Related papers: New probability distributions in astrophysics: V. …
Context: Two-point correlation functions are used throughout cosmology as a measure for the statistics of random fields. When used in Bayesian parameter estimation, their likelihood function is usually replaced by a Gaussian approximation.…
The Median Based Unit Weibull is a new 2 parameter unit Weibull distribution defined on the unit interval (0,1). Estimation of the parameters using MLE encountered some problems like large variance. Using generalized method of moments…
The Kumaraswamy Inverse Weibull distribution has the ability to model failure rates that have unimodal shapes and are quite common in reliability and biological studies. The three-parameter Kumaraswamy Inverse Weibull distribution with…
A multivariate survival function of Weibull Distribution is developed by expanding the theorem by Lu and Bhattacharyya (1990). From the survival function, the probability density function, the cumulative probability function, the…
The wrapped normal distribution arises when a the density of a one-dimensional normal distribution is wrapped around the circle infinitely many times. At first look, evaluation of its probability density function appears tedious as an…
First-order statistics of scattered light is described using the representation of probability density cloud which visualizes a two-dimensional distribution for complex amplitude. The geometric parameters of the cloud are studied in detail…
We apply machine learning in the form of a nearest neighbor instance-based algorithm (NN) to generate full photometric redshift probability density functions (PDFs) for objects in the Fifth Data Release of the Sloan Digital Sky Survey (SDSS…
The characteristic function of the folded normal distribution and its moment function are derived. The entropy of the folded normal distribution and the Kullback--Leibler from the normal and half normal distributions are approximated using…
For the basic maximum likelihood estimating function of the two parameters Weibull distribution, a simple proof on its global monotonicity is given to ensure the existence and uniqueness of its solution. The boundary of the function's…
The search for a luminosity function for galaxies both alternative or companion to a Schechter function is a key problem in the reduction of data from catalogs of galaxies. Two luminosity functions for galaxies can be built starting from…
The Weibull distribution, with shape parameter $k>0$ and scale parameter $\lambda>0$, is one of the most popular parametric distributions in survival analysis with complete or censored data. Although inference of the parameters of the…
We present an approximate form for the weak lensing magnification distribution of standard candles, valid for all cosmological models, with arbitrary matter distributions, over all redshifts. Our results are based on a universal probability…
We extend existing methods for using cross-correlations to derive redshift distributions for photometric galaxies, without using photometric redshifts. The model presented in this paper simultaneously yields highly accurate and unbiased…
The initial mass function (IMF) for the stars is usually fitted by three straight lines, which means seven parameters. The presence of brown dwarfs (BD) increases to four the straight lines and to nine the parameters. Another common fitting…
The gamma density function is usually defined in interval between zero and infinity. This paper introduces an upper and a lower boundary to this distribution. The parameters which characterize the truncated gamma distribution are evaluated.…
Benford's law states that many data sets have a bias towards lower leading digits (about $30\%$ are 1s). There are numerous applications, from designing efficient computers to detecting tax, voter and image fraud. It's important to know…
The Gumbel-Softmax probability distribution allows learning discrete tokens in generative learning, while the Gumbel-Argmax probability distribution is useful in learning discrete structures in discriminative learning. Despite the efforts…
In experiment, the multiplicity distributions of inelastic processes are truncated due to finite energy, insufficient statistics or special choice of events. It is shown that the moments of such truncated multiplicity distributions possess…
We analyse the bivariate distribution, in color versus absolute magnitude (u-r vs. M_r), of a low redshift sample of galaxies from the Sloan Digital Sky Survey (SDSS; 2400 deg^2, 0.004<z<0.08, -23.5<M_r<-15.5). We trace the bimodality of…
We develop a new method which measures the projected density distribution w_p(r_p)n of photometric galaxies surrounding a set of spectroscopically-identified galaxies, and simultaneously the projected correlation function w_p(r_p) between…