First Order Autoregressive Gamma Sequences and Point Processes.

摘要: It is shown that there an innovation process {∊ n } such the sequence of random variables {X generated by linear, additive first-order autoregressive scheme X = pXn-1 + ∊ are marginally distributed as gamma (λ, k) if 0 ≦p ≦ 1. This useful for modelling a wide range observed phenomena. Properties sums from this studied, well Laplace-Stieltjes transforms adjacent and joint moments with different separations. The not time-reversible has zero-defect which makes parameter estimation straightforward. Other positive-valued extensions generating sequences given marginal distributions negative serial correlations.