Related papers: Acknowledgment of priority: Usage of the Lambert W…
Probability metrics constitute an important tool in probability theory and statistics \cite{DKS91}, \cite{R91}, \cite{Z83} as they are specific metrics on spaces of random variables which, by satisfying an extra condition, concord well with…
For complex latent variable models, the likelihood function is not available in closed form. In this context, a popular method to perform parameter estimation is Importance Weighted Variational Inference. It essentially maximizes the…
Maximum likelihood estimation and a test of fit based on the Anderson-Darling statistic is presented for the case of the power law distribution when the parameters are estimated from a left-censored sample. Expressions for the maximum…
The likelihood ratio is a crucial quantity for statistical inference in science that enables hypothesis testing, construction of confidence intervals, reweighting of distributions, and more. Many modern scientific applications, however,…
A connection between fractional calculus and statistical distribution theory has been established by the authors recently. Some extensions of the results to matrix-variate functions were also considered. In the present article, more results…
Consider a pair of cumulative distribution functions $F$ and $G$, where $F$ is unknown and $G$ is a known reference distribution. Given a sample from $F$, we propose tests to detect the convexity or the concavity of $G^{-1}\circ F$ versus…
Empirical likelihood approach is one of non-parametric statistical methods, which is applied to the hypothesis testing or construction of confidence regions for pivotal unknown quantities. This method has been applied to the case of…
A generalization of the Lambert W function called the logarithmic Lambert function is found to be a solution to the thermostatics of the three-parameter entropy of classical ideal gas in adiabatic ensembles. The derivative, integral, Taylor…
Problems formulated in terms of logarithmic or exponential equations often use the Lambert $W$ function in their solutions. Expansions, approximations and bounds on $W$ have been derived in an effort to gain a better understanding of the…
The likelihood function plays a crucial role in statistical inference and experimental design. However, it is computationally intractable for several important classes of statistical models, including energy-based models and simulator-based…
We deal with a general class of extreme-value regression models introduced by Barreto- Souza and Vasconcellos (2011). Our goal is to derive an adjusted likelihood ratio statistic that is approximately distributed as \c{hi}2 with a high…
Nonparametric generalized likelihood ratio test is popularly used for model checking for regressions. However, there are two issues that may be the barriers for its powerfulness. First, the bias term in its liming null distribution causes…
A refinement of Bennett's inequality is introduced which is strictly tighter than the classical bound. The new bound establishes the convergence of the average of independent random variables to its expected value. It also carefully…
Azzalini & Dalla Valle (1996) have recently discussed the multivariate skew-normal distribution which extends the class of normal distributions by the addition of a shape parameter. The first part of the present paper examines further…
We describe likelihood-based statistical tests for use in high energy physics for the discovery of new phenomena and for construction of confidence intervals on model parameters. We focus on the properties of the test procedures that allow…
Since its introduction by Fisher, the method of hypothesis testing that relies on computing error probabilities has witnessed several developments. Perhaps the most significant development was the seminal contributions of Neyman and Pearson…
Since its introduction, the skew-$t$ distribution has received much attention in the literature both for the study of theoretical properties and as a model for data fitting in empirical work. A major motivation for this interest is the high…
Statistical significance measures the reliability of a result obtained from a random experiment. We investigate the number of repetitions needed for a statistical result to have a certain significance. In the first step, we consider…
Ratios of random variables often appear in probability and statistical applications. We aim to approximate the moments of such ratios under several dependence assumptions. Extending the ideas in Collomb [C. R. Acad. Sci. Paris 285 (1977)…
Inference based on the penalized density ratio model is proposed and studied. The model under consideration is specified by assuming that the log--likelihood function of two unknown densities is of some parametric form. The model has been…