Related papers: Asymptotic inversion of the binomial and negative …
The inversion of linear systems is a fundamental step in many inverse problems. Computational challenges exist when trying to invert large linear systems, where limited computing resources mean that only part of the system can be kept in…
In this paper an iterated function system on the space of distribution functions is built. The inverse problem is introduced and studied by convex optimization problems. Some applications of this method to approximation of distribution…
The paper considers a universal approach that allows one to quite simply obtain nonlinear asymptotic estimates of various summation functions. It is shown the application of this approach to the asymptotic estimation of divergent Dirichlet…
In this paper, we provide explicit formulas, in terms of the covariances of sample covariances or sample correlations, for the asymptotic covariances of unrotated factor loading estimates and unique variance estimates. These estimates are…
The distribution function of the sum of i.i.d. random variables of the special form is considered. Such sum describes messages posterior probabilities for random coding in binary symmetric channel. Close non-asymptotic lower and upper…
The beta distribution is the best-known distribution for modelling doubly-bounded data, \eg percentage data or probabilities. A new generalization of the beta distribution is proposed, which uses a cubic transformation of the beta random…
Varying domains and biased datasets can lead to differences between the training and the target distributions, known as covariate shift. Current approaches for alleviating this often rely on estimating the ratio of training and target…
We consider the asymptotic evaluation of the integral transform $\int_0^\infty f(x) \, \sin^n(\lambda x)/x^n \,\text{d} x$ of an exponential type function $f(x)$ of type $\tau>0$, for large values of the parameter $\lambda$, where $n$ is a…
Negative binomial regression is commonly employed to analyze overdispersed count data. With small to moderate sample sizes, the maximum likelihood estimator of the dispersion parameter may be subject to a significant bias, that in turn…
We perform differential expression analysis of high-throughput sequencing count data under a Bayesian nonparametric framework, removing sophisticated ad-hoc pre-processing steps commonly required in existing algorithms. We propose to use…
Motivated by applications in Bayesian analysis we introduce a multidimensional beta distribution in an ordered simplex. We study properties of this distribution and connect them with the generalized incomplete beta function. This function…
For a variant of the algorithm in [Pit19] (arXiv:1903.10816) to compute the approximate density or distribution function of a linear mixture of independent random variables known by a finite sample, it is presented a proof of the functional…
The cumulative distribution function (CDF) of the doubly non-central beta distribution can be expressed as an infinite double series. By truncating the sum of this series, one can obtain an approximate value of the CDF. Although numerous…
The negative binomial distribution (NBD) has been theorized to express a scale-invariant property of many-body systems and has been consistently shown to outperform other statistical models in both describing the multiplicity of…
We consider binomial and inverse binomial sums at infinity and rewrite them in terms of a small set of constants, such as powers of $\pi$ or $\log(2)$. In order to perform these simplifications, we view the series as specializations of…
We describe a general method for the construction of a confidence region for the two parameters of the Negative Binomial Distribution. This is achieved by expanding the sampling distribution of Method-of-Moments estimators, using the…
In this paper we study a broad class of distribution functions which is defined by means of reflected generalized beta distribution. This class includes that of Beta-generated distribution as a special case. In particular, we use this class…
Asymptotic equivalence theory developed in the literature so far are only for bounded loss functions. This limits the potential applications of the theory because many commonly used loss functions in statistical inference are unbounded. In…
In this paper we show how to use Fourier transform methods to analyze the asymptotic behavior of kernel distribution function estimators. Exact expressions for the mean integrated squared error in terms of the characteristic function of the…
Asymptotic concentration behaviors of linear combinations of weight distributions on the random linear code ensemble are presented. Many important properties of a binary linear code can be expressed as the form of a linear combination of…