Bayesian inference for double Pareto lognormal queues

Ramírez‐Cobo, Pepa; Lillo, Rosa E.; Wilson, Simon; Wiper, Michael P.

doi:10.1214/10-aoas336

Cited by 33 publications

(22 citation statements)

References 22 publications

(39 reference statements)

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“…In the second empirical illustration, we analyze Internet traffic data, which have already been analyzed from a Bayesian point of view in references [53] and [54]. This data set consists of 3143 transferred bytes/second within consecutive seconds.…”

Section: Internet Traffic Datamentioning

confidence: 99%

Distributions and Composite Models for Size-Type Data

Dominicy¹,

Sinner²

2017

Advances in Statistical Methodologies and Their Application to Real Problems

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In the first part of this chapter, we present a sample of the best known and most used classical size distributions with their main statistical properties. In the second part, we introduce the concept of composite models and based on the size distributions of the first part, we describe those which already exist in the literature. In the last part of this chapter, we apply the described statistical size distributions and some of the composite models to two real data examples and compare their goodness-of-fit.

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Section: Internet Traffic Datamentioning

confidence: 99%

Distributions and Composite Models for Size-Type Data

Dominicy¹,

Sinner²

2017

Advances in Statistical Methodologies and Their Application to Real Problems

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Section: Internet Traffic Datamentioning

confidence: 99%

“…In this example we analyse the teletraffic data set studied in Ramirez-Cobo et al (2010), which contains n = 3143 observations, representing transferred bytes/sec within consecutive seconds. Ramirez-Cobo et al (2010) propose the use of a Normal Laplace distribution to model these data after a logarithmic transformation. The Normal Laplace distribution is obtained as the convolution of a Normal distribution and a two-piece Laplace distribution with location 0 and two parameters (α, β) that jointly control the scale and the skewness.…”

Section: Internet Traffic Datamentioning

confidence: 99%

Bayesian modelling of skewness and kurtosis with Two-Piece Scale and shape distributions

Rubio¹,

Steel²

2015

Electron. J. Statist.

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We formalise and generalise the definition of the family of univariate double two-piece distributions, obtained by using a densitybased transformation of unimodal symmetric continuous distributions with a shape parameter. The resulting distributions contain five interpretable parameters that control the mode, as well as the scale and shape in each direction. Four-parameter subfamilies of this class of distributions that capture different types of asymmetry are discussed. We propose interpretable scale and location-invariant benchmark priors and derive conditions for the propriety of the corresponding posterior distribution. The prior structures used allow for meaningful comparisons through Bayes factors within flexible families of distributions. These distributions are applied to data from finance, internet traffic and medicine, comparing them with appropriate competitors.

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“…The Bayesian model uses gamma processes (see van Noortwick ()), which have not been considered previously in the queueing literature. Although there is a rich body of literature on Bayesian queueing analyses, starting in the 1990s (eg, see Armero, ; Ramirez‐Cobo, Lillo, Wilson, & Wiper, ; Aktekin & Soyer, ; Rios Insua, Ruggeri, & Wiper, ; Aktekin & Ekin, ), nonparametric Bayesian models for queues have only recently gained attention. Furthermore, the nonparametric approaches proposed by Aktekin () and Ventz and Muliere () do not consider queueing systems with abandonments.…”

Section: Introductionmentioning

confidence: 99%

Bayesian modeling of abandonments in ticket queues

Kuzu

Soyer

2018

Naval Research Logistics

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Ticket queues (TQs) issue tickets to customers upon arrival, and are often used in the public and private sectors. Abandonment data collected by TQs is interval censored, which makes predicting customer abandonments a challenging problem. In this paper, we build a Bayesian framework for predicting abandonment counts in TQs to assist managers in workforce planning. In doing so, we propose parametric and semiparametric modulated Poisson process models and develop their Bayesian analyses using Markov chain Monte Carlo methods. We implement our models using actual abandonment data from a bank's TQ, and illustrate how we can provide managerial insights related to abandonment counts and server allocation policies.

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Bayesian inference for double Pareto lognormal queues

Cited by 33 publications

References 22 publications

Distributions and Composite Models for Size-Type Data

Distributions and Composite Models for Size-Type Data

Bayesian modelling of skewness and kurtosis with Two-Piece Scale and shape distributions

Bayesian modeling of abandonments in ticket queues

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