Distribution Of Compounds Research Articles

Poisson-New Quadratic-Exponential Distribution

This proposed distribution is a discrete compound probability distribution with only one parameter. To get this distribution, Poisson distribution has been mixed with the New Quadratic-Exponential distribution of Sah (2022). Hence, it is named as “Poisson-New Quadratic-Exponential Exponential Distribution (PNLED)”. The important statistical characteristics needed to check the validity of this distribution have been derived and clearly explained. To check the validity of the theoretical works of this distribution, while using goodness of fit on some over-dispersed count data, what we have been found that this distribution seems a better alternative of Poisson-Lindley distribution (PLD) of Sankaran (1970), Poisson Mishra distribution (PMD) of Sah (2017) and Poisson-Modified Mishra distribution (PMMD) of Sah and Sahani (2023).

Generalised Poisson-Modified Mishra distribution

This distribution is a compound probability distribution constructed by compounding generalised Poisson distribution of Consul and Jain (1973) with Modified Mishra distribution of Sah (2022). All the important characteristics required for this distribution have been obtained and explained. In order to check the validity of the theoretical work, goodness of fit has been applied to some secondary data which have been used by others. It has been observed that this distribution gives a better fit than Poisson-Lindley distribution of Sankaran (1970) as well as Poisson-Modified Mishra distribution of Sah and Sahani (2023).

Heat transfer with interfacial barrier in a fine scale mixture of two highly different conductive materials

The paper deals with the asymptotic behavior of the heat transfer in a bounded domain formed by two $\eps$-periodically interwoven components, of highly different conductivities. Both components might be connected. At the interface, the heat flux is continuous and the temperature subjects to a first-order jump condition. The homogeneous Dirichlet condition is imposed on the exterior boundary. We determine the macroscopic law when the order of magnitude of the jump transmission coefficient is $\eps^r, -1 r \leq 1$, using the two-scale convergence technique of the homogenization theory.

On a novel skewed generalized t distribution: Properties, estimations, and its applications

With the progress of information technology, large amounts of asymmetric, leptokurtic, and heavy-tailed data are arising in various fields, such as finance, engineering, genetics, and medicine. It is very challenging to model those kinds of data, especially for extremely skewed data, accompanied by very high kurtosis or heavy tails. In this article, we propose a class of novel skewed generalized t distribution (SkeGTD) as a scale mixture of skewed generalized normal. The proposed SkeGTD has excellent adaptiveness to various data, because of its capability of allowing for a large range of skewness and kurtosis and its compatibility of the separated location, scale, skewness, and shape parameters. We investigate some important properties of this family of distributions. The maximum likelihood estimation, L-moments estimation, and two-step estimation for the SkeGTD are explored. To illustrate the usefulness of the proposed methodology, we present simulation studies and analyze two real datasets.

Assessment of extreme records in environmental data through the study of stochastic orders for scale mixtures of skew normal vectors

Scale mixtures of skew normal distributions are flexible models well-suited to handle departures from multivariate normality. This paper is concerned with the stochastic comparison of vectors that belong to the family of scale mixtures of skew normal distributions. The paper revisits some of their properties with a proposal that allows to carry out tail weight stochastic comparisons. The connections of the proposed stochastic orders with the non-normality parameters of the multivariate model are also studied for some popular distributions within the family. The role played by these parameters to tackle the non-normality of multivariate data is enhanced as a result. This work is motivated by the analysis of multivariate data in environmental studies which usually collect maximum or minimum values exhibiting departures from normality. The implications of our theoretical results in addressing the stochastic comparison of extreme environmental records is illustrated with an application to a real data study on maximum temperatures in the Iberian Peninsula throughout the last century. The resulting findings may elucidate whether extreme temperatures are evolving for such a long period.

Irrigated urban agriculture: a mixture of farming scales, water flows and actors in Nairobi, Kenya

ABSTRACT Irrigated urban agriculture (IUA) is important for urban food systems and livelihoods but has many unknown socio-technical configurations. This article examines the dynamics of farm irrigation and associated sociotechnical arrangements in the Nairobi catchment. The research shows that there are five principal forms of IUA, differentiated according to land sizes, water sources and suitability, technicality, actors, and market orientation. The city service does not provide arrangements for hydraulic infrastructure or agricultural extension, and state agencies do not take IUA practices into account. The complexity of the socio-technical configurations calls for flexible governance arrangements that go beyond the established models.

