Maximum likelihood estimation of the geometric niche preemption model

The geometric series or niche preemption model is an elementary ecological model in biodiversity studies. The preemption parameter of this model is usually estimated by regression or iteratively by using May’s equation. This article proposes a maximum likelihood estimator for the niche preemption model, assuming a known number of species and multinomial sampling. A simulation study shows that the maximum likelihood estimator outperforms the classical estimators in this context in terms of bias and precision. We obtain the distribution of the maximum likelihood estimator and use it to obtain confidence intervals for the preemption parameter and to develop a preemption t test that can address the hypothesis of equal geometric decay in two samples. We illustrate the use of the new estimator with some empirical data sets taken from the literature and provide software for its use.

COUNT AND DURATION TIME SERIES WITH EQUAL CONDITIONAL STOCHASTIC AND MEAN ORDERS

We consider a positive-valued time series whose conditional distribution has a time-varying mean, which may depend on exogenous variables. The main applications concern count or duration data. Under a contraction condition on the mean function, it is shown that stationarity and ergodicity hold when the mean and stochastic orders of the conditional distribution are the same. The latter condition holds for the exponential family parametrized by the mean, but also for many other distributions. We also provide conditions for the existence of marginal moments and for the geometric decay of the beta-mixing coefficients. We give conditions for consistency and asymptotic normality of the Exponential Quasi-Maximum Likelihood Estimator of the conditional mean parameters. Simulation experiments and illustrations on series of stock market volumes and of greenhouse gas concentrations show that the multiplicative-error form of usual duration models deserves to be relaxed, as allowed in this paper.

Absolute regularity of semi-contractive GARCH-type processes

We prove existence and uniqueness of a stationary distribution and absolute regularity for nonlinear GARCH and INGARCH models of order (p, q). In contrast to previous work we impose, besides a geometric drift condition, only a semi-contractive condition which allows us to include models which would be ruled out by a fully contractive condition. This results in a subgeometric rather than the more usual geometric decay rate of the mixing coefficients. The proofs are heavily based on a coupling of two versions of the processes.

Bifurcation and Chaos in the Logistic Map with Memory

We describe the dynamics of the logistic map [Formula: see text] endowed with memory [Formula: see text] of past iterations with geometric decay. We find that most of the relevant properties of the dynamics can be explained by means of a scaling of the standard logistic map without memory. The bifurcation diagram is therefore a scaled version of the standard map, with the extreme values of the logistic parameter [Formula: see text] for confined trajectories following also the scaling law. However, contrary to the ahistoric model, the trajectories may diverge for smaller values of [Formula: see text], depending on the initial condition [Formula: see text]. Simple conditions for divergence with given logistic map and memory are provided.

Individual Gap Measures from Generalized Zeckendorf Degompositions

Zeckendorf's theorem states that every positive integer can be decomposed uniquely as a sum of nonconsecutive Fibonacci numbers. The distribution of the number of summands converges to a Gaussian, and the individual measures on gajw between summands for m € [Fn,Fn+1) converge to geometric decay for almost all m as n→ ∞. While similar results are known for many other recurrences, previous work focused on proving Gaussianity for the number of summands or the average gap measure. We derive general conditions, which are easily checked, that yield geometric decay in the individual gap measures of generalized Zerkendorf decompositions attached to many linear recurrence relations.

VAR INTERPRETATIONS OF HAAVELMO’S MARKET MODEL OF CAPITAL AND INVESTMENT

In the paper attempts are made to integrate two parts of Trygve Haavelmo’s work: investment theory and dynamic econometric models of interrelated markets. Specifically, the duality in the representation of the capital service price and the capital quantity in relation to the investment price and quantity are brought to the forefront and confronted with elements from simultaneous equation modeling of vector autoregressive systems containing exogenous variables (VARX), using linear four-equation models. The role of the interest rate and the modeling of the expectation element in the capital service price and the capital’s retirement pattern, and their joint effect on the model’s investment quantity and price dynamics are discussed. Stability conditions are illustrated by examples. Extensions relaxing geometric decay and ways of accounting for forward-looking behavior, including rational expectations, are outlined. Some remarks on the theory-data confrontation of this kind of model are given.

Several Types of Convergence Rates of the M/G/1 Queueing System

We study the workload process of the M/G/1 queueing system. Firstly, we give the explicit criteria for the geometric rate of convergence and the geometric decay of stationary tail. And the parametersε0ands0for the geometric rate of convergence and the geometric decay of the stationary tail are obtained, respectively. Then, we give the explicit criteria for the rate of convergence and decay of stationary tail for three specific types of subgeometric cases. And we give the parametersε1ands1of the rate of convergence and the decay of the stationary tail, respectively, for the subgeometric rater(n)=exp(sn1/(1+α)),s>0,α>0.

ON THE PROBABILITY DISTRIBUTION OF JOIN QUEUE LENGTH IN A FORK-JOIN MODEL

In this article, we consider the two-node fork-join model with a Poisson arrival process and exponential service times of heterogeneous service rates. Using a mapping from the queue lengths in the parallel nodes to the join queue length, we first derive the probability distribution function of the join queue length in terms of joint probabilities in the parallel nodes and then study the exact tail asymptotics of the join queue length distribution. Although the asymptotics of the joint distribution of the queue lengths in the parallel nodes have three types of characterizations, our results show that the asymptotics of the join queue length distribution are characterized by two scenarios: (1) an exact geometric decay and (2) a geometric decay with the prefactor n−1/2.

An extension of a norm inequality for a semi-discrete g*λ function

A norm inequality for a semi-discrete g*?(f) function is obtained for functions, f, that can be written as a sum whose terms consist of a numerical coefficient multiplying a member of a family of functions that have properties of geometric decay, minimal smoothness and almost orthogonality condition. The theorem is applied to the rate of change of u, a solution to Lu = div?f in a bounded, nonsmooth domain ? Rd, d?3, u = 0 on ??.