Related papers: Emperical Study on Various Symmetric Distributions…
This paper considers an extension of the multivariate symmetric Laplace distribution to matrix variate case. The symmetric Laplace distribution is a scale mixture of normal distribution. The maximum likelihood estimators (MLE) of the…
Mixture models whose components have skewed hypercube contours are developed via a generalization of the multivariate shifted asymmetric Laplace density. Specifically, we develop mixtures of multiple scaled shifted asymmetric Laplace…
Due to the skessed distribution, high peak and thick tail and asymmetry of financial return data, it is difficult to describe the traditional distribution. In recent years, generalized autoregressive score (GAS) has been used in many fields…
In this short note the theory for multivariate asset allocation with elliptically symmetric distributions of returns, as developed in the author's prior work, is specialized to the case of returns drawn from a multivariate Laplace…
A discrete-time stochastic process derived from a model of basketball is used to generalize any discrete distribution. The generalized distributions can have one or two more parameters than the parent distribution. Those derived from…
In this paper we consider a telegraph equation with time-dependent coefficients, governing the persistent random walk of a particle moving on the line with a time-varying velocity $c(t)$ and changing direction at instants distributed…
Probabilistic forecasting of time series is an important matter in many applications and research fields. In order to draw conclusions from a probabilistic forecast, we must ensure that the model class used to approximate the true…
We consider a stationary linear AR($p$) model with observations subject to gross errors (outliers). The autoregression parameters as well as the distribution function (d.f.) $G$ of innovations are unknown. The distribution of outliers $\Pi$…
We examine the efficiency of the Asymmetric Power ARCH (APARCH) model in the case where the residuals follow the standardized Pearson type IV distribution. The model is tested with a variety of loss functions and the efficiency is examined…
The hierarchical distribution matching (Hi-DM) approach for probabilistic shaping is described. The potential of Hi-DM in terms of trade-off between performance,complexity, and memory is illustrated through three case studies.
This paper presents non-parametric baseline models for time series forecasting. Unlike classical forecasting models, the proposed approach does not assume any parametric form for the predictive distribution and instead generates predictions…
This article demonstrates that flexible and statistically tractable multi-modal diffusion models can be attained by transformation of simple well-known diffusion models such as the Ornstein-Uhlenbeck model, or more generally a Pearson…
Random variables of the generalized Pareto distribution, can be transformed to that of the Pareto distribution. Explicit expressions exist for the maximum likelihood estimators of the parameters of the Pareto distribution. The performance…
The paper deals with planar segment processes given by a density with respect to the Poisson process. Parametric models involve reference distributions of directions and/or lengths of segments. These distributions generally do not coincide…
Well-calibrated probabilistic regression models are a crucial learning component in robotics applications as datasets grow rapidly and tasks become more complex. Unfortunately, classical regression models are usually either probabilistic…
Conway-Maxwell-Poisson (CMP) distributions are flexible generalizations of the Poisson distribution for modelling overdispersed or underdispersed counts. The main hindrance to their wider use in practice seems to be the inability to…
In this paper, we study the maximum likelihood estimation of the parameters of the multivariate and matrix variate symmetric Laplace distributions through group actions. The multivariate and matrix variate symmetric Laplace distributions…
We propose a Bayesian approach using improper priors for hierarchical linear mixed models with flexible random effects and residual error distributions. The error distribution is modelled using scale mixtures of normals, which can capture…
In regression tasks, aleatoric uncertainty is commonly addressed by considering a parametric distribution of the output variable, which is based on strong assumptions such as symmetry, unimodality or by supposing a restricted shape. These…
The likelihood for the parameters of a generalized linear mixed model involves an integral which may be of very high dimension. Because of this intractability, many approximations to the likelihood have been proposed, but all can fail when…