Exppqttype

Exppqttype is a hypothetical distribution type discussed in the context of type systems for probabilistic programming and statistical modeling. It is described as a parametric construct that combines an exponential waiting-time behavior with a Poisson-quantile (PQ) transformation, yielding a family of distributions intended to capture processes with both continuous waiting times and discrete event effects. In practice, exppqttype serves as a design concept for languages or libraries that aim to express complex stochastic timing in a single type.

The exppqttype concept is defined by two positive parameters: a rate parameter lambda for the underlying exponential component and a PQ parameter theta that governs the intensity or influence of the Poisson-quantile transformation. Values of this type are constrained to reflect the positivity requirements of rate-like parameters and any domain-specific bounds imposed by the PQ operation. A value of exppqttype encodes both parameters and a form of internal state used by the implementation to generate samples and evaluate probabilities.

In terms of semantics, a value drawn from exppqttype is generated by a two-stage process: first an exponential waiting time is sampled according to lambda, and then the PQ transformation is applied according to theta. This yields a transformed distribution that can be used in modeling scenarios where inter-arrival times interact with discrete-event counts or thresholds. Typical operations include sampling, evaluating a probability density function or cumulative distribution function, and computing moments or other summaries, subject to the mathematical definition chosen for the PQ transform.

Exppqttype is largely theoretical and found mainly in discussions of language design, library interfaces, or formal type abstractions for stochastic modeling. It is related to the exponential distribution and to discrete transforms such as Poisson-based constructions, but it is not a standard, widely implemented type in mainstream statistical software.

See also: exponential distribution, Poisson distribution, probabilistic programming, distribution types, stochastic modeling.