gammairration

Gammairration is a term used in theoretical modeling to describe a hypothetical measure of how gamma-distributed fluctuations in an input signal propagate into irregular, burst-like output dynamics in a complex system. The word combines gamma, in reference to the gamma distribution, with irration, signaling irregular growth patterns.

In a stochastic model where inputs X_t follow a Gamma(k, θ) distribution, gammairration G is a dimensionless quantity that expresses the amplification of input variability in the output over time. Practically, G can be viewed as the long-run ratio between the variability of the cumulative output and the variability of the input, with higher values indicating greater burstiness.

G is nonnegative; it increases as the shape parameter k decreases (heavier tails) and as scale θ grows. The exact form is not standardized and may depend on the modeling framework, so gammairration is used descriptively rather than as a fixed invariant.

It appears in exploratory models of queueing, network traffic, finance, and biology where inputs are gamma-distributed. It offers a simple language to compare systems by their propensity to convert input variability into output irregularity.

In a two-state producer-consumer model with gamma-distributed arrivals, lowering k raises gammairration, producing longer quiet periods followed by bursts of activity.

See also: gamma distribution; burstiness; stochastic process.

References: The concept is not standardized; readers may consult standard texts on gamma processes and burstiness for background.