Pkerroin

Pkerroin is a term used in certain statistical and mathematical modelling contexts to denote a multiplicative coefficient that relates a dependent variable to one or more predictors in a power-law or multiplicative form. In its simplest form, a Pkerroin p is defined in the model Y = α X^p, where α is a scale parameter and p is the Pkerroin. In log-transformed coordinates, this becomes log Y = log α + p log X, making p the slope of the relationship on a log–log plot. The Pkerroin therefore represents the elasticity of Y with respect to X: it measures the proportional change in Y for a proportional change in X, and remains constant across scales in a pure power-law model. A positive p indicates a direct, increasing relationship, while a negative p indicates an inverse relationship; the magnitude indicates the strength of the response.

Estimation is typically done by nonlinear regression on the original scale or by linear regression after log transformation, assuming Y and X are positive. Confidence intervals for p are derived from standard errors of the estimate. Applications of the Pkerroin appear across disciplines, including economics for allometric-like growth in demand models, biology and ecology for allometric scaling, and physics for power-law phenomena. The term is not universally standardized, and different authors may discuss analogous quantities under related names, such as elasticity, exponent, or allometric coefficient. See also elasticity and power-law models.