Related papers: Generalizing the normality: a novel towards differ…
Accurately estimating data density is crucial for making informed decisions and modeling in various fields. This paper presents a novel nonparametric density estimation procedure that utilizes bivariate penalized spline smoothing over…
A great deal of inference in statistics is based on making the approximation that a statistic is normally distributed. The error in doing so is generally $O(n^{-1/2})$ and can be very considerable when the distribution is heavily biased or…
The paper by Leiva et al. (2010) introduced a skewed version of the sinh-normal distribution, discussed some of its properties and characterized an extension of the Birnbaum-Saunders distribution associated with this distribution. In this…
In this work, we investigate the use of normalizing flows to model conditional distributions. In particular, we use our proposed method to analyze inverse problems with invertible neural networks by maximizing the posterior likelihood. Our…
We explain Kossovsky's generalization of Benford's law which is a formula that approximates the distribution of leftmost digits in finite sequences of natural data and apply it to six sequences of data including populations of US cities and…
Finite mixture models have been widely used to model and analyze data from a heterogeneous populations. Moreover, data of this kind can be missing or subject to some upper and/or lower detection limits because of the restriction of…
Sequential data collection has emerged as a widely adopted technique for enhancing the efficiency of data gathering processes. Despite its advantages, such data collection mechanism often introduces complexities to the statistical inference…
Two approaches are suggested to the definition of asymmetric generalized Weibull distribution. These approaches are based on the representation of the two-sided Weibull distributions as variance-mean normal mixtures or more general…
Normalizing flows are a flexible class of probability distributions, expressed as transformations of a simple base distribution. A limitation of standard normalizing flows is representing distributions with heavy tails, which arise in…
The normality assumption on data set is very restrictive approach for modelling. The generalized form of normal distribution, named as an exponential power (EP) distribution, and its scale mixture form have been considered extensively to…
Normalizing flows provide an elegant approach to generative modeling that allows for efficient sampling and exact density evaluation of unknown data distributions. However, current techniques have significant limitations in their…
A random phenomenon may have two sources of random variation: an unstable identity and a set of external variation-generating factors. When only a single source is active, two mutually exclusive extreme scenarios may ensue that result in…
It is well known that the independence of the sample mean and the sample variance characterizes the normal distribution. By using Anosov's theorem, we further investigate the analogous characteristic properties in terms of the sample mean…
Normalizing flows are a class of generative models that enable exact likelihood evaluation. While these models have already found various applications in particle physics, normalizing flows are not flexible enough to model many of the…
The beta normal distribution is a generalization of both the normal distribution and the normal order statistics. Some of its mathematical properties and a few applications have been studied in the literature. We provide a better foundation…
Estimating the normalizing constant of an unnormalized probability distribution has important applications in computer science, statistical physics, machine learning, and statistics. In this work, we consider the problem of estimating the…
Normalizing flows transform a latent distribution through an invertible neural network for a flexible and pleasingly simple approach to generative modelling, while preserving an exact likelihood. We propose FlowGMM, an end-to-end approach…
Several generalizations of the logistic distribution, and certain related models, are proposed by many authors for modeling various random phenomena such as those encountered in data engineering, pattern recognition, and reliability…
This study focuses on the novel application of a normalizing flow as a method of domain adaptation. Normalizing flows offer a way to transform data points between two different distributions. The present study investigates a method of…
As in other estimation scenarios, likelihood based estimation in the normal mixture set-up is highly non-robust against model misspecification and presence of outliers (apart from being an ill-posed optimization problem). A robust…