Extremes of censored and uncensored lifetimes in survival data

Extremes - We consider a random censoring model for survival analysis, allowing the possibility that only a proportion of individuals in the population are susceptible to death or failure, and the...     

Multivariate Regular Variation of Discrete Mass Functions with Applications to Preferential Attachment Networks

Regular variation of a multivariate measure with a Lebesgue density implies the regular variation of its density provided the density satisfies some regularity conditions. Unlike the univariate case, the converse also requires regularity conditions. We extend these arguments to discrete mass functions and their associated measures using the concept that the mass function can be embedded in a joint density function with continuous arguments. We give two different conditions, monotonicity and convergence on the unit sphere, both of which can make the discrete function embeddable. Our results are then applied to the preferential attachment network model, and we conclude that the joint mass function of in- and out-degree is embeddable and thus regularly varying.     

Activity periods of an infinite server queue and performance of certain heavy tailed fluid queues

A fluid queue with ON periods arriving according to a Poisson process and having a long-tailed distribution has long range dependence. As a result, its performance deteriorates. The extent of this performance deterioration depends on a quantity determined by the average values of the system parameters. In the case when the the performance deterioration is the most extreme, we quantify it by studying the time until the amount of work in the system causes an overflow of a large buffer. This turns out to be strongly related to the tail behavior of the increase in the buffer content during a busy period of the M/G/∞ queue feeding the buffer. A large deviation approach provides a powerful method of studying such tail behavior. This revised version was published online in June 2006 with corrections to the Cover Date.     

Extremal dependence analysis of network sessions

We refine a stimulating study by Sarvotham et al. (Comput Networks 48:335–350, 2005) which highlighted the influence of peak transmission rate on network burstiness. From TCP packet headers, we amalgamate packets into sessions where each session is characterized by a 5-tuple (S,D,R,R ^∨,Γ)=(total payload, duration, average transmission rate, peak transmission rate, initiation time). After careful consideration, a new definition of peak rate is required. Unlike Sarvotham et al. (Comput Networks 48:335–350, 2005) who segmented sessions into two groups labelled alpha and beta, we segment into 10 sessions according to the empirical quantiles of the peak rate variable as a demonstration that the beta group is far from homogeneous. Our more refined segmentation reveals additional structure that is missed by segmentation into two groups. In each segment, we study the dependence structure of (S,D,R) and find that it varies across the groups. Furthermore, within each segment, session initiation times are well approximated by a Poisson process whereas this property does not hold for the data set taken as a whole. Therefore, we conclude that the peak rate level is important for understanding structure and for constructing accurate simulations of data in the wild. We outline a simple method of simulating network traffic based on our findings.     

Effects of frequency modulation on absolute, masked, and reflex thresholds

Behavioral and acoustic reflex thresholds were determined for five normal-hearing subjects in response to carrier signals of 500 and 2000 Hz which were unmodulated or modulated sinusoidally at rates of 2, 20, and 200 times per second with frequency deviations (delta f) of 30, 100, and 300 Hz. Behavioral (absolute and masked) thresholds were determined using an adaptive two-alternative forced-choice procedure. Acoustic reflex thresholds were determined by visual inspection of stored reflex waveforms. Frequency modulation was not found to exert a systematic effect at absolute threshold. Frequency modulation did affect threshold estimates systematically, but differentially, at masked threshold and acoustic reflex threshold. Increasing the frequency deviation of the modulation was associated with an increase in masked threshold and with a decrease in acoustic reflex threshold at both test frequencies. The findings are discussed in terms of critical band phenomena.