2010, Vol. 34, Núm. 2http://hdl.handle.net/2099/107482024-03-02T22:31:38Z2024-03-02T22:31:38ZMarkovian arrivals in stochastic modelling: a survey and some new resultsArtalejo, Jesús R.Gómez-Corral, AntonioHe, Qi-Minghttp://hdl.handle.net/2099/112442020-07-22T22:08:33Z2011-11-02T19:01:03ZMarkovian arrivals in stochastic modelling: a survey and some new results
Artalejo, Jesús R.; Gómez-Corral, Antonio; He, Qi-Ming
This paper aims to provide a comprehensive review on Markovian arrival processes (MAPs),
which constitute a rich class of point processes used extensively in stochastic modelling. Our
starting point is the versatile process introduced by Neuts (1979) which, under some simplified
notation, was coined as the batch Markovian arrival process (BMAP). On the one hand, a general
point process can be approximated by appropriate MAPs and, on the other hand, the MAPs
provide a versatile, yet tractable option for modelling a bursty flow by preserving the Markovian
formalism. While a number of well-known arrival processes are subsumed under a BMAP as
special cases, the literature also shows generalizations to model arrival streams with marks, nonhomogeneous
settings or even spatial arrivals. We survey on the main aspects of the BMAP,
discuss on some of its variants and generalizations, and give a few new results in the context of a
recent state-dependent extension.
2011-11-02T19:01:03ZArtalejo, Jesús R.Gómez-Corral, AntonioHe, Qi-MingThis paper aims to provide a comprehensive review on Markovian arrival processes (MAPs),
which constitute a rich class of point processes used extensively in stochastic modelling. Our
starting point is the versatile process introduced by Neuts (1979) which, under some simplified
notation, was coined as the batch Markovian arrival process (BMAP). On the one hand, a general
point process can be approximated by appropriate MAPs and, on the other hand, the MAPs
provide a versatile, yet tractable option for modelling a bursty flow by preserving the Markovian
formalism. While a number of well-known arrival processes are subsumed under a BMAP as
special cases, the literature also shows generalizations to model arrival streams with marks, nonhomogeneous
settings or even spatial arrivals. We survey on the main aspects of the BMAP,
discuss on some of its variants and generalizations, and give a few new results in the context of a
recent state-dependent extension.On ratio and product methods with certain known population parameters of auxiliary variable in sample surveysSingh, Housila. P.Tailor, RiteshTailor, Rajeshhttp://hdl.handle.net/2099/112432020-07-22T22:08:33Z2011-11-02T19:00:20ZOn ratio and product methods with certain known population parameters of auxiliary variable in sample surveys
Singh, Housila. P.; Tailor, Ritesh; Tailor, Rajesh
This paper proposes two ratio and product-type estimators using transformation based on known
minimum and maximum values of auxiliary variable. The biases and mean squared errors of the
suggested estimators are obtained under large sample approximation. Conditions are obtained
under which the suggested estimators are superior to the conventional unbiased estimator, usual
ratio and product estimators of population mean. The superiority of the proposed estimators are
also established through some natural population data sets
2011-11-02T19:00:20ZSingh, Housila. P.Tailor, RiteshTailor, RajeshThis paper proposes two ratio and product-type estimators using transformation based on known
minimum and maximum values of auxiliary variable. The biases and mean squared errors of the
suggested estimators are obtained under large sample approximation. Conditions are obtained
under which the suggested estimators are superior to the conventional unbiased estimator, usual
ratio and product estimators of population mean. The superiority of the proposed estimators are
also established through some natural population data setsOn the use of simulation methods to compute probabilities: application to the first division Spanish soccer leagueDíaz-Emparanza, IgnacioNúñez-Antón, Vicentehttp://hdl.handle.net/2099/112422020-07-22T22:08:32Z2011-11-02T18:59:10ZOn the use of simulation methods to compute probabilities: application to the first division Spanish soccer league
Díaz-Emparanza, Ignacio; Núñez-Antón, Vicente
We consider the problem of using the points a given team has in the First Division Spanish Soccer
League to estimate its probabilities of achieving a specific objective, such as, for example, staying
in the first division or playing the European Champions League. We started thinking about this
specific problem and how to approach it after reading that some soccer coaches indicate that a
team in the first division guarantees its staying in that division if it has a total of 42 points at the
end of the regular season. This problem differs from the typical probability estimation problem
because we only know the actual cumulative score a given team has at some point during the
regular season. Under this setting a series of different assumptions can be made to predict the
probability of interest at the end of the season. We describe the specific theoretical probability
model using the multinomial distribution and, then, introduce two approximations to compute the
probability of interest, as well as the exact method. The different proposed methods are then
evaluated and also applied to the example that motivated them. One interesting result is that the
predicted probabilities can then be dynamically evaluated by using data from the current soccer
competition.