Joint Learning of Full-Structure Noise in Hierarchical Bayesian Regression Models.

We consider the reconstruction of brain activity from electroencephalography (EEG). This inverse problem can be formulated as a linear regression with independent Gaussian scale mixture priors for both the source and noise components. Crucial factors influencing the accuracy of the source estimation are not only the noise level but also its correlation structure, but existing approaches have not addressed the estimation of noise covariance matrices with full structure. To address this shortcoming, we develop hierarchical Bayesian (type-II maximum likelihood) models for observations with latent variables for source and noise, which are estimated jointly from data. As an extension to classical sparse Bayesian learning (SBL), where across-sensor observations are assumed to be independent and identically distributed, we consider Gaussian noise with full covariance structure. Using the majorization-maximization framework and Riemannian geometry, we derive an efficient algorithm for updating the noise covariance along the manifold of positive definite matrices. We demonstrate that our algorithm has guaranteed and fast convergence and validate it in simulations and with real MEG data. Our results demonstrate that the novel framework significantly improves upon state-of-the-art techniques in the real-world scenario where the noise is indeed non-diagonal and full-structured. Our method has applications in many domains beyond biomagnetic inverse problems.

Bayes Estimation for the Mean Matrix of the SSMESN Family of Matrix Variate Distributions

In this paper, the problem of finding a Bayes estimation for the mean matrix of the scale and shape mixtures of matrix variate extended skew normal distributions is considered, and its applications in the multivariate linear regression and the stress-strength models are described. Finally, a simulation study and a real data analysis are presented for applications.

Prediction Penalized Analysis of Stroke Based on New Bayesian Hierarchical Priors Model

The penalized or the regularization methods nowadays are the most statistical popular tools used for model selection and variable selection procedure. The quality of the regression parameter estimates depends on the prediction accuracy of the estimated model and the model interpretability. Penalized operator methods usually produced the most parsimonious model (less number of predictor and more explanation). This paper utilized new scale mixture of Rayleigh mixing with normal density to study the relationship between the stroke size and some predictors. New hierarchical priors model has developed as well new Gibbs sampling algorithm. The results demonstrated that the proposed model is comparable to some exists regularization models.

Scale Mixture of Exponential Distribution with an Application

This article presents an extended distribution that builds upon the exponential distribution. This extension is based on a scale mixture between the exponential and beta distributions. By utilizing this approach, we obtain a distribution that offers increased flexibility in terms of the kurtosis coefficient. We explore the general density, properties, moments, asymmetry, and kurtosis coefficients of this distribution. Statistical inference is performed using both the moments and maximum likelihood methods. To show the performance of this new model, it is applied to a real dataset with atypical observations. The results indicate that the new model outperforms two other extensions of the exponential distribution.

Statistical inference for scale mixture models via Mellin transform approach

This paper deals with statistical inference for the scale mixture models. We study an estimation approach based on the Mellin–Stieltjes transform that can be applied to both discrete and absolute continuous mixing distributions. The accuracy of the corresponding estimate is analysed in terms of its expected pointwise error. As an important technical result, we prove the analogue of the Berry–Esseen inequality for the Mellin transforms. The proposed statistical approach is illustrated by numerical examples.

The generalized scale mixtures of asymmetric generalized normal distributions with application to stock data

<abstract><p>In this paper, we introduced a family of distributions with a very flexible shape named generalized scale mixtures of generalized asymmetric normal distributions (GSMAGN). We investigated the main properties of the new family including moments, skewness, kurtosis coefficients and order statistics. A variant of the expectation maximization (EM)-type algorithm was established by combining the proflie likihood approach (PLA) with the classical expectation conditional maximization (ECM) algorithm for parameter estimation of this model. This approach with analytical expressions in the E-step and tractable M-step can greatly improve the computational speed and efficiency of the algorithm. The performance of the proposed algorithm was assessed by some simulation studies. The feasibility of the proposed methodology was illustrated through two real datasets.</p></abstract>

