Related papers: On the computation of the cumulative distribution …
For random variables produced through the inverse transform method, approximate random variables are introduced, which are produced by approximations to a distribution's inverse cumulative distribution function. These approximations are…
Using a recently derived integral in terms of elementary functions, we derive new asymptotic expansions of the normal inverse Gaussian cumulative distribution function. One of the asymptotic representations is in terms of the normal…
There are three main types of numerical computations for the Bessel function of the second kind: series expansion, continued fraction, and asymptotic expansion. In addition, they are combined in the appropriate domain for each. However,…
We obtain exact formulas for the cumulative distribution function of the variance-gamma distribution, as infinite series involving the modified Bessel function of the second kind and the modified Lommel function of the first kind. From…
We propose an algorithm for evaluation of the cumulative bivariate normal distribution, building upon Marsaglia's ideas for evaluation of the cumulative univariate normal distribution. The algorithm is mathematically transparent, delivers…
Doubly intractable distributions arise in many settings, for example in Markov models for point processes and exponential random graph models for networks. Bayesian inference for these models is challenging because they involve intractable…
Modified Bessel functions of the second kind are widely used in physics, engineering, spatial statistics, and machine learning. Since contemporary scientific applications, including machine learning, rely on GPUs for acceleration, providing…
In this paper we consider Bayesian estimation for the parameters of inverse Gaussian distribution. Our emphasis is on Markov Chain Monte Carlo methods. We provide complete implementation of the Gibbs sampler algorithm. Assuming an…
The generalized inverse Gaussian, denoted $\mathrm{GIG}(p, a, b)$, is a flexible family of distributions that includes the gamma, inverse gamma, and inverse Gaussian distributions as special cases. In addition to its applications in…
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…
In this article, we propose a new three parameter distribution by compounding negative binomial with reciprocal inverse Gaussian model called negative binomial-reciprocal inverse Gaussian distribution. This model is tractable with some…
The computation and inversion of the binomial and negative binomial cumulative distribution functions play a key role in many applications. In this paper, we explain how methods used for the central beta distribution function (described in…
Thesis is devoted to the application of cumulant analysis in the estimation of impulse response functions for continuous time-invariant linear systems, including systems with inner noises. The main assumption of the work is the second-order…
In this study, a numerical quadrature for the generalized inverse Gaussian distribution is derived from the Gauss-Hermite quadrature by exploiting its relationship with the normal distribution. The proposed quadrature is not Gaussian, but…
The normal or Gaussian distribution plays a prominent role in almost all fields of science. However, it is well known that the Gauss (or Euler--Poisson) integral over a finite boundary, as it is necessary for instance for the error function…
The inverse Gaussian distribution (IGD) is a well known and often used probability distribution for which fully reliable numerical algorithms have not been available. Our aim in this article is to develop software for this distribution for…
Non-Gaussian distributions are commonly observed in collisionless space plasmas. Generating samples from non-Gaussian distributions is critical for the initialization of particle-in-cell simulations that investigate their driven and…
We investigate a family of integrals involving modified Bessel functions that arise in the context of neutrino scattering. Recursive formulas are derived for evaluating these integrals and their asymptotic expansions are computed. We prove…
In distributed optimization and distributed numerical linear algebra, we often encounter an inversion bias: if we want to compute a quantity that depends on the inverse of a sum of distributed matrices, then the sum of the inverses does not…
We introduce an approach to quickly and accurately approximate the cumulative distribution function of multivariate Gaussian distributions arising from spatial Gaussian processes. This approximation is trivially parallelizable and simple to…