2011-11-02T18:59:10ZDíaz-Emparanza, IgnacioNúñez-Antón, VicenteWe consider the problem of using the points a given team has in the First Division Spanish Soccer
League to estimate its probabilities of achieving a specific objective, such as, for example, staying
in the first division or playing the European Champions League. We started thinking about this
specific problem and how to approach it after reading that some soccer coaches indicate that a
team in the first division guarantees its staying in that division if it has a total of 42 points at the
end of the regular season. This problem differs from the typical probability estimation problem
because we only know the actual cumulative score a given team has at some point during the
regular season. Under this setting a series of different assumptions can be made to predict the
probability of interest at the end of the season. We describe the specific theoretical probability
model using the multinomial distribution and, then, introduce two approximations to compute the
probability of interest, as well as the exact method. The different proposed methods are then
evaluated and also applied to the example that motivated them. One interesting result is that the
predicted probabilities can then be dynamically evaluated by using data from the current soccer
competition.Optimal inverse Beta(3,3) transformation in kernel density estimationBolancé, Catalinahttp://hdl.handle.net/2099/112292020-07-22T22:08:34Z2011-10-28T15:02:56ZOptimal inverse Beta(3,3) transformation in kernel density estimation
Bolancé, Catalina
A double transformation kernel density estimator that is suitable for heavy-tailed distributions is
presented. Using a double transformation, an asymptotically optimal bandwidth parameter can be
calculated when minimizing the expression of the asymptotic mean integrated squared error of
the transformed variable. Simulation results are presented showing that this approach performs
better than existing alternatives. An application to insurance claim cost data is included
2011-10-28T15:02:56ZBolancé, CatalinaA double transformation kernel density estimator that is suitable for heavy-tailed distributions is
presented. Using a double transformation, an asymptotically optimal bandwidth parameter can be
calculated when minimizing the expression of the asymptotic mean integrated squared error of
the transformed variable. Simulation results are presented showing that this approach performs
better than existing alternatives. An application to insurance claim cost data is includedApplication of receiver operating characteristic (ROC) methodology in biological studies on marine resources: sex determination of Paracentrotus lividus (Lamarck, 1816)Lustres-Pérez, VicenteRodríguez-Álvarez, María XoséPata, María P.Fernández Pulpeiro, EugenioCadarso-Suárez, Carmenhttp://hdl.handle.net/2099/112282020-07-22T22:08:34Z2011-10-28T15:02:04ZApplication of receiver operating characteristic (ROC) methodology in biological studies on marine resources: sex determination of Paracentrotus lividus (Lamarck, 1816)
Lustres-Pérez, Vicente; Rodríguez-Álvarez, María Xosé; Pata, María P.; Fernández Pulpeiro, Eugenio; Cadarso-Suárez, Carmen
The receiver operating characteristic (ROC) curve is usually used in biomedicine as an indicator
of the accuracy of diagnostic tests. However, this measure of discrimination has been little used
in other areas, such as animal biology or ecology. We present a novel application of an ROC
analysis in which gonad colour was used to determine the sex of Paracentrotus lividus (Lamarck,
1816), a sea urchin of considerable commercial interest. A better classifier than gonad colour was
obtained by transforming these colours through flexible logistic generalized additive models.
2011-10-28T15:02:04ZLustres-Pérez, VicenteRodríguez-Álvarez, María XoséPata, María P.Fernández Pulpeiro, EugenioCadarso-Suárez, CarmenThe receiver operating characteristic (ROC) curve is usually used in biomedicine as an indicator
of the accuracy of diagnostic tests. However, this measure of discrimination has been little used
in other areas, such as animal biology or ecology. We present a novel application of an ROC
analysis in which gonad colour was used to determine the sex of Paracentrotus lividus (Lamarck,
1816), a sea urchin of considerable commercial interest. A better classifier than gonad colour was
obtained by transforming these colours through flexible logistic generalized additive models.Bayes linear spacesvan den Boogaart, Karl GeraldEgozcue Rubí, Juan JoséPawlowsky Glahn, Verahttp://hdl.handle.net/2099/112272022-05-30T12:48:22Z2011-10-28T14:54:46ZBayes linear spaces
van den Boogaart, Karl Gerald; Egozcue Rubí, Juan José; Pawlowsky Glahn, Vera
Linear spaces consisting of -finite probability measures and infinite measures (improper priors
and likelihood functions) are defined. The commutative group operation, called perturbation, is
the updating given by Bayes theorem; the inverse operation is the Radon-Nikodym derivative.
Bayes spaces of measures are sets of classes of proportional measures. In this framework, basic
notions of mathematical statistics get a simple algebraic interpretation. For example, exponential
families appear as affine subspaces with their sufficient statistics as a basis. Bayesian statistics, in
particular some well-known properties of conjugated priors and likelihood functions, are revisited
and slightly extended.
2011-10-28T14:54:46Zvan den Boogaart, Karl GeraldEgozcue Rubí, Juan JoséPawlowsky Glahn, VeraLinear spaces consisting of -finite probability measures and infinite measures (improper priors
and likelihood functions) are defined. The commutative group operation, called perturbation, is
the updating given by Bayes theorem; the inverse operation is the Radon-Nikodym derivative.
Bayes spaces of measures are sets of classes of proportional measures. In this framework, basic
notions of mathematical statistics get a simple algebraic interpretation. For example, exponential
families appear as affine subspaces with their sufficient statistics as a basis. Bayesian statistics, in
particular some well-known properties of conjugated priors and likelihood functions, are revisited
and slightly extended.