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 INAR (1) process. Distributional properties of the INAR (1) process are described. We revisit the Bernoulli-geometric INAR (1) process of Bourguignon and Weiß (Test 26(4):847–868, 2017. https://doi.org/10.1007/s11749-017-0536-4) and we introduce a new stationary INAR (1) 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 \(\mathbf{Z}_+\).
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Aly, EE.A.A., Bouzar, N. Expectation Thinning Operators Based on Linear Fractional Probability Generating Functions. J Indian Soc Probab Stat 20, 89–107 (2019). https://doi.org/10.1007/s41096-018-0056-x
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DOI: https://doi.org/10.1007/s41096-018-0056-x