Stats — Open Access Journal

The popular concept of slash distribution is generalized by considering the quotient Z = X/Y of independent random variables X and Y, where X is any continuous random variable and Y has a general beta distribution. The density of Z can usually be expressed by means of generalized hypergeometric functions. We study the distribution of Z for various parent distributions of X and indicate a possible application in finance. Full article

In this paper, we use a corpus of about 100,000 happy moments written by people of different genders, marital statuses, parenthood statuses, and ages to explore the following questions: Are there differences between men and women, married and unmarried individuals, parents and non-parents, and people of different age groups in terms of their causes of happiness and how they express happiness? Can gender, marital status, parenthood status and/or age be predicted from textual data expressing happiness? The first question is tackled in two steps: first, we transform the happy moments into a set of topics, lemmas, part of speech sequences, and dependency relations; then, we use each set as predictors in multi-variable binary and multinomial logistic regressions to rank these predictors in terms of their influence on each outcome variable (gender, marital status, parenthood status and age). For the prediction task, we use character, lexical, grammatical, semantic, and syntactic features in a machine learning document classification approach. The classification algorithms used include logistic regression, gradient boosting, and fastText. Our results show that textual data expressing moments of happiness can be quite beneficial in understanding the “causes of happiness” for different social groups, and that social characteristics like gender, marital status, parenthood status, and, to some extent age, can be successfully predicted form such textual data. This research aims to bring together elements from philosophy and psychology to be examined by computational corpus linguistics methods in a way that promotes the use of Natural Language Processing for the Humanities. Full article

Classification has applications in a wide range of fields including medicine, engineering, computer science and social sciences among others. In statistical terms, classification is inference about the unknown parameters, i.e., the true classes of future objects. Hence, various standard statistical approaches can be used, such as point estimators, confidence sets and decision theoretic approaches. For example, a classifier that classifies a future object as belonging to only one of several known classes is a point estimator. The purpose of this paper is to propose a confidence-set-based classifier that classifies a future object into a single class only when there is enough evidence to warrant this, and into several classes otherwise. By allowing classification of an object into possibly more than one class, this classifier guarantees a pre-specified proportion of correct classification among all future objects. An example is provided to illustrate the method, and a simulation study is included to highlight the desirable feature of the method. Full article

In this paper, we propose a Bayesian model for the analysis of categorical data with an ordered outcome. The method provides a latent variable approach with an informative prior transformed from a Dirichlet distribution for the boundary parameters. A simulation study is carried out to assess the performance of the methods under various settings of the data structure. Our method produces predictive accuracy over the conventional classification procedures. Real data are analyzed to demonstrate the efficiency of the proposed method. Full article

While most of the literature about INARMA models (integer-valued autoregressive moving-average) concentrates on the purely autoregressive INAR models, we consider INARMA models that also include a moving-average part. We study moment properties and show how to efficiently implement maximum likelihood estimation. We analyze the estimation performance and consider the topic of model selection. We also analyze the consequences of choosing an inadequate model for the given count process. Two real-data examples are presented for illustration. Full article

Dengue fever is a mosquito-borne viral disease prevalent in more than one hundred tropical and subtropical countries. Annually, an estimated 390 million infections occur worldwide. It is transmitted by the bite of an Aedes mosquito infected with the virus. It has become a major public health challenge in recent years for many countries, including Sri Lanka. It is known that climate factors such as rainfall, temperature, and relative humidity influence the generation of mosquito offspring, thus increasing dengue incidences. Identifying the climate factors that affect the spread of dengue fever would be helpful in order for the relevant authorities to take necessary actions. The objective of this study is to build a model for predicting the likelihood of having high dengue incidences based on climate factors. A logistic regression approach was utilized for model formulation. This study found a significant association between high numbers of dengue incidences and rainfall. Furthermore, it was observed that the influence of rainfall on dengue incidences was expected to be visible after some lag period. Full article

For statistical evaluations that involve within-group and between-group variance components (denoted ${\sