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29
Characterizing the Variability of Arrival Processes with Indices of Dispersion
 IEEE Journal on Selected Areas in Communications
, 1990
"... We propose to characterize the burstiness of packet arrival processes with indices of dispersion for intervals and for counts. These indices, which are functions of the variance of intervals and counts, are relatively straightforward to estimate and convey much more information than simpler indic ..."
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Cited by 69 (0 self)
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We propose to characterize the burstiness of packet arrival processes with indices of dispersion for intervals and for counts. These indices, which are functions of the variance of intervals and counts, are relatively straightforward to estimate and convey much more information than simpler indices, such as the coefficient of variation, that are often used to describe burstiness quantitatively.
Source coding for communication concentrators
 ELECTRON. SYST. LAB., MASSACHUSETTS INST. TECHNOL
, 1978
"... ..."
A Brownian model for recurrent earthquakes
 Bull. Seism. Soc. Am
, 2002
"... Abstract We construct a probability model for rupture times on a recurrent earthquake source. Adding Brownian perturbations to steady tectonic loading produces a stochastic loadstate process. Rupture is assumed to occur when this process reaches a criticalfailure threshold. An earthquake relaxes t ..."
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Cited by 12 (1 self)
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Abstract We construct a probability model for rupture times on a recurrent earthquake source. Adding Brownian perturbations to steady tectonic loading produces a stochastic loadstate process. Rupture is assumed to occur when this process reaches a criticalfailure threshold. An earthquake relaxes the load state to a characteristic ground level and begins a new failure cycle. The loadstate process is a Brownian relaxation oscillator. Intervals between events have a Brownian passagetime distribution that may serve as a temporal model for timedependent, longterm seismic forecasting. This distribution has the following noteworthy properties: (1) the probability of immediate rerupture is zero; (2) the hazard rate increases steadily from zero at t � 0 to a finite maximum near the mean recurrence time and then decreases asymptotically to a quasistationary level, in which the conditional probability of an event becomes time independent; and (3) the quasistationary failure rate is greater than, equal to, or less than the mean failure rate because the coefficient of variation is less than, equal to, or greater than 1 / �2 � 0.707. In addition, the model provides expressions for the hazard rate and probability of rupture on faults for which only a bound can be placed on the time of the last rupture. The Brownian relaxation oscillator provides a connection between observable event times and a formal state variable that reflects the macromechanics of stress and strain accumulation. Analysis of this process reveals that the quasistationary distance to failure has a gamma distribution, and residual life has a related exponential distribution. It also enables calculation of “interaction ” effects due to external perturbations to the state, such as stresstransfer effects from earthquakes outside the target source. The influence of interaction effects on recurrence times is transient and strongly dependent on when in the loading cycle step perturbations occur. Transient effects may be much stronger than would be predicted by the “clock change ” method and characteristically decay inversely with elapsed time after the perturbation.
Object oriented data analysis: Sets of trees
 The Annals of Statistics
"... Object Oriented Data Analysis is the statistical analysis of populations of complex objects. In the special case of Functional Data Analysis, these data objects are curves, where standard Euclidean approaches, such as principal components analysis, have been very successful. Recent developments in m ..."
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Cited by 8 (1 self)
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Object Oriented Data Analysis is the statistical analysis of populations of complex objects. In the special case of Functional Data Analysis, these data objects are curves, where standard Euclidean approaches, such as principal components analysis, have been very successful. Recent developments in medical image analysis motivate the statistical analysis of populations of more complex data objects which are elements of mildly nonEuclidean spaces, such as Lie Groups and Symmetric Spaces, or of strongly nonEuclidean spaces, such as spaces of treestructured data objects. These new contexts for Object Oriented Data Analysis create several potentially large new interfaces between mathematics and statistics. This point is illustrated through the careful development of a novel mathematical framework for statistical analysis of populations of tree structured objects. 1. Introduction Object Oriented Data Analysis (OODA) is the statistical analysis of data sets of complex objects. The area is understood through consideration
The Demand for M4: A Sectoral Analysis Part 2  The Corporate Sector”, Working Paper, No 62
, 1997
"... by ..."
A Markov Renewal Model for Rainfall Occurrences
, 1987
"... A probabilistic model for the temporal description of daily rainfall occurrences at a single location is presented. By defining an event as a day with measurable precipitation the model is cast into the discretetime point process framework. In the proposed model the sequence of times between events ..."
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Cited by 7 (0 self)
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A probabilistic model for the temporal description of daily rainfall occurrences at a single location is presented. By defining an event as a day with measurable precipitation the model is cast into the discretetime point process framework. In the proposed model the sequence of times between events is formed by sampling from two geometric distributions, according to transition probabilities specified by a Markov chain. The model belongs to the class of Markov renewal processes and exhibits clustering relative to the independent Bernoulli process. As a special case, it reduces to a renewal model with a mixture distribution for the interarrival times. The rainfall occurrence model coupled with a mixed exponential distribution for the nonzero daily rainfall amounts was applied to the daily rainfall series for Snoqualmie Falls, Washington, and was successful in preserving the shortterm structure of the occurrence process, as well as the distributional properties of the seasonal rainfall amounts.
