A discrete Ramos-Louzada distribution for asymmetric and over-dispersed data with leptokurtic-shaped: Properties and various estimation techniques with inference

<abstract> <p>In this paper, a flexible probability mass function is proposed for modeling count data, especially, asymmetric, and over-dispersed observations. Some of its distributional properties are investigated. It is found that all its statistical and reliability properties can be expressed in explicit forms which makes the proposed model useful in time series and regression analysis. Different estimation approaches including maximum likelihood, moments, least squares, Andersonӳ-Darling, Cramer von-Mises, and maximum product of spacing estimator, are derived to get the best estimator for the real data. The estimation performance of these estimation techniques is assessed via a comprehensive simulation study. The flexibility of the new discrete distribution is assessed using four distinctive real data sets ԣoronavirus-flood peaks-forest fire-Leukemia? Finally, the new probabilistic model can serve as an alternative distribution to other competitive distributions available in the literature for modeling count data.</p> </abstract>

The New Novel Discrete Distribution with Application on COVID-19 Mortality Numbers in Kingdom of Saudi Arabia and Latvia

This paper aims to introduce a superior discrete statistical model for the coronavirus disease 2019 (COVID-19) mortality numbers in Saudi Arabia and Latvia. We introduced an optimal and superior statistical model to provide optimal modeling for the death numbers due to the COVID-19 infections. This new statistical model possesses three parameters. This model is formulated by combining both the exponential distribution and extended odd Weibull family to formulate the discrete extended odd Weibull exponential (DEOWE) distribution. We introduced some of statistical properties for the new distribution, such as linear representation and quantile function. The maximum likelihood estimation (MLE) method is applied to estimate the unknown parameters of the DEOWE distribution. Also, we have used three datasets as an application on the COVID-19 mortality data in Saudi Arabia and Latvia. These three real data examples were used for introducing the importance of our distribution for fitting and modeling this kind of discrete data. Also, we provide a graphical plot for the data to ensure our results.

Dynamical Characteristics of Recurrent Neuronal Networks Are Robust Against Low Synaptic Weight Resolution

The representation of the natural-density, heterogeneous connectivity of neuronal network models at relevant spatial scales remains a challenge for Computational Neuroscience and Neuromorphic Computing. In particular, the memory demands imposed by the vast number of synapses in brain-scale network simulations constitute a major obstacle. Limiting the number resolution of synaptic weights appears to be a natural strategy to reduce memory and compute load. In this study, we investigate the effects of a limited synaptic-weight resolution on the dynamics of recurrent spiking neuronal networks resembling local cortical circuits and develop strategies for minimizing deviations from the dynamics of networks with high-resolution synaptic weights. We mimic the effect of a limited synaptic weight resolution by replacing normally distributed synaptic weights with weights drawn from a discrete distribution, and compare the resulting statistics characterizing firing rates, spike-train irregularity, and correlation coefficients with the reference solution. We show that a naive discretization of synaptic weights generally leads to a distortion of the spike-train statistics. If the weights are discretized such that the mean and the variance of the total synaptic input currents are preserved, the firing statistics remain unaffected for the types of networks considered in this study. For networks with sufficiently heterogeneous in-degrees, the firing statistics can be preserved even if all synaptic weights are replaced by the mean of the weight distribution. We conclude that even for simple networks with non-plastic neurons and synapses, a discretization of synaptic weights can lead to substantial deviations in the firing statistics unless the discretization is performed with care and guided by a rigorous validation process. For the network model used in this study, the synaptic weights can be replaced by low-resolution weights without affecting its macroscopic dynamical characteristics, thereby saving substantial amounts of memory.

Characterizations of Twenty (2020-2021) Proposed Discrete Distributions

In this paper, certain characterizations of twenty newly proposed discrete distributions: the discrete gen- eralized Lindley distribution of El-Morshedy et al.(2021), the discrete Gumbel distribution of Chakraborty et al.(2020), the skewed geometric distribution of Ong et al.(2020), the discrete Poisson X gamma distri- bution of Para et al.(2020), the discrete Cos-Poisson distribution of Bakouch et al.(2021), the size biased Poisson Ailamujia distribution of Dar and Para(2021), the generalized Hermite-Genocchi distribution of El-Desouky et al.(2021), the Poisson quasi-xgamma distribution of Altun et al.(2021a), the exponentiated discrete inverse Rayleigh distribution of Mashhadzadeh and MirMostafaee(2020), the Mlynar distribution of Fr¨uhwirth et al.(2021), the flexible one-parameter discrete distribution of Eliwa and El-Morshedy(2021), the two-parameter discrete Perks distribution of Tyagi et al.(2020), the discrete Weibull G family distribution of Ibrahim et al.(2021), the discrete Marshall–Olkin Lomax distribution of Ibrahim and Almetwally(2021), the two-parameter exponentiated discrete Lindley distribution of El-Morshedy et al.(2019), the natural discrete one-parameter polynomial exponential distribution of Mukherjee et al.(2020), the zero-truncated discrete Akash distribution of Sium and Shanker(2020), the two-parameter quasi Poisson-Aradhana distribution of Shanker and Shukla(2020), the zero-truncated Poisson-Ishita distribution of Shukla et al.(2020) and the Poisson-Shukla distribution of Shukla and Shanker(2020) are presented to complete, in some way, the au- thors’ works.

