The Poisson and Normal probability distributions poorly match the dark current histogram of a typical image sensor. The histogram has only positive values, and is positively skewed (with a long tail). The Normal distribution is symmetric (and possesses negative values), while the Poisson distribution is discrete. Image sensor characterization and simulation would benefit from a different distri...

This paper presents the basic scheme and the log-normal, log-gamma and lognegative inverted gamma scenarios to establish the Rényi function for infinite products of homogeneous isotropic random fields on R. We also present our scheme for a field on the spherical surface in R, which is related to the CMRB problem in Cosmology. In the presentation, we need to employ spherical harmonics for some c...

Development of new flexible distributions for modeling non-negative measurements occuring in lifetime or reliability studies is a prominent research area Statistics. As being the most favoured positive definite form, Gamma distribution poses basis such improvements. It well known that transforming variable with another continuous random (X) creates Gamma-X family distributions. Following this p...

Drought assessment and trend analysis of precipitation temperature time series are essential in the planning management water resources. Long-term historical records (monthly for 41 years, from 1980 to 2020) used investigate annual drought characteristics Somalia’s northern region. Six indices normal Standardized Precipitation Index (normal-SPI), log (log-SPI), using gamma distribution (Gamma-S...

We study stability of the sharp Poincaré constant invariant probability measure a reversible diffusion process satisfying some natural conditions. The proof is based on spectral interpretation inequalities and Stein’s method. In particular, these results are applied to gamma distributions, Brownian motion spheres Brascamp-Lieb inequality for one-dimensional log-concave measures.

Variance-Gamma distributions are widely used in financial modelling and contain as special cases the normal, Gamma and Laplace distributions. In this paper we extend Stein’s method to this class of distributions. In particular, we obtain a Stein equation and smoothness estimates for its solution. This Stein equation has the attractive property of reducing to the known normal and Gamma Stein equ...

Let $G$ be a finite group. The prime graph of $G$ is a graph $Gamma(G)$ with vertex set $pi(G)$, the set of all prime divisors of $|G|$, and two distinct vertices $p$ and $q$ are adjacent by an edge if $G$ has an element of order $pq$. In this paper we prove that if $Gamma(G)=Gamma(G_2(5))$, then $G$ has a normal subgroup $N$ such that $pi(N)subseteq{2,3,5}$ and $G/Nequiv G_2(5)$.

There are two methods for identifying formation interface in oil wells: core analysis, which is a precise approach but costly and time consuming, and well logs analysis, which petrophysists perform, which is subjective and not completely reliable. In this paper, a novel coupled method was proposed to detect the formation interfaces using GR logs. Second approximation level (a2) of GR log gained...

We theoretically study the performance of multiple-input multiple-output (MIMO) free-space optical (FSO) systems using subcarrier quadrature modulation (SC-QAM) signaling. The system average symbolerror rate (ASER) is derived taking into account the atmospheric turbulence effects on the MIMO/FSO channel, which is modeled by log-normal and the gamma-gamma distributions for weak and moderate-to-s...