We propose a nonparametric estimator for the rate of spread of an introduced population. We prove that the limit distribution of the estimator is normal or stable, depending on the behavior of the moment generating function. We show that resampling methods can also be used to approximate the distribution of the estimators. © 2001 Elsevier Science B.V. All rights reserved MSC: primary 62G05; sec...

For maximal ratio combining (MRC) diversity over correlated fading channels with Gaussian channel gains, we utilize unitary diagonalization to decorrelate the physical channels into uncorrelated virtual channels to easily obtain the moment generating function (MGF) of the received signalto-noise ratio (SNR). The MGF thus obtained has a compact form and can be universally applied to various popu...

In this study, the authors investigate the error rate performance of amplify-and-forward relaying over N∗Nakagami fading channels. This is a recently introduced channel model that involves the product of N Nakagami-m-distributed random variables. Employing the moment generating function approach, the authors derive symbol error rate expressions for a single-relay system under instantaneous powe...

Let X1,X2, ... be independent and symmetric random variables such that Sn = X1+ ...+Xn converges to a finite valued random variable S a.s. and let S = sup1≤n<∞ Sn (which is finite a.s.). We construct upper and lower bounds for sy and s ∗ y, the upper 1 y th quantile of Sy and S , respectively. Our approximations rely on an explicitly computable quantity q y for which we prove that 1 2 q y/2 < s...

We derive tight and computable bounds on the bias of statistical estimators, or more generally of quantities of interest, when evaluated on a baseline model P rather than on the typically unknown true model Q. Our proposed method combines the scalable information inequality derived by P. Dupuis, K.Chowdhary, the authors and their collaborators together with classical concentration inequalities ...

In this letter, new exact and approximated moment generating functions (MGF) for generalized fading distributions are derived and presented. Specifically, we consider the η-λ-μ, αμ, α-η-μ, α-μ, α-μ, and α-η-μ generalized distributions. In contrast to earlier results in the literature, both the new exact and approximated MGFs avoids complicated and computationally expensive special functions suc...

The main aim of this article is to characterize and investigate the three parameter exponentiated exponential Poisson probability distribution EEP(α, β, λ) by giving explicit closed form expressions for its characteristic function φξ(t) and moment generating function Mξ(t), and finally, to show that the existing series and integral form expressions for positive integer order moments Eξ , ν ∈ N ...

The large deviations principle (LDP) is known to hold for U-statistics of real valued kernel functions of Polish space valued i. i. d. random variables, where moreover appropriate exponential tail conditions are assumed to hold. We prove that similar conditions suuce for the large deviations principle to carry over to the partial sums U-processes corresponding to the statistics. x1 Introduction...

We propose a correlated stochastic process of which the novel non-Gaussian probability mass function is constructed by exactly solving moment generating function. The calculation of cumulants and auto-correlation shows that the process is convergent and scale invariant in the large but finite time limit. We demonstrate that the model infers the correlation strength in a discrete correlated time...