A New Skewed Discrete Model: Properties, Inference, and Applications

In this paper, a new probability discrete distribution for analyzing over-dispersed count data encountered in biological sciences was proposed. The new discrete distribution, with one parameter, has a log-concave probability mass function and an increasing hazard rate function, for all choices of its parameter. Several properties of the proposed distribution including the mode, moments and index of dispersion, mean residual life, mean past life, order statistics and L- moment statistics have been established. Two actuarial or risk measures were derived. The numerical computations for these measures are conducted for several parametric values of the model parameter. The parameter of the introduced distribution is estimated using eight frequentist estimation methods. Detailed Monte Carlo simulations are conducted to explore the performance of the studied estimators. The performance of the proposed distribution has been examined by three over-dispersed real data sets from biological sciences.

Quantitative Description for Sand Void Fabric with the Principle of Stereology

Based on the principle of stereology to describe void fabric, the fabric tensor is redefined by the idea of normalization, and a novel quantitative description method for the orthotropic fabric of granular materials is presented. The scan line is described by two independent angles in the stereo space, and the projection of the scan line on three orthogonal planes is used to determine the plane tensor. The second-order plane tensor can be described equivalently by two invariants, which describe the degree and direction of anisotropy of the material, respectively. In the three-dimensional orthogonal space, there are three measurable amplitude parameters on the three orthogonal planes. Due to the normalized definition of tensor in this paper, there are only two independent variations of the three amplitude parameters, and any two amplitude parameters can be used to derive the three-dimensional orthotropic fabric tensor. Therefore, the same orthorhombic anisotropy structure can be described by three fabrics, which enriches the theoretical description of orthotropy greatly. As the geometric relationship of the stereoscopic space scan line changes, the three sets of orthotropic fabrics degenerate into different forms of transversely isotropic and isotropic fabrics naturally and have a clear physical meaning. The novel fabric tensor is quantitatively determined based on mathematical probability and statistics. The discrete distribution of voids in space is projected as a scalar measurable parameter on a plane. This parameter is related to the macroscopic constitutive relationship directly and can be used to describe the effect of microscopic voids on the macroscopic phenomenon of materials.

Magnetization of an elastic ferromagnet

At the macroscopic level, ferromagnetism is a quantum mechanical phenomenon. To describe magnetic materials, it is necessary to create a heuristic model that in terms of continuum mechanics describes the interaction between the lattice continuum, which is a carrier of deformations, and the magnetization field, which is associated with the spin continuum through the gyromagnetic effect. According to the laws of quantum mechanics, each individual particle is associated with a magnetic moment and an internal angular momentum – spin. Electrons mainly contribute to the magnetic moment of the atom. Therefore, the continuum is continuously associated with the discrete distribution of individual spins in a real ferromagnetic body known as the electron spin continuum. In addition, it is necessary to formulate field equations that, together with Maxwell’s equations, describe the electron spin continuum. After that, it is necessary to consider the interaction between the lattice continuum and the electron spin continuum. Elastic ferromagnets should be described with due regard to the spin density and couple stresses. The spin system is a carrier of the magnetic properties, and the mechanical properties are associated with the lattice. Thus, spin–lattice interactions indicate the relationship between magnetic and mechanical properties.

Fine Mapping and Distribution Analysis of Hybrid Necrosis Genes Ne1 and Ne2 in Wheat in China

Hybrid necrosis of wheat is caused by two dominant complementary genes Ne1 and Ne2 present in normal phenotype parents and is regarded as a barrier to gene flow between crop species. However, the necrosis alleles still occur at high frequency in modern wheat varieties. In this study, we constructed two high-density genetic maps of Ne1 and Ne2 in winter wheat. In these cultivars, Ne1 was found to be located in a span interval of 0.50 centimorgan (cM) on chromosome 5BL delimited by markers Nwu_5B_4137 and Nwu_5B_5114, while Ne2 co-segregated with markers Lseq102 and TC67744 on 2BS. Statistical analysis confirmed that the dosage effect of Ne alleles also existed in moderate and severe hybrid necrosis systems, and the symptoms of necrosis can also be affected by the genetic background. Furthermore, we clarified the discrete distribution and proportion of the Ne1 and Ne2 in China’s major wheat regions, and concluded that introduced modern cultivars directly affect the frequencies of necrosis genes in modern Chinese cultivars (lines), especially that of Ne2. Taking investigations in spring wheat together, we proposed that hybrid necrosis alleles could positively affect breeding owing to their linked excellent genes. Additionally, based on the pedigree, we speculated that the Ne1 and Ne2 in winter wheat may directly originate from wild emmer and introduced cultivars or hexaploid triticale, respectively.