A flexible generalization of the skew normal distribution based on a weighted normal distribution

The skew normal distribution of Azzalini (Scand J Stat 12:171–178, 1985) has been found suitable for unimodal density but with some skewness present. Through this article, we introduce a flexible extension of the Azzalini (Scand J Stat 12:171–178, 1985) skew normal distribution based on a symmetric component normal distribution (Gui et al. in J Stat Theory Appl 12(1):55–66, 2013). The proposed model can efficiently capture the bimodality, skewness and kurtosis criteria and heavy-tail property. The paper presents various basic properties of this family of distributions and provides two stochastic representations which are useful for obtaining theoretical properties and to simulate from the distribution. Further, maximum likelihood estimation of the parameters is studied numerically by simulation and the distribution is investigated by carrying out comparative fitting of three real datasets.     

Bayesian elastic net single index quantile regression

Single index model conditional quantile regression is proposed in order to overcome the dimensionality problem in nonparametric quantile regression. In the proposed method, the Bayesian elastic net is suggested for single index quantile regression for estimation and variables selection. The Gaussian process prior is considered for unknown link function and a Gibbs sampler algorithm is adopted for posterior inference. The results of the simulation studies and numerical example indicate that our propose method, BENSIQReg, offers substantial improvements over two existing methods, SIQReg and BSIQReg. The BENSIQReg has consistently show a good convergent property, has the least value of median of mean absolute deviations and smallest standard deviations, compared to the other two methods.     

The discrepancy of P-values and posterior probability: Two-sided hypothesis of variance of normal distribution with unknown mean

This article is concerned with the comparison of P-value and Bayesian measure in point null hypothesis for the variance of Normal distribution with unknown mean. First, using fixed prior for test parameter, the posterior probability is obtained and compared with the P-value when an appropriate prior is used for the mean parameter. In the second, lower bounds of the posterior probability of H₀ under a reasonable class of prior are compared with the P-value. It has been shown that even in the presence of nuisance parameters, these two approaches can lead to different results in the statistical inference.     

Upper Bound for p-Value of the Test of Multivariate Normal Ordered Mean Vectors Against all Alternatives

Consider the problem of testing the isotonic of several p-variate normal mean vectors against all alternatives. It is difficult to compute the exact p-value for this problem of testing with the classical method when the covariance matrices are completely unknown. In the present paper, a test statistic is proposed for this problem of testing. A reformulation of the test statistic is given based on the orthogonal projections on the closed convex cones and then the upper bound for p-value of the test statistic is computed.     

Irreconcilability of P-value and Bayesian measure in two-sided hypothesis: Pareto distribution with the presence of nuisance parameter

Abstract

This article is concerned with the comparison of Bayesian and classical testing of a point null hypothesis for the Pareto distribution when there is a nuisance parameter. In the first stage, using a fixed prior distribution, the posterior probability is obtained and compared with the P-value. In the second case, lower bounds of the posterior probability of H₀, under a reasonable class of prior distributions, are compared with the P-value. It has been shown that even in the presence of nuisance parameters for the model, these two approaches can lead to different results in statistical inference.     

The Bayesian elastic net regression

A Bayesian elastic net approach is presented for variable selection and coefficient estimation in linear regression models. A simple Gibbs sampling algorithm was developed for posterior inference using a location-scale mixture representation of the Bayesian elastic net prior for the regression coefficients. The penalty parameters are chosen through an empirical method that maximizes the data marginal likelihood. Both simulated and real data examples show that the proposed method performs well in comparison to the other approaches.     

On the Optimal Parameters for Reconstruction and Forecasting in Singular Spectrum Analysis

There are two main parameters in Singular Spectrum Analysis (SSA). The aim of this study is to determine whether the optimal values of these parameters are different for reconstruction and forecasting stages, and if those are worth the extra computational effort and time which they require. Here, we evaluate these issues using simulation study.     

Social resources and Arab women’s perinatal mental health: A systematic review

Background

Women’s mental health in the perinatal period is understudied worldwide and in Arab countries especially.

Economic statistical design of x ¥ control charts for systems with gamma ( 5 ,2) in-control times

In this paper, gamma ( 5 ,2) distribution is considered as a failure model for the economic statistical design of x ¥ control charts. The study shows that the statistical performance of control charts can be improved significantly, with only a slight increase in the cost, by adding constraints to the optimization problem. The use of an economic statistical design instead of an economic design results in control charts that may be less expensive to implement, that have lower false alarm rates, and that have a higher probability of detecting process shifts. Numerical examples are presented to support this proposition. The results of economic statistical design are compared with those of a pure economic design. The effects of adding constraints for statistical performance measures, such as Type I error rate and the power of the chart, are extensively investigated.