Related papers: Generalizing the log-Moyal distribution and regres…

Risk assessment for rare events is essential for understanding systemic stability in complex systems. As rare events are typically highly correlated, it is important to study heavy-tailed multivariate distributions of the relevant…

This paper studies distributed estimation and support recovery for high-dimensional linear regression model with heavy-tailed noise. To deal with heavy-tailed noise whose variance can be infinite, we adopt the quantile regression loss…

Datasets with extreme observations and/or heavy-tailed error distributions are commonly encountered and should be analyzed with careful consideration of these features from a statistical perspective. Small deviations from an assumed model,…

It has been pointed out by Patriarca et al. (2005) that the power-law tailed equilibrium distribution in heterogeneous kinetic exchange models with a distributed saving parameter can be resolved as a mixture of Gamma distributions…

In this article, a generalized inverse xgamma distribution (GIXGD) has been introduced as the generalized version of the inverse xgamma distribution. The proposed model exhibits the pattern of non-monotone hazard rate and belongs to family…

Maximum likelihood estimation of generalized linear mixed models(GLMMs) is difficult due to marginalization of the random effects. Computing derivatives of a fitted GLMM's likelihood (with respect to model parameters) is also difficult,…

It is well known that the probability distribution of high-frequency financial returns is characterized by a leptokurtic, heavy-tailed shape. This behavior undermines the typical assumption of Gaussian log-returns behind the standard…

In this paper, we introduce a new two-parameter lifetime distribution, called the exponential-generalized truncated logarithmic (EGTL) distribution, by compounding the exponential and generalized truncated logarithmic distributions. Our…

This paper presents a score-based weighted likelihood estimator (SWLE) for robust estimations of generalized linear model (GLM) for insurance loss data. The SWLE exhibits a limited sensitivity to the outliers, theoretically justifying its…

The power law distribution is usually used to fit data in the upper tail of the distribution. However, commonly it is not valid to model data in all the range. In this paper, we present a new family of distributions, the so-called…

A novel approach to adding two additional parameters to a family of distributions for better adaptability has been put forth. This approach yields a versatile class of distributions supported on the positive real line. We proceed to analyze…

We develop a class of non-life reserving models using a stable-1/2 random bridge to simulate the accumulation of paid claims, allowing for an essentially arbitrary choice of a priori distribution for the ultimate loss. Taking an…

This paper presents a simulation study comparing the performance of generalized joint regression models (GJRM) with generalized linear mixed models (GLMM) and generalized estimating equations (GEE) for regression of longitudinal data with…

I present all the details in calculating the posterior distribution of the conjugate Normal-Gamma prior in Bayesian Linear Models (BLM), including correlated observations, prediction, model selection and comments on efficient numeric…

We provide a general framework for designing Generative Adversarial Networks (GANs) to solve high dimensional robust statistics problems, which aim at estimating unknown parameter of the true distribution given adversarially corrupted…

Fragmentary data is becoming more and more popular in many areas which brings big challenges to researchers and data analysts. Most existing methods dealing with fragmentary data consider a continuous response while in many applications the…

The estimation of loss distributions for dynamic portfolios requires the simulation of scenarios representing realistic joint dynamics of their components. We propose a novel data-driven approach for simulating realistic, high-dimensional…

Despite rapid progress in large language models (LLMs), the statistical structure of their weights, activations, and gradients-and its implications for initialization, training dynamics, and efficiency-remains largely unexplored. We…

The generalised extreme value (GEV) distribution is a three parameter family that describes the asymptotic behaviour of properly renormalised maxima of a sequence of independent and identically distributed random variables. If the shape…

In clinical trials, studies often present longitudinal data or clustered data. These studies are commonly analyzed using linear mixed models (LMMs), usually considering Gaussian assumptions for random effect and error terms. Recently,…