Characterizations of probability distributions via bivariate regression of record values

Bairamov et al. (Aust N Z J Stat 47:543-547, 2005) characterize the exponential distribution in terms of the regression of a function of a record value with its adjacent record values as covariates. We extend these results to the case of non-adjacent covariates. We also consider a more general setting involving monotone transformations. As special cases, we present characterizations involving weighted arithmetic, geometric, and harmonic means.Comment: accepted in Metrik

Stability Analysis of Frame Slotted Aloha Protocol

Frame Slotted Aloha (FSA) protocol has been widely applied in Radio Frequency Identification (RFID) systems as the de facto standard in tag identification. However, very limited work has been done on the stability of FSA despite its fundamental importance both on the theoretical characterisation of FSA performance and its effective operation in practical systems. In order to bridge this gap, we devote this paper to investigating the stability properties of FSA by focusing on two physical layer models of practical importance, the models with single packet reception and multipacket reception capabilities. Technically, we model the FSA system backlog as a Markov chain with its states being backlog size at the beginning of each frame. The objective is to analyze the ergodicity of the Markov chain and demonstrate its properties in different regions, particularly the instability region. By employing drift analysis, we obtain the closed-form conditions for the stability of FSA and show that the stability region is maximised when the frame length equals the backlog size in the single packet reception model and when the ratio of the backlog size to frame length equals in order of magnitude the maximum multipacket reception capacity in the multipacket reception model. Furthermore, to characterise system behavior in the instability region, we mathematically demonstrate the existence of transience of the backlog Markov chain.Comment: 14 pages, submitted to IEEE Transaction on Information Theor

Generalized Mittag-Leffler Distributions and Processes for Applications in Astrophysics and Time Series Modeling

Geometric generalized Mittag-Leffler distributions having the Laplace transform $\frac{1}{1+\beta\log(1+t^\alpha)},00$ is introduced and its properties are discussed. Autoregressive processes with Mittag-Leffler and geometric generalized Mittag-Leffler marginal distributions are developed. Haubold and Mathai (2000) derived a closed form representation of the fractional kinetic equation and thermonuclear function in terms of Mittag-Leffler function. Saxena et al (2002, 2004a,b) extended the result and derived the solutions of a number of fractional kinetic equations in terms of generalized Mittag-Leffler functions. These results are useful in explaining various fundamental laws of physics. Here we develop first-order autoregressive time series models and the properties are explored. The results have applications in various areas like astrophysics, space sciences, meteorology, financial modeling and reliability modeling.Comment: 12 pages, LaTe

A fluid model for a relay node in an ad-hoc network: the case of heavy-tailed input

Relay nodes in an ad hoc network can be modelled as fluid queues, in which the available service capacity is shared by the input and output. In this paper such a relay node is considered; jobs arrive according to a Poisson process and bring along a random amount of work. The total transmission capacity is fairly shared, meaning that, when n jobs are present, each job transmits traffic into the queue at rate 1/(n + 1) while the queue is drained at the same rate of 1/(n + 1). Where previous studies mainly concentrated on the case of exponentially distributed job sizes, the present paper addresses regularly varying jobs. The focus lies on the tail asymptotics of the sojourn time S. Using sample-path arguments, it is proven that P {S > x} behaves roughly as the residual job size, i.e., if the job sizes are regularly varying of index -nu, the tail of S is regularly varying of index 1 - nu. In addition, we address the tail asymptotics of other performance metrics, such as the workload in the queue, the flow transfer time and the queueing delay

Spontaneous Emergence of Multiple Drug Resistance in Tuberculosis before and during Therapy

The emergence of drug resistance in M. tuberculosis undermines the efficacy of tuberculosis (TB) treatment in individuals and of TB control programs in populations. Multiple drug resistance is often attributed to sequential functional monotherapy, and standard initial treatment regimens have therefore been designed to include simultaneous use of four different antibiotics. Despite the widespread use of combination therapy, highly resistant M. tb strains have emerged in many settings. Here we use a stochastic birth-death model to estimate the probability of the emergence of multidrug resistance during the growth of a population of initially drug sensitive TB bacilli within an infected host. We find that the probability of the emergence of resistance to the two principal anti-TB drugs before initiation of therapy ranges from 10−5 to 10−4; while rare, this is several orders of magnitude higher than previous estimates. This finding suggests that multidrug resistant M. tb may not be an entirely “man-made” phenomenon and may help explain how highly drug resistant forms of TB have independently emerged in many settings

On the number of records near the maximum

Recent work has considered properties of the number of observations Xj, independently drawn from a discrete law, which equal the sample maximum X(n) The natural analogue for continuous laws is the number Kn(a) of observations in the interval (X(n)–a, X(n)], where a > 0. This paper derives general expressions for the law, first moment, and probability generating function of Kn(a), mentioning examples where evaluations can be given. It seeks limit laws for n→ and finds a central limit result when a is fixed and the population law has a finite right extremity. Whenever the population law is attracted to an extremal law, a limit theorem can be found by letting a depend on n in an appropriate manner; thus the limit law is geometric when the extremal law is the Gumbel type. With these results, the paper obtains limit laws for ‘top end’ spacings X(n) ‐ X(n‐j) with j fixed