Related papers: Constructing a bivariate distribution function wit…
A new luminosity function for galaxies can be built starting from the product of two random variables X and Y represented by a gamma variate with argument 2 >. The mean, the standard deviation and the distribution function of this new…
In this paper we fit an analytic function to the Bivariate Brightness Distribution (BBD) of galaxies. It is a combination of the classical Schechter Function convolved with a Gaussian distribution in surface brightness: thus incorporating…
The omnipotence of copulas when modeling dependence given marg\-inal distributions in a multivariate stochastic situation is assured by the Sklar's theorem. Montes et al.\ (2015) suggest the notion of what they call an \emph{imprecise…
We show how to construct the implied copula process of response values from a Bayesian additive regression tree (BART) model with prior on the leaf node variances. This copula process, defined on the covariate space, can be paired with any…
The coefficients a and b of the Fundamental Plane relation R ~ Sigma^a I^b depend on whether one minimizes the scatter in the R direction or orthogonal to the Plane. We provide explicit expressions for a and b (and confidence limits) in…
We have derived the bivariate luminosity function for the far ultraviolet (1530Angstroms) and far infrared (60 microns). We used matched GALEX and IRAS data, and redshifts from NED and PSC-z. We have derived a total star formation…
With the advent of large scale surveys (i.e., Legacy Surveys) it is now possible to start looking beyond the galaxy luminosity function (LF) to more detailed statistical representations of the galaxy population, i.e., multivariate…
The accumulation of {\it Swift} observed gamma-ray bursts (GRBs) gradually makes it possible to directly derive a GRB luminosity function (LF) from observational luminosity distribution, where however two complexities must be involved as…
Dynamical processes in various natural and social phenomena have been described by a series of events or event sequences showing non-Poissonian, bursty temporal patterns. Temporal correlations in such bursty time series can be understood…
We introduce the coverage correlation coefficient, a novel nonparametric measure of statistical association designed to quantifies the extent to which two random variables have a joint distribution concentrated on a singular subset with…
Generalized additive models for location, scale and shape (GAMLSS) are a popular extension to mean regression models where each parameter of an arbitrary distribution is modelled through covariates. While such models have been developed for…
This invited feature article introduces and provides an extensive simulation study of a new Approximate Bayesian Computation (ABC) framework for estimating the posterior distribution and the maximum likelihood estimate (MLE) of the…
This paper investigates the probabilistic properties that determine the existence of space-time transformations between diffusion processes. We prove that two diffusions are related by a monotone space-time transformation if and only if…
Weak gravitational lensing requires precise measurements of galaxy shapes and therefore an accurate knowledge of the PSF model. The latter can be a source of systematics that affect the shear two-point correlation function. A key stake of…
Gaussian copulas are widely used in the industry to correlate two random variables when there is no prior knowledge about the co-dependence between them. The perturbed Gaussian copula approach allows introducing the skew information of both…
We discuss a bivariate beta distribution that can model arbitrary beta-distributed marginals with a positive correlation. The distribution is constructed from six independent gamma-distributed random variates. We show how the parameters of…
We develop the tools necessary to assess the statistical significance of resonant features in the CMB correlation functions, combining power spectrum and bispectrum measurements. This significance is typically addressed by running a large…
We utilize copulas to constitute a unified framework for constructing and optimizing variational proposals in hierarchical Bayesian models. For models with continuous and non-Gaussian hidden variables, we propose a semiparametric and…
Seaman and Keogh (Biometrical Journal 2024) proposed a method for simulating data compatible with a marginal structural model (MSM) for the hazard of a survival time outcome. In this short report, I propose two extensions of this method.…
We present an approach for simulating the collisional evolution of spherical isotropic stellar systems based on the one-dimensional Fokker-Planck equation. A novel aspect is that we use the phase volume as the argument of the distribution…