Related papers: Generalized Estimating Equation for the Student-t …
We consider the Student-t and Student-r distributions, which maximise Renyi entropy under a covariance condition. We show that they have information-theoretic properties which mirror those of the Gaussian distributions, which maximise…
Recently, Verma et al. (2025) introduced a novel generalized class of Kavya-Manoharan distributions, which have demonstrated significant utility in reliability analysis and the modeling of lifetime data. This paper proposes an extension of…
This paper considers the robust and efficient implementation of Gaussian process regression with a Student-t observation model. The challenge with the Student-t model is the analytically intractable inference which is why several…
It has been repeatedly stated that maximum likelihood (ML) estimates of exponents of power-law distributions can only be reliably obtained for exponents smaller than minus one. The main argument that power laws are otherwise not…
We study shrinkage estimation of the mean parameters of a class of multivariate distributions for which the diagonal entries of the corresponding covariance matrix are certain quadratic functions of the mean parameter. This class of…
The mathematical properties of a family of generalized beta distribution, including beta-normal, skewed-t, log-F, beta-exponential, beta-Weibull distributions have recently been studied in several publications. This paper applies these…
The asymptotic correspondence between the probability mass function of the $q$-deformed multinomial distribution and the $q$-generalised Kullback-Leibler divergence, also known as Tsallis relative entropy, is established. The probability…
An amended MaxEnt formulation for systems displaced from the conventional MaxEnt equilibrium is proposed. This formulation involves the minimization of the Kullback-Leibler divergence to a reference $Q$ (or maximization of Shannon…
This undergraduate thesis focuses on calculating maximum likelihood estimates of parameters in the generalized Gamma distribution using the SeLF algorithm. As an extension of the Gamma distribution, the generalized Gamma distribution can…
Distributed learning of probabilistic models from multiple data repositories with minimum communication is increasingly important. We study a simple communication-efficient learning framework that first calculates the local maximum…
Standard maximum likelihood estimation cannot be applied to discrete energy-based models in the general case because the computation of exact model probabilities is intractable. Recent research has seen the proposal of several new…
We analyze the problem of maximum likelihood estimation for Gaussian distributions that are multivariate totally positive of order two (MTP2). By exploiting connections to phylogenetics and single-linkage clustering, we give a simple proof…
In this paper, we introduce a new class of distributions by compounding the exponentiated extended Weibull family and power series family. This distribution contains several lifetime models such as the complementary extended Weibull-power…
In this paper, we establish the links between the Lehmer and H\"older mean families and maximum weighted likelihood estimator. Considering the regular one-parameter exponential family of probability density functions, we show that the…
Let $(x_{i}, y_{i})_{i=1,\dots,n}$ denote independent samples from a general mixture distribution $\sum_{c\in\mathcal{C}}\rho_{c}P_{c}^{x}$, and consider the hypothesis class of generalized linear models $\hat{y} = F(\Theta^{\top}x)$. In…
The pathway model of Mathai (2005) mainly deals with the rectangular matrix-variate case. In this paper the scalar version is shown to be associated with a large number of probability models used in physics. Different families of densities…
Aggregation methods have emerged as a powerful and flexible framework in statistical learning, providing unified solutions across diverse problems such as regression, classification, and density estimation. In the context of generalized…
It is well known that, under standard regularity conditions, the maximum likelihood estimator (MLE) satisfies a central limit theorem and converges in distribution to a Gaussian random variable as the sample size grows. This paper…
Relative entropy is a fundamental class of distances between probability distributions, with widespread applications in probability theory, statistics, and machine learning. In this work, we study relative entropy from a categorical…
The Generalized Central Limit Theorem is a remarkable generalization of the Central Limit Theorem, showing that the sum of a large number of independent, identically-distributed (i.i.d) random variables with infinite variance may converge…