Log-Logistic Transformation (LL4-like)

Description

Applies a log-logistic like transformation, specifically log_base(x^lambda + 1) / lambda. This transformation is useful for compressing data that spans several orders of magnitude while handling zero values gracefully (as x=0 yields 0). It's a variation related to the Box-Cox transformation or a generalized logarithm.

Usage

ll4(x, lambda = 4, base = 10)

Arguments

x	A numeric vector or scalar of non-negative values to be transformed.
lambda	A positive numeric scalar, the lambda parameter of the transformation. Controls the curvature. Default is 4.
base	A positive numeric scalar, the base of the logarithm. Default is 10.

Value

A numeric vector or scalar of the transformed values. Returns NaN for x < 0 if lambda results in non-real numbers (e.g., even root of negative). However, the intended domain is x >= 0.

Examples

ll4(0)
ll4(1)
ll4(10)
ll4(100)
ll4(c(0, 1, 10, 100, 1000))

# Using a different lambda or base
ll4(10, lambda = 2)
ll4(10, base = exp(1)) # Natural log base

beezdemand documentation built on March 3, 2026, 9:07 a.m.