Related papers: On Generalized q-logistic Distribution and its Cha…
In this paper, a new exponential and logarithm related to the non-extensive statistical physics is proposed by using the q-sum and q-product which satisfy the distributivity. And we discuss the q-mapping from an ordinary probability to…
Large-scale rare events data are commonly encountered in practice. To tackle the massive rare events data, we propose a novel distributed estimation method for logistic regression in a distributed system. For a distributed framework, we…
We propose an asymptotic theory for distribution forecasting from the log normal chain-ladder model. The theory overcomes the difficulty of convoluting log normal variables and takes estimation error into account. The results differ from…
Generalized linear models and the quasi-likelihood method extend the ordinary regression models to accommodate more general conditional distributions of the response. Nonparametric methods need no explicit parametric specification, and the…
In many real-world prediction tasks, class labels contain information about the relative order between labels that are not captured by commonly used loss functions such as multicategory cross-entropy. Recently, the preference for unimodal…
We review the main tools which allow for the statistical characterization of weighted networks. We then present two case studies, the airline connection network and the scientific collaboration network, which are representative of critical…
Distributed learning provides an attractive framework for scaling the learning task by sharing the computational load over multiple nodes in a network. Here, we investigate the performance of distributed learning for large-scale linear…
We propose a simple generalization of the explosive percolation process [Achlioptas et al., Science 323, 1453 (2009)], and investigate its structural and transport properties. In this model, at each step, a set of q unoccupied bonds is…
Copulas, generalized estimating equations, and generalized linear mixed models promote the analysis of grouped data where non-normal responses are correlated. Unfortunately, parameter estimation remains challenging in these three…
We study the distribution of the maximum likelihood estimate (MLE) in high-dimensional logistic models, extending the recent results from Sur (2019) to the case where the Gaussian covariates may have an arbitrary covariance structure. We…
The maximum ${\log}_q$ likelihood estimation method is a generalization of the known maximum $\log$ likelihood method to overcome the problem for modeling non-identical observations (inliers and outliers). The parameter $q$ is a tuning…
The QQ plot is a commonly used technique for informally deciding whether a univariate random sample of size n comes from a specified distribution F. The QQ plot graphs the sample quantiles against the theoretical quantiles of F and then a…
Several new geometric quantile-based measures for multivariate dispersion, skewness, kurtosis, and spherical asymmetry are defined. These measures differ from existing measures, which use volumes and are easy to calculate. Some theoretical…
Multivariate generalized Pareto distributions arise as the limit distributions of exceedances over multivariate thresholds of random vectors in the domain of attraction of a max-stable distribution. These distributions can be parametrized…
The aim of this paper is to extend Azzalini's method. This extension is done in two stages: consider two dependent and non-identically distributed random variables say $X_1$ and $X_2$; model the dependence between $X_1$ and $X_2$ by a…
The unified skew-t (SUT) is a flexible parametric multivariate distribution that accounts for skewness and heavy tails in the data. A few of its properties can be found scattered in the literature or in a parameterization that does not…
Skew density matrices can be diagonalized to yield probability interpretation. The power-counting prediction of perturbative QCD is found consistent with recent CEBAF data on $F_2(Q^2)/F_1(Q^2)$
Motivated by the need for parametric families of rich and yet tractable distributions in financial mathematics, both in pricing and risk management settings, but also considering wider statistical applications, we investigate a novel…
We introduce a multivariate hidden Markov model to jointly cluster time-series observations with different support, i.e. circular and linear. Relying on the general projected normal distribution, our approach allows for bimodal and/or…
In this article we review recent generalisations of the central limit theorem for the sum of specially correlated (or q-independent) variables, focusing on q greater or equal than 1. Specifically, this kind of correlation turns the…