Transient analysis of a finite source discrete-time queueing system using homogeneous Markov system with state size capacities (HMS/c)

Abstract

In this article, a finite source discrete-time queueing system is modeled as a discrete-time homogeneous Markov system with finite state size capacities (HMS/c) and transition priorities. This Markov system is comprised of three states. The first state of the HMS/c corresponds to the source and the second one to the state with the servers. The second state has a finite capacity which corresponds to the number of servers. The members of the system which can not enter the second state, due to its finite capacity, enter the third state which represents the system's queue. In order to examine the variability of the state sizes recursive formulae for their factorial and mixed factorial moments are derived in matrix form. As a consequence the probability mass function of each state size can be evaluated. Also the expected time in queue is computed by means of the interval transition probabilities. The theoretical results are illustrated by a numerical example.     

Characterization of a mixture of gamma distributions via conditional finite moments

A necessary and sufficient condition that a continuous, positive random variable follow a gamma distribution is given in terms of any one of its conditional finite moments and an expression involving its failure rate. The results are then used to develop a characterization for a mixture of two gamma distributions. The general results about characterization of a mixture of gamma distributions yield several special cases that have appeared separately in recent literature, including characterization of a single exponential distribution, characterization of a single gamma distribution (in terms of either first or second moments) and a sufficient condition for a mixture of two exponential distributions (in terms of first moments). The condition in this last result is shown to be necessary also. Numerous other cases are possible, using different choices for distribution parameters along with a selection of the mixing parameter, for either individual or mixtures of distributions. Various characterizations can be expressed using higher order moments, too.     

On the performance of the nearest proportional to size sampling design

Assuming a super-population model the expected variance of the generalized difference estimator (Basu,1971) based on the nearest proportional to size sampling design introduced by Gabler(1987) is shown to be less than that of the same estimator based on an arbitrary sampling design from which the former design is realized. The former strategy is also shown to fare better than an unbiased ratio-cum-generalized difference estimator based on the nearest proportional to size sampling design in the sense of having less expected design variance under the same model.     

BEADS,BAGS, BAYES,AND THE FUNDAMENTAL PROBLEM OF SAMPLING THEORY

Motivated by a discussion of an elementary probability puzzle provided by Anderson and Provost [1] Anderson, O. D. and Provost, S. B. 1992. Beads, bags and Bayes. Int. J. Math. Educ. Sci. Technol., 23: 25–37. [Taylor & Francis Online] , [Google Scholar], we review what may be called the fundamental problem of finite population sampling theory and propose that only super-model or Bayesian approaches to finite population sampling are acceptable.     

Implementation of recursive nonparametric kernel estimation and a monte carlo study on its finite sample properties

The recursive estimator for the conditional mean of a nonparametric regression model with independent observations was thoroughly explored by Ahmad and Lin (1976), and Singh and Ullah (1986). Their studies are mainly concerned with the estimator's asymptotic behaviour. However, they do not include much discussion on the strategy of computing the estimates. In this paper, we provide a convenient implementation of the recursive estimator and examine its finite sample properties through simulation studies. Our study has demonstrated that for relatively short length of recursive updating, the estimates are generally equivalent to their fixed window width counterparts However, we found that substantial recursive updating can seriously lower the estimator's efficiency even though it is a consistent estimator.     

Finite Sample Properties of the Two-Step Empirical Likelihood Estimator

ABSTRACT

We investigate the finite sample properties of two-step empirical likelihood (EL) estimators. These estimators are shown to have the same third-order bias properties as EL itself. The Monte Carlo study provides evidence that (i) higher order asymptotics fails to provide a good approximation in the sense that the bias of the two-step EL estimators can be substantial and sensitive to the number of moment restrictions and (ii) the two-step EL estimators may have heavy tails.     

Finite Sample Comparison of Parametric,Semiparametric, and Wavelet Estimators of Fractional Integration

ABSTRACT

In this paper we compare through Monte Carlo simulations the finite sample properties of estimators of the fractional differencing parameter, d. This involves frequency domain, time domain, and wavelet based approaches, and we consider both parametric and semiparametric estimation methods. The estimators are briefly introduced and compared, and the criteria adopted for measuring finite sample performance are bias and root mean squared error. Most importantly, the simulations reveal that (1) the frequency domain maximum likelihood procedure is superior to the time domain parametric methods, (2) all the estimators are fairly robust to conditionally heteroscedastic errors, (3) the local polynomial Whittle and bias-reduced log-periodogram regression estimators are shown to be more robust to short-run dynamics than other semiparametric (frequency domain and wavelet) estimators and in some cases even outperform the time domain parametric methods, and (4) without sufficient trimming of scales the wavelet-based estimators are heavily biased.     

A Subjective Spin on Roulette Wheels

We provide a simple behavioral definition of ‘subjective mixture’ of acts for a large class of (not necessarily expected‐utility) preferences. Subjective mixtures enjoy the same algebraic properties as the ‘objective mixtures’ used to great advantage in the decision setting introduced by Anscombe and Aumann (1963). This makes it possible to formulate mixture‐space axioms in a fully subjective setting. For illustration, we present simple subjective axiomatizations of some models of choice under uncertainty, including Bewley's model of choice with incomplete preferences (2002).