Geostatistical spatial count data in finite populations can be seen in many applications, such as urban management and medicine. The traditional model for analyzing these data is the spatial logit-binomial model. In the most applied situations, these data have overdispersion alongside the spatial variability. The binomial model is not the appropriate candidate to account for the overdispersion. The proper alternative is a beta-binomial model that has sufficient flexibility to account for the extra variability due to the possible overdispersion of counts. In this paper, we describe a Bayesian spatial beta-binomial for geostatistical count data by using a combination of the integrated nested Laplace approximation and the stochastic partial differential equations methods. We apply the methodology for analyzing the number of people injured/killed in car crashes in Mashhad, Iran. We further evaluate the performance of the model using a simulation study.

One of the most critical discussions in regression models is the selection of the optimal model, by identifying critical explanatory variables and negligible variables and more easily express the relationship between the response variable and explanatory variables. Given the limitations of selecting variables in classical methods, such as stepwise selection, it is possible to use penalized regression methods. One of the penalized regression models is the Lasso regression model, in which it is assumed that errors follow a normal distribution. In this paper, we introduce the Bayesian Lasso regression model with an asymmetric distribution error and the high dimensional setting. Then, using the simulation studies and real data analysis, the performance of the proposed model's performance is discussed.

This article aims to joint modeling of longitudinal CD4 cells count and time to death in HIV patients based on the AFT model. The modeling of the longitudinal count response, a GLME model under the family of PSD, was used. In contrast, for the TTE data, the parametric AFT model under the Weibull distribution was investigated. These two responses are linked through random effects correlated with the normal distribution. The longitudinal and survival data are then assumed independent, given the latent linking process and any available covariates. Considering excess zeros for two responses and right censoring, presented a joint model that has not yet been investigated by other researchers. The parameters were also estimated using MCMC methods.

The panel data model is used in many areas, such as economics, social sciences, medicine, and epidemiology. In recent decades, inference on regression coefficients has been developed in panel data models. In this paper, methods are introduced to test the equality models of the panel model among the groups in the data set. First, we present a random quantity that we estimate its distribution by two methods of approximation and parametric bootstrap. We also introduce a pivotal quantity for performing this hypothesis test. In a simulation study, we compare our proposed approaches with an available method based on the type I error and test power. We also apply our method to gasoline panel data as a real data set.

Redundancy and reduction are two main methods for improving system reliability. In a redundancy method, system reliability can be improved by adding extra components  to some original components of the system. In a reduction method, system reliability increases by reducing the failure rate at all or some components of the system. Using the concept of reliability equivalence factors, this paper investigates equivalence between the reduction and redundancy methods. A closed formula is obtained for computing the survival equivalence factor. This factor determines the amount of reduction in the failure rate of a system component(s) to reach the reliability of the same system when it is improved. The effect of component importance measure is also studied in our derivations. 

In this paper, estimation and prediction for the Poisson-exponential distribution are studied based on lower records and inter-record times. The estimation is performed with the help of maximum likelihood and Bayesian methods based on two symmetric and asymmetric loss functions. As it seems that the integrals of the Bayes estimates do not possess closed forms, the Metropolis-Hastings within Gibbs and importance sampling methods are applied to approximating these integrals. Moreover, the Bayesian prediction of future records is also investigated. A simulation study and an application example are presented to evaluate and show the applicability of the paper's results and also to compare the numerical results when the inference is based on records and inter-record times with those when the inference is based on records alone. 

This paper presents new bounds for the left and right fractional mean-square stochastic integrals based on convex stochastic processes. Then a range is proposed that includes a linear combination of the left and right fractional mean-square stochastic integrals. Finally, the previous results presented in this subject are improved.

In this paper, the lifetime model based on series systems with a random number of components from the family of power series distributions has been considered. First, some basic theoretical results have been obtained, which have been used to optimize the number of components in series systems. The average lifetime of the system, the cost function, and the total time on test have been used as an objective function in optimization. The issue has been investigated in detail when the lifetimes of system components have Weibull distribution, and the number of components has geometric, logarithmic, or zero-truncated Poisson distributions. The results have been given analytically and numerically. Finally, a real data set has been used to illustrate the obtained results.   

This paper discusses stochastic comparisons of the parallel and series systems comprising multiple-outlier scale components. Under uncertain conditions on the baseline reversed hazard rate, hazard rate functions and scale parameters, the likelihood ratio, dispersive and mean residual life orders between parallel and series systems are established. We then apply the results for two exceptional cases of the multiple-outlier scale model: gamma and Pareto multiple-outlier components to illustrate the found results.

This paper discusses the hazard rate order of the fail-safe systems arising from two sets of independent multiple-outlier scale distributed components. Under certain conditions on scale parameters in the scale model and the submajorization order between the sample size vectors, the hazard rate ordering between the corresponding fail-safe systems from multiple-outlier scale random variables is established. Under certain conditions on the Archimedean copula and scale parameters, we also discuss the usual stochastic order of these systems with dependent components.

The prevalence of Covid-19 is greatly affected by the location of the patients. From the beginning of the pandemic, many models have been used to analyze the survival time of  Covid-19 patients. These models often use the Gaussian random field to include this effect in the survival model. But the assumption of Gaussian random effects is not realistic. In this paper, by considering a spatial skew Gaussian random field for random effects and a new spatial survival model is introduced. Then, in a simulation study, the performance of the proposed model is evaluated.  Finally, the application of the model to analyze the survival time data of Covid-19 patients in Tehran is presented.

The Gaussian random field is commonly used to analyze spatial data. One of the important features of this random field is having essential properties of the normal distribution family, such as closure under linear transformations, marginalization and conditioning, which makes the marginal consistency condition of the Kolmogorov extension theorem. Similarly, the skew-Gaussian random field is used to model skewed spatial data. Although the skew-normal distribution has many of the properties of the normal distribution, in some definitions of the skew-Gaussian random field, the marginal consistency property is not satisfied. This paper introduces a stationery skew-Gaussian random field, and its marginal consistency property is investigated. Then, the spatial correlation model of this skew random field is analyzed using an empirical variogram. Also, the likelihood analysis of the introduced random field parameters is expressed with a simulation study, and at the end, a discussion and conclusion are presented.