Defect detection enhancement using Gaussian Sparse Models

Detecting defects is critical in industrial fabrication, such as pipe welding, where radiography testing (RT) is the gold standard as a non-destructive method for monitoring weld quality and weld corrosion. The extraction of seamless information from radiographic images is critical for this approach. Image processing techniques can improve the quality of radiographic images by enhancing image contrast, especially in flawed regions. In this study, a method based on Gaussian mixture models was implemented and applied to radiographs of welded objects to improve visualization and detectability. In the Sparse Coding and Gaussian Scale Mixture method (SSC-GSM), the local image patches are described as a mixture of Gaussian distributions. Given the different levels of noise in the individual images, the background was determined and subtracted from each original image. The results show that the proposed techniques can maintain and improve the edge information in radiographs and defective regions. The density of pixels along the analyzed profile lines has yielded enhancement by a factor of approximately two for the reconstructed images as compared to the original images. We tested the SSC-GSM method on GD-Xray database with 68 radiographs of the weld. In total, the SSC-GSM technique can improve the contrast of radiography image by back ground removal method and show the defects better that exist in weld radiographs, compared to traditional method for the detection of weld defects.

Data Augmentation for Bayesian Deep Learning

Deep Learning (DL) methods have emerged as one of the most powerful tools for functional approximation and prediction. While the representation properties of DL have been well studied, uncertainty quantification remains challenging and largely unexplored. Data augmentation techniques are a natural approach to provide uncertainty quantification and to incorporate stochastic Monte Carlo search into stochastic gradient descent (SGD) methods. The purpose of our paper is to show that training DL architectures with data augmentation leads to efficiency gains. We use the theory of scale mixtures of normals to derive data augmentation strategies for deep learning. This allows variants of the expectation-maximization and MCMC algorithms to be brought to bear on these high dimensional nonlinear deep learning models. To demonstrate our methodology, we develop data augmentation algorithms for a variety of commonly used activation functions: logit, ReLU, leaky ReLU and SVM. Our methodology is compared to traditional stochastic gradient descent with back-propagation. Our optimization procedure leads to a version of iteratively re-weighted least squares and can be implemented at scale with accelerated linear algebra methods providing substantial improvement in speed. We illustrate our methodology on a number of standard datasets. Finally, we conclude with directions for future research.

Locally adaptive spatial quantile smoothing: Application to monitoring crime density in Tokyo

Spatial trend estimation under potential heterogeneity is an important problem to extract spatial characteristics and hazards such as criminal activity. By focusing on quantiles, which provide substantial information on distributions compared with commonly used summary statistics such as means, it is often useful to estimate not only the average trend but also the high (low) risk trend additionally. In this paper, we propose a Bayesian quantile trend filtering method to estimate the non-stationary trend of quantiles on graphs and apply it to crime data in Tokyo between 2013 and 2017. By modeling multiple observation cases, we can estimate the potential heterogeneity of spatial crime trends over multiple years in the application. To induce locally adaptive Bayesian inference on trends, we introduce general shrinkage priors for graph differences. Introducing so-called shadow priors with multivariate distribution for local scale parameters and mixture representation of the asymmetric Laplace distribution, we provide a simple Gibbs sampling algorithm to generate posterior samples. The numerical performance of the proposed method is demonstrated through simulation studies.

Robust learning of parsimonious deep neural networks

We propose a simultaneous learning and pruning algorithm capable of identifying and eliminating irrelevant structures in a neural network during the early stages of training. Simultaneous learning and pruning presents serious challenges such as premature pruning of units that can lead to poor performance. Our method is capable of overcoming such challenges and is robust, i.e., it gives consistent pruning levels and prediction accuracy regardless of weight initialization or the size of the starting network. Thus, it allows for substantial computational cost savings during training, besides that of inference, and it can enable the training of very deep networks when transfer learning to obtain fully trained deep networks that can be pruned after training is not possible. Our approach is based on variational inference principles using Gaussian scale mixture priors on the neural network weights. The variational posterior distribution of Bernoulli random variables multiplying the units/filters is learned, similarly to adaptive dropout. We construct a novel hyper-prior distribution over the prior parameters to impose properties crucial for their optimal selection and the overall robustness of our algorithm. It is shown in the context of our algorithm that the parameters of the posterior distributions practically converge to either 0 or 1, establishing a deterministic final network. Convergence is proved analytically based on dynamical systems theory and from the theoretical results, practical pruning conditions are established. The proposed algorithm is evaluated on the MNIST, CIFAR-10 and ImageNet data sets and the commonly used fully connected, convolutional and residual architectures LeNet, VGG16 and ResNet. The simulations show that our method typically achieves better pruning levels while maintaining test-accuracy on par with state-of the-art methods for structured pruning in a manner robust with respect to network initialization and initial size.

