Expectation thinning operators based on linear fractional probability generating functions

TL;DR

This paper introduces a new two-parameter expectation thinning operator based on linear fractional probability generating functions, and explores its application to defining and analyzing integer-valued autoregressive processes with novel distributional properties.

Contribution

The paper presents a new expectation thinning operator, applies it to develop a novel INAR(1) process, and introduces a generalized monotonicity concept for distributions on positive integers.

Findings

Describes distributional properties of the new INAR(1) process.

Revisits the Bernoulli-geometric INAR(1) process from prior work.

Introduces a stationary INAR(1) process with a compound negative binomial distribution.

Abstract

We introduce a two-parameter expectation thinning operator based on a linear fractional probability generating function. The operator is then used to define a first-order integer-valued autoregressive \inar1 process. Distributional properties of the \inar1 process are described. We revisit the Bernoulli-geometric \inar1 process of Bourguignon and Wei{\ss} (2017) and we introduce a new stationary \inar1 process with a compound negative binomial distribution. Lastly, we show how a proper randomization of our operator leads to a generalized notion of monotonicity for distributions on \bzp.