Penalized Maximum Likelihood Estimator for Finite Skew-Laplace-Normal Mixtures

Skew-Laplace-Normal Mixture models is a more flexible framework than the normal mixture models for heterogeneous data with asymmetric behaviors. But it’s likelihood function have some bad math properties, such as the unboundedness of likelihood function and the divergency of skewness parameter, it often mislead statistic inference. In this paper, we given a penalizing the likelihood function method to deal with these problem simultaneously, and we given the detail of proof on parameter have strongly consistency. We also give a modified penalized EM-type algorithms to compute penalized estimators.

Differentially private density estimation with skew-normal mixtures model

The protection of private data is a hot research issue in the era of big data. Differential privacy is a strong privacy guarantees in data analysis. In this paper, we propose DP-MSNM, a parametric density estimation algorithm using multivariate skew-normal mixtures (MSNM) model to differential privacy. MSNM can solve the asymmetric problem of data sets, and it is could approximate any distribution through expectation–maximization (EM) algorithm. In this model, we add two extra steps on the estimated parameters in the M step of each iteration. The first step is adding calibrated noise to the estimated parameters based on Laplacian mechanism. The second step is post-processes those noisy parameters to ensure their intrinsic characteristics based on the theory of vector normalize and positive semi definition matrix. Extensive experiments using both real data sets evaluate the performance of DP-MSNM, and demonstrate that the proposed method outperforms DPGMM.

Impact of Natural Products on Developing New Treatments for Corona Virus Disease (COVID-19): Review

COVID-19 is dominatingly considered as an unavoidable pandemic, and researchers are exceptionally inquisitive about how to give the best assurance to people in general before an immunization can be made accessible. Normal items have consistently assumed an essential part in drug advancement measure against different illnesses, which brought about screening of such specialists to battle emanant freaks of infections. Contingent upon the construction, component of activity and hazard elements of Covid-19, this audit centers around those normal mixtures that showed promising outcomes against Corona infections. Although restraint of viral replication is frequently considered as an overall component for antiviral action of many of the characteristic items, contemplates have shown that some regular items can connect with key viral proteins that are related with destructiveness. Supplementation of natural products might be a affect to reduce risk through different mechanisms. In this unique circumstance, a portion of the regular items have antiviral action in the nanomolar fixation and could be leads for additional medication advancement all alone or as a format for drug plan. Also, a decent number of normal items with against Covid action are the significant constituents of some regular dietary enhancements, which can be abused to improve the resistance of everyone in specific scourges The candidate compounds identified by us may help to speed up the drug development against COVID-19.

Do Prior Type and Sample Size have Effect on Mixtures of Normal? The Monte Carlo evidence

Overtime finite mixtures of Normal in regression have gained popularity and also shown to be useful in modelling heterogeneous data. This study examines the effects of prior and sample size in regression mixtures of Normal models with Bayesian approach. Monte Carlo experiment was carried out on the Normal mixtures model in order to examine the strength of priors and also to know the suitable sample size to produce stable results. Results obtained from the experiment indicate that an informative prior gives a reliable estimate than non-informative prior while large sample sizes maybe needed to obtain stable results.

Differentially Private Density Estimation with Skew-Normal Mixtures Model

The protection of private data is a hot research issue in the era of big data. Differential privacy is a strong privacy guarantees in data analysis. In this paper, we propose DP-MSNM, a parametric density estimation algorithm using Multivariate Skew-Normal Mixtures (MSNM) model to differential privacy. MSNM can solve the asymmetric problem of datasets, and it is could approximate any distribution through Expectation-Maximization (EM) algorithm. In this model,we add two extra steps on the estimated parameters in the M step of each iteration. The first step is adding calibrated noise to the estimated parameters based on Laplacian mechanism. The second step is post-processes those noisy parameters to ensure their intrinsic characteristics based on the theory of vector normalize and positive semi definition matrix. Extensive experiments using both real datasets evaluate the performance of DP-MSNM, and demonstrate that the proposed method outperforms DP-GMM.

Track Models

The chapter shows how the equations of motion for charged particles in a homogeneous or inhomogeneous magnetic field are solved. Various types of parametrizations are presented, and formulas for track propagation and error propagation are derived. As the effects of the detector material on the trajectory have to be taken into account, the statistical properties of multiple Coulomb scattering, energy loss by ionization, and energy loss by bremsstrahlung are discussed; then it is shown how the effects can be treated in the track reconstruction. As multiple scattering in thin layers and energy loss by bremsstrahlung have distinctive non-Gaussian features, an approximation by normal mixtures is presented.

Modeling Particle Size Distribution in Lunar Regolith via a Central Limit Theorem for Random Sums

A version of the central limit theorem is proved for sums with a random number of independent and not necessarily identically distributed random variables in the double array limit scheme. It is demonstrated that arbitrary normal mixtures appear as the limit distribution. This result is used to substantiate the log-normal finite mixture approximations for the particle size distributions of the lunar regolith. This model is used as the theoretical background of the two different statistical procedures for processing real data based on bootstrap and minimum χ2 estimates. It is shown that the cluster analysis of the parameters of the proposed models can be a promising tool for revealing the structure of such real data, taking into account the physico-chemical interpretation of the results. Similar methods can be successfully used for solving problems from other subject fields with grouped observations, and only some characteristic points of the empirical distribution function are given.