The Spectral Structure of TES Processes
 Stochastic Models
, 1994
"... TES (TransformExpandSample) is a versatile class of stochastic sequences consisting of marginally uniform autoregressive schemes with modulo1 reduction, followed by various transformations. TES modeling aims to fit a TES model to empirical records by simultaneously capturing both firstorder and ..."
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Cited by 6 (6 self)
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TES (TransformExpandSample) is a versatile class of stochastic sequences consisting of marginally uniform autoregressive schemes with modulo1 reduction, followed by various transformations. TES modeling aims to fit a TES model to empirical records by simultaneously capturing both firstorder and secondorder properties of the empirical data. In this paper we study the spectral properties of general TES processes and their component innovation sequences, thus generalizing the results reported in Jagerman and Melamed [9]. We derive formulas for the power spectral density function and the spectral distribution function which are suitable for efficient numerical computation, and exemplify them for TES processes with uniform and exponential marginals. The results contribute to the understanding of TES sequences as models of autocorrelated sequences, particularly in a Monte Carlo simulation context. Keywords and Phrases: TES Processes, Stochastic Processes, Spectrum, Spectral Density, Spe...
Traffic Characteristics of OnLine Services
"... This paper presents a statistical characterization of online service traffic. The traffic is parameterized by the call holding times, the aggregate number of bytes and the number of packets transferred during the call. Particular attention is paid to modeling the stochastic rate function describing ..."
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Cited by 5 (1 self)
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This paper presents a statistical characterization of online service traffic. The traffic is parameterized by the call holding times, the aggregate number of bytes and the number of packets transferred during the call. Particular attention is paid to modeling the stochastic rate function describing the call arrivals. The time of day and day of the week seasonal features produce long term correlations in the arrival process. In addition, short term correlations are found to exist within the hourly time scale. The arrival rates are in general nonstationary in the mean rate. This is attributed to the daily influx of new subscribers and other exogenous influences such as promotions and advertisements that trigger increased usage. A time series modeling methodology is used to identify and quantify these features. Under suitable transformations, a stationary rendition of the arrival process is derived and characterized by the short and long term correlation coefficients. The second order characterization of the arrival process is used to predict resource usage.
A MarkovRenewalModulated Tes Model for VBR "Star Wars" Video
, 1995
"... This paper describes a general methodology for constructing accurate source models of long sequences (movies) of fullmotion compressed VBR (variable bit rate) video, directly from empirical data sets of observed bit rate (frame size) records. The practical goal of this modeling methodology is to ..."
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Cited by 2 (0 self)
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This paper describes a general methodology for constructing accurate source models of long sequences (movies) of fullmotion compressed VBR (variable bit rate) video, directly from empirical data sets of observed bit rate (frame size) records. The practical goal of this modeling methodology is to construct suites of highfidelity traffic benchmark models, suitable for driving realistic Monte Carlo simulations of broadband telecommunications networks. The fidelity criteria imposed are are relatively stringent, in that they call for the simultaneous capture of both firstorder and secondorder statistics of the empirical data, as well as its "qualitative appearance", including burstiness. The methodology is illustrated by a detailed outline of the construction of a stochastic model for the VBR video of the "Star Wars" movie, compressed under a JPEGlike coding.
DOUBLY STOCHASTIC POISSON PROCESS AND THE PRICING OF CATASTROPHE REINSURANCE CONTRACT
"... We use a doubly stochastic Poisson process (or the Cox process) to model the claim arrival process for catastrophic events. The shot noise process is used for the claim intensity function within the Cox process. The Cox process with shot noise intensity is examined by piecewise deterministic Markov ..."
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Cited by 2 (2 self)
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We use a doubly stochastic Poisson process (or the Cox process) to model the claim arrival process for catastrophic events. The shot noise process is used for the claim intensity function within the Cox process. The Cox process with shot noise intensity is examined by piecewise deterministic Markov process theory. We apply the Cox process incorporating the shot noise process as its intensity to price a stoploss catastrophe reinsurance contract. The asymptotic (stationary) distribution of the claim intensity is used to derive pricing formulae for a stoploss reinsurance contract for catastrophic events. We achieve an absence of arbitrage opportunities in the market by using an equivalent martingale probability measure in the pricing model for catastrophe reinsurance contract. The Esscher transform is employed to change the probability measure. KEYWORDS Doubly stochastic Poisson process. Shot noise process. Piecewise deterministic Markov process theory. Stoploss reinsurance contract. Equivalent martingale probability measure. Esscher transform. 1.