Related papers: The Difference-of-Log-Normals Distribution: Proper…
The logarithmic-normal (lognormal) distribution is one of the most frequently observed distributions in nature and describes a large number of physical, biological and even sociological phenomena. The origin of this distribution is…
Gradually Truncated Log-normal distribution - Size distribution of firms Abstract Many natural and economical phenomena are described through power law or log- normal distributions. In these cases, probability decreases very slowly with…
The law of large numbers (LLN) and central limit theorem (CLT) are long and widely been known as two fundamental results in probability theory. Recently problems of model uncertainties in statistics, measures of risk and superhedging in…
In this manuscript we introduce a generalisation of the log-Normal distribution that is inspired by a modification of the Kaypten multiplicative process using the $q$-product of Borges [Physica A \textbf{340}, 95 (2004)]. Depending on the…
The log-normal distribution is used to describe the positive data, that it has skewed distribution with small mean and large variance. This distribution has application in many sciences for example medicine, economics, biology and…
A comprehensive investigation of logN-logS distributions of gamma-ray sources discovered by EGRET has been performed for subsequent use in population studies. Existing models explaining the spatial arrangement of unidentified sources do not…
The normal distribution is well-known for several results that it is the only to fulfil. The aim of the present paper is to show that many of these characterizations actually follow from the fact that the derivative of the log-density of…
The log-normal distribution is one of the most common distributions used for modeling skewed and positive data. It frequently arises in many disciplines of science, specially in the biological and medical sciences. The statistical analysis…
The central limit theorem ensures that a sum of random variables tends to a Gaussian distribution as their total number tends to infinity. However, for a class of positive random variables, we find that the sum tends faster to a log-normal…
Dirichlet-multinomial (DMN) distribution is commonly used to model over-dispersion in count data. Precise and fast numerical computation of the DMN log-likelihood function is important for performing statistical inference using this…
Label distribution learning (LDL) is a general learning framework, which assigns to an instance a distribution over a set of labels rather than a single label or multiple labels. Current LDL methods have either restricted assumptions on the…
A new distribution on (0, 1), generalized Log-Lindley distribution, is proposed by extending the Log-Lindley distribution. This new distribution is shown to be a weighted Log-Lindley distribution. Important probabilistic and statistical…
Probability density functions (PDF) of statistical distributions of cluster sizes N, where N is the number of particles in the cluster, often seem to have less freedom than expected from considering the number of degrees of freedom at the…
The bivariate Gaussian distribution has been a key model for many developments in statistics. However, many real-world phenomena generate data that follow asymmetric distributions, and consequently bivariate normal model is inappropriate in…
We quantitatively study the probability distribution function (PDF) of cosmological nonlinear density fluctuations from N-body simulations with Gaussian initial condition. In particular, we examine the validity and limitations of one-point…
We study numerically and analytically the moments of the dimensionless level curvature for one-dimensional disordered rings of the circumference L pierced by a magnetic flux. The negative moments of the curvature distribution can be…
In this paper, we proposed a new lifetime distribution namely generalized weighted Lindley (GLW) distribution. The GLW distribution is a useful generalization of the weighted Lindley distribution, which accommodates increasing, decreasing,…
Employing profits data of Japanese firms in 2003--2005, we kinematically exhibit the static log-normal distribution in the middle scale region. In the derivation, a Non-Gibrat's law under the detailed balance is adopted together with…
In one dimension, the theory of the $G$-normal distribution is well-developed, and many results from the classical setting have a nonlinear counterpart. Significant challenges remain in multiple dimensions, and some of what has already been…
A common task in physics, information theory, and other fields is the analysis of properties of subsystems of a given system. Given the covariance matrix $M$ of a system of $n$ coupled variables, the covariance matrices of the subsystems…