Related papers: The Difference-of-Log-Normals Distribution: Proper…
Here in this paper, it is tried to obtain and compare the ML estimations based on upper record values and a random sample. In continue, some theorems have been proven about the behavior of these estimations asymptotically.
In this article, the exponentiated discrete Lindley distribution is presented and studied. Some important distributional properties are discussed. Using the maximum likelihood method, estimation of the model parameters is investigated.…
A previously established frequency distribution model combining a log-normal distribution with a logarithmic equation describes fluctuations in the email size during send requests. Although the frequency distribution fit was considered…
We present Linear Diffusion Networks (LDNs), a novel architecture that reinterprets sequential data processing as a unified diffusion process. Our model integrates adaptive diffusion modules with localized nonlinear updates and a…
This thesis focuses on characterizing the distribution of points and galaxies using multifractal analysis. In this attempt the main emphasis is on calculating the Minkowski-Bouligand fractal dimension (Dq) of the distribution of points over…
Distribution learning finds probability density functions from a set of data samples, whereas clustering aims to group similar data points to form clusters. Although there are deep clustering methods that employ distribution learning…
The main statistical distributions applicable to the analysis of genome architecture and genome tracks are briefly discussed and critically assessed. Although the observed features in distributions of element lengths can be equally well…
We introduce a solvable model of randomly growing systems consisting of many independent subunits. Scaling relations and growth rate distributions in the limit of infinite subunits are analysed theoretically. Various types of scaling…
In this paper, an alternative Discrete skew Logistic distribution is proposed, which is derived by using the general approach of discretizing a continuous distribution while retaining its survival function. The properties of the…
Counts of galaxies as a function of apparent magnitude are among the most time-honored observations in cosmology. In this Letter, we focus on some statistical properties of these counts which are fundamental in order to characterize the…
There are given characterizations of the exponential distribution by the properties of the independence of linear forms with random coefficients. Related results based on the constancy of regression of one statistic on a linear form are…
Modern analysis on parton distribution functions (PDFs) requires calculations of the log-likelihood functions from thousands of experimental data points, and scans of multi-dimensional parameter space with tens of degrees of freedom. In…
We study the parametric description of the city size distribution (CSD) of 70 different countries (developed and developing) using seven models, as follows: the lognormal (LN), the loglogistic (LL), the double Pareto lognormal (dPLN), the…
This paper mainly focuses on studying the Shannon Entropy and Kullback-Leibler divergence of the multivariate log canonical fundamental skew-normal (LCFUSN) and canonical fundamental skew-normal (CFUSN) families of distributions, extending…
We propose that the distribution of DNA words in genomic sequences can be primarily characterized by a double Pareto-lognormal distribution, which explains lognormal and power-law features found across all known genomes. Such a distribution…
Many-body stochastic processes with weighted multiplicative interactions are investigated analytically and numerically. An interaction rate between particles with quantities $x, y$ is controlled by a homogeneous symmetric kernel $K(x, y)…
Distributed order fractional Langevin-like equations are introduced and applied to describe anomalous diffusion without unique diffusion or scaling exponent. It is shown that these fractional Langevin equations of distributed order can be…
We study unit-level expenditure on consumption across multiple countries and multiple years, in order to extract invariant features of consumption distribution. We show that the bulk of it is lognormally distributed, followed by a power law…
Machine Learning (ML) models are extensively used in various applications due to their significant advantages over traditional learning methods. However, the developed ML models often underperform when deployed in the real world due to the…
The paper presents some distributional properties of logistic order statistics subject to independent exponential one-sided and two-sided shifts. Utilizing these properties, we extend several known results and obtain some new…