Benford’s distribution,also known as first-digit law, is used to detect several kinds of frauds on the basis of data. Several statistical tests are used to verify that real-life sources of data have Benford’s distribution. In this paper we consider in detail the well-known chi-square test and the Kolmogorov test of goodness of fit. The considerations are focused on determining the sample size that provides the assumed significance level as well as the power of the test. The necessary sample size is evaluated on the basis of simulation analysis under reasonable formulated alternative distributions to Benford’s distribution and under assumed significance levels and powers of the statistical tests.
Joint models under generalized linear mixed model framework have received lot of attention among researchers in the field of psychology to analyse data with more than one response variable. The presence of aberrant observations in the data may influence the estimation of parameters in the existing method of estimation such as maximum likelihood, quasi-likelihood, etc. Hence, there exists a need for robust method of estimation under joint modelling to reduce the effect of influential data points. In this paper, two methods of robust estimation namely robust Maximum Likelihood method and robust Monte Carlo Newton-Raphson for joint longitudinal model has been compared with the usual maximum likelihood method to examine the association between the outcome variables of Spearman’s G and S factors of human intelligence along with other covariates based on school lunch intervention data. In addition, a parametric bootstrap study is adopted to find the sensitivity and efficiency of the robust method in resampling techniques with varying sample sizes.
This paper extends the work of Elal-Olivero (2010) on the alpha-skew normal distribution. The extension is a multivariate version of Elal-Olivero’s univariate case. Then we study the statistical properties of the new extension such as marginal and conditional distribution, closure under convolution with normal random variate. Furthermore, we illustrate the performance of the distribution using simulated data obtained from the generalized distribution via the Metropolis-Hasting algorithm.
Business cycle volatility has been extensively studied by means of the well-known ARCH and GARCH processes. Aim of this paper is to show that the score-driven models are instead more accurate in predicting business cycle volatility than the GARCH-type models. Motivated by fact that the empirical evidence do not support the hypothesis of Gaussianity also for business cycles, we assume the Generalized Error Distribution and its extension for skewness in estimating the volatility models within the GARCH framework. After reviewing the basic properties of the score-driven approaches, we carry out an empirical analysis with respect to the business cycles of the United States and Japan. We show that the score-driven models provide superior performances than both Gaussian and non-Gaussian GARCH processes in forecasting business cycle volatility.
The World Happiness Report (WHR) has drawn international attention since the first initiative in 2012 as it can help the policy makers to evaluate their policy options. There are six factors to describe the variation of the happiness across the countries, i.e., gross domestic product per capita, social support, healthy life expectancy, freedom to make life choices, perception of corruption, and generosity. This study aims to cluster the countries according to the WHR 2020. Nine clustering algorithms (k-means, k-means++, k-medoids, clustering large applications, affinity propagation, spectral clustering, density-based spatial clustering of applications with noise, agglomerative nesting, and divisive analysis) are presented and three internal validation indices (silhouette index, Dunn’s index, and Calinski-Harabasz’ index) are utilized to compare the algorithms. This study is expected to give an insight about how to implement clustering algorithms into the real world (not artificial) data set and how to interpret the result.