arXiv subjects

Ayse Kizilersu

Publications and source records attributed to Ayse Kizilersu.

10 recordsLinked to original sources

arXiv2022

Maximum likelihood estimation for left-truncated log-logistic distributions with a given truncation point

The maximum likelihood estimation of the left-truncated log-logistic distribution with a given truncation point is analyzed in detail from both mathematical and numerical perspectives. These maximum likelihood equations often do not possess a solution, even for small truncations. A simple criterion is provided for the existence of a regular maximum likelihood solution. In this case a profile likelihood function can be constructed and the optimisation problem is reduced to one dimension. When the maximum likelihood equations do not admit a solution for certain data samples, it is shown that the Pareto distribution is the $L^1$-limit of the degenerated left-truncated log-logistic distribution. Using this mathematical information, a highly efficient Monte Carlo simulation is performed to obtain critical values for some goodness-of-fit tests. The confidence tables and an interpolation formula are provided and several applications to real world data are presented.

stat.ME↗

arXiv2020

Censored EM algorithm for Weibull mixtures: application to arrival times of market orders

In a previous analysis the problem of "zero-inflated" time data (caused by high frequency trading in the electronic order book) was handled by left-truncating the inter-arrival times. We demonstrated, using rigorous statistical methods, that the Weibull distribution describes the corresponding stochastic dynamics for all inter-arrival time differences except in the region near zero. However, since the truncated Weibull distribution was not able to describe the huge "zero-inflated" probability mass in the neighbourhood of zero (making up approximately 50\% of the data for limit orders), it became clear that the entire probability distribution is a mixture distribution of which the Weibull distribution is a significant part. Here we use a censored EM algorithm to analyse data for the difference of the arrival times of market orders, which usually have a much lower percentage of zero inflation, for four selected stocks trading on the London Stock Exchange.

q-fin.ST↗

arXiv2014

Dynamical mass generation in unquenched QED using the Dyson--Schwinger equations

We present a comprehensive numerical study of dynamical mass generation for unquenched QED in four dimensions, in the absence of four-fermion interactions, using the Dyson--Schwinger approach. We begin with an overview of previous investigations of criticality in the quenched approximation. To this we add an analysis using a new fermion-antifermion-boson interaction ansatz, the Kizilersu-Pennington (KP) vertex, developed for an unquenched treatment. After surveying criticality in previous unquenched studies, we investigate the performance of the KP vertex in dynamical mass generation using a renormalized fully unquenched system of equations. This we compare with the results for two hybrid vertices incorporating the Curtis--Pennington vertex in the fermion equation. We conclude that the KP vertex is as yet incomplete, and its relative gauge-variance is due to its lack of massive transverse components in its design.

hep-ph↗

arXiv2013

Fractional Poisson processes and their representation by infinite systems of ordinary differential equations

Fractional Poisson processes, a rapidly growing area of non-Markovian stochastic processes, are useful in statistics to describe data from counting processes when waiting times are not exponentially distributed. We show that the fractional Kolmogorov-Feller equations for the probabilities at time t can be representated by an infinite linear system of ordinary differential equations of first order in a transformed time variable. These new equations resemble a linear version of the discrete coagulation-fragmentation equations, well-known from the non-equilibrium theory of gelation, cluster-dynamics and phase transitions in physics and chemistry.

math.CA↗

arXiv2013

Strongly-Coupled Unquenched QED4 Propagators Using Schwinger-Dyson Equations

We study unquenched QED in four dimensions using renormalised Schwinger-Dyson equations and focus on the behaviour of the fermion and photon propagators. For this purpose we use an improved Kizilersu-Pennington (KP) vertex which respects gauge invariance, multiplicative renormalizability for the massless case, agrees with perturbation theory in the weak coupling regime and is free of kinematic singularities. We find that the KP vertex performs very well as expected specially in comparison with other vertex choices. We find that the Landau pole problem familiar from perturbative QED persists in the nonperturbative case with the renormalised inverse photon propagator having zero crossing.

hep-ph↗

arXiv2007

Quark-gluon vertex in general kinematics

We compute the quark-gluon vertex in quenched lattice QCD, in the Landau gauge using an off-shell mean-field O(a)-improved fermion action. The Dirac-vector part of the vertex is computed for arbitrary kinematics. We find a substantial infrared enhancement of the interaction strength regardless of the kinematics.

hep-lat↗

arXiv2004

Quark-gluon vertex in arbitrary kinematics

We compute the quark-gluon vertex in quenched lattice QCD, in the Landau gauge using an off-shell mean-field O(a)-improved fermion action. The complete vertex is computed in two specific kinematical limits, while the Dirac-vector part is computed for arbitrary kinematics. We find a nontrivial and rich tensor structure, including a substantial infrared enhancement of the interaction strength regardless of kinematics.

hep-lat↗

arXiv2002

The nonperturbative quark-gluon vertex

We show results for the quark-gluon vertex in the Landau gauge, using a mean-field improved Sheikholeslami-Wohlert fermion action. We compute all the three non-zero form factors of the vertex at zero gluon momentum, and compare them to the abelian vertex. The quark mass dependence of the vertex is also investigated and found to be negligible for the range of masses considered.

hep-lat↗

arXiv2002

Quark-gluon vertex from lattice QCD

The quark-gluon vertex in Landau gauge is studied in the quenched approximation using the Sheikholeslami-Wohlert (SW) fermion action with mean-field improvement coefficients in the action and for the quark fields. We see that the form factor that includes the running coupling is substantially enhanced in the infrared, over and above the enhancement arising from the infrared suppression of the quark propagator alone. We define two different momentum subtraction renormalisation schemes -- \MOMT (asymmetric) and \MOMB\ (symmetric) -- and determine the running coupling in both schemes. We find Lambda_msbar(N_f=0)=300(+150/-180)(55)(30) MeV from the asymmetric scheme. This is somewhat higher than other determinations of this quantity, but the uncertainties -- both statistical and systematic -- are large. In the symmetric scheme, statistical noise prevents us from obtaining a meaningful estimate for Lambda_msbar.

hep-ph↗

arXiv2000

On conditions for the nonperturbative equivalence of ultraviolet cut-off and dimensional regularization schemes

We consider procedures through which an ultraviolet cut-off regularization scheme can be modified to reproduce the same results for nonperturbative renormalized Green's functions as obtained from a dimensional regularization scheme. These issues are considered within the Dyson-Schwinger equation framework, where ultraviolet cut-off regularization can lead to explicit violations of gauge invariance. As a specific illustration, we consider the electron self-energy in quenched QED_4 in both schemes and establish those procedures for which the UV cut-off scheme can be expected to lead to the dimensional regularization results. We also compare results from precise numerical studies using the two types of regularization.

hep-ph↗