An alternative multivariate skew Laplace distribution: properties and estimation

A special case of the multivariate exponential power distribution is considered as a multivariate extension of the univariate symmetric Laplace distribution. In this paper, we focus on this multivariate symmetric Laplace distribution, and extend it to a multivariate skew distribution. We call this skew extension of the multivariate symmetric Laplace distribution the “multivariate skew Laplace (MSL) distribution” to distinguish between the asymmetric multivariate Laplace distribution proposed by Kozubowski and Podgórski (Comput Stat 15:531–540, 2000a) Kotz et al. (The Laplace distribution and generalizations: a revisit with applications to communications, economics, engineering, and finance, Chap. 6. Birkhäuser, Boston, 2001) and Kotz et al. (An asymmetric multivariate Laplace Distribution, Working paper, 2003). One of the advantages of (MSL) distribution is that it can handle both heavy tails and skewness and that it has a simple form compared to other multivariate skew distributions. Some fundamental properties of the multivariate skew Laplace distribution are discussed. A simple EM-based maximum likelihood estimation procedure to estimate the parameters of the multivariate skew Laplace distribution is given. Some examples are provided to demonstrate the modeling strength of the skew Laplace distribution.     

Parameter estimation for mixtures of skew Laplace normal distributions and application in mixture regression modeling

In this article, we propose mixtures of skew Laplace normal (SLN) distributions to model both skewness and heavy-tailedness in the neous data set as an alternative to mixtures of skew Student-t-normal (STN) distributions. We give the expectation–maximization (EM) algorithm to obtain the maximum likelihood (ML) estimators for the parameters of interest. We also analyze the mixture regression model based on the SLN distribution and provide the ML estimators of the parameters using the EM algorithm. The performance of the proposed mixture model is illustrated by a simulation study and two real data examples.     

Effects of changes in rainfall and temperature on age- and sex-specific patterns of rural-urban migration in sub-Saharan Africa

We evaluate how changes in weather patterns affected rural-urban migration across 41 sub-Saharan African countries, by age and sex, over the 1980–2015 period. We combine recent age- and sex-specific estimates of net rural-urban migration with historical data on rainfall and temperature from the Climate Research Unit (CRU). We also compare standard unweighted estimates of rainfall and temperature to estimates weighted by the proportion of the country’s total rural population in the CRU grid. Results show that rural out-migration of young adults is the most sensitive to shifts in weather patterns, with lower rainfall, lower variability in rainfall, and higher temperatures increasing subsequent rural out-migration—though the last of these is not observed in weighted models. The strength of these effects has grown stronger over time for 20–24 year olds, though weaker above age 30. In contrast, increasing temperature variability is associated with a higher rural in-migration of children (0–9) and older adults (55–64). Gender differences in these effects are minimal and concentrated in areas which experienced heavy reductions in rainfall.

     

Survival of the fittest: capacity building for small nonprofit organizations

This paper discusses capacity building activities designed for small nonprofits who are members of the Second Harvest Food Bank of Central Florida's ADEPT program. The Second Harvest Food Bank of Central Florida (SHFBCF) is a nonprofit organization that collects, stores and distributes donated food to more than 450 nonprofit partners in Brevard, Lake, Orange, Osceola, Seminole and Volusia counties. This project sought to delineate, design, and implement the capacity building trainings desired by ADEPT member agencies. It also analyzed the relationship between the number of clients served, number of staff, number of volunteers, and the training needs. At the conclusion of the capacity building trainings, data was collected to gauge participants' perceptions of the capacity building trainings and their perceived impact on the effectiveness of the ADEPT Program and its member agencies. The generalizability and applicability of the research results to other small community-based organizations providing social and human services is also discussed.     

One-step M-estimators: Jones and Faddy's skewed t-distribution

One-step M (OSM)-estimator needs some initial/preliminary estimates at the beginning of the calculation process. In this study, we propose to use new initial estimates for the calculation of the OSM-estimator. We consider simple location and simple linear regression models when the distribution of the error terms is Jones and Faddy's skewed t. Monte-Carlo simulation study shows that the OSM estimator(s) based on the proposed initial estimates is/are more efficient than the OSM estimator(s) based on the traditional initial estimates especially for the skewed cases. We also analyze some real data sets taken from the literature at the end of the paper.     

Doubly reweighted estimators for the parameters of the multivariate t-distribution

The t-distribution (univariate and multivariate) has many useful applications in robust statistical analysis. The parameter estimation of the t-distribution is carried out using maximum likelihood (ML) estimation method, and the ML estimates are obtained via the Expectation-Maximization (EM) algorithm. In this article, we will use the maximum Lq-likelihood (MLq) estimation method introduced by Ferrari and Yang (2010 Ferrari, D., and Y. Yang. 2010. Maximum lq-likelihood estimation. The Annals of Statistics 38 (2):753–83.[Crossref], [Web of Science ®] , [Google Scholar]) to estimate all the parameters of the multivariate t-distribution. We modify the EM algorithm to obtain the MLq estimates. We provide a simulation study and a real data example to illustrate the performance of the MLq estimators over the ML estimators.