Bayesian boundary trend filtering

Estimating boundary curves has many applications such as economics, climate science, and medicine. Bayesian trend filtering has been developed as one of locally adaptive smoothing methods to estimate the non-stationary trend of data. This paper develops a Bayesian trend filtering for estimating the boundary trend. To this end, the truncated multivariate normal working likelihood and global-local shrinkage priors based on the scale mixtures of normal distribution are introduced. In particular, well-known horseshoe prior for difference leads to locally adaptive shrinkage estimation for boundary trend. However, the full conditional distributions of the Gibbs sampler involve high-dimensional truncated multivariate normal distribution. To overcome the difficulty of sampling, an approximation of truncated multivariate normal distribution is employed. Using the approximation, the proposed models lead to an efficient Gibbs sampling algorithm via the Pólya-Gamma data augmentation. The proposed method is also extended by considering a nearly isotonic constraint. The performance of the proposed method is illustrated through some numerical experiments and real data examples.

Estimates of the Convergence Rate in the Generalized Rényi Theorem with a Structural Digamma Distribution Using Zeta Metrics

This paper considers a generalization of the Rényi theorem to the case of a structural distribution with a scale parameter. In terms of the zeta metric, some estimates of the convergence rate in the generalized Rényi theorem are obtained when the structural mixed Poisson distribution of the summation index is a scale mixture of the generalized gamma distribution. Estimates of the convergence rate for the structural digamma distribution are given as a special case. The paper extends the results previously obtained for the generalized gamma distribution.

Incorporation of Perillyl Alcohol into Lipid-Based Nanocarriers Enhances the Antiproliferative Activity in Malignant Glioma Cells.

Perillyl alcohol (PA), a naturally existing monocyclic terpene related to limonene, is characterized by its poor aqueous solubility and very limited bioavailability. Its potential anti-cancer activity against malignant glioma has been reported. The aim was to develop PA-loaded lipid-based nanocarriers (LNCs), and to investigate their anti-cancer activity against two different brain cell lines. Non-medicated and PA-loaded LNCs were prepared and characterized. The mechanism of cytotoxic activity of PA was conducted using a molecular docking technique. The cell viabilities against A172 and ANGM-CSS cells were evaluated. The results revealed that the average particle size of the prepared LNCs ranged from 248.67 ± 12.42 to 1124.21 ± 12.77 nm, the polydispersity index was 0.418 ± 0.043-0.509 ± 0.064, while the zeta potential ranged from -36.91 ± 1.31 to -15.20 ± 0.96 mV. The molecular docking studies demonstrated that the drug had binding activity to human farnesyltransferase. Following exposure of the two glioblastoma cell lines to the PA-loaded nanoformulations, MTS assays were carried out, and the data showed a far lower half-maximal inhibitory concentration in both cell lines when compared to pure drug and non-medicated nanocarriers. These results indicate the potential in vitro antiproliferative activity of PA-loaded LNCs. Therefore, the prepared PA-loaded nanocarriers could be used to enhance drug delivery across the blood-brain barrier (BBB) in order to treat brain cancer, especially when formulated in a suitable dosage form. The size, surface charge, and lipid composition of the LNCs make them promising for drug delivery across the BBB. Detailed pharmacokinetic and pharmacodynamic assessments, including the evaluation of BBB penetration, are necessary to better understand the compound's distribution and effects within the brain.

The skewness of mean–variance normal mixtures

Mean–variance mixtures of normal distributions are very flexible: they model many nonnormal features, such as skewness, kurtosis and multimodality. Special cases include generalized asymmetric Laplace distributions, mixtures of two normal distributions with proportional covariance matrices, scale mixtures of normal distributions and normal distributions. This paper investigates the skewness of multivariate mean–variance normal mixtures. The special case of mixtures of two normal distributions with proportional covariance matrices is treated in greater detail. The paper derives the analytical forms of prominent measures of multivariate skewness and applies them to model-based clustering, normalizing linear transformations, projection pursuit and normality testing. The practical relevance of the theoretical results is assessed with both real and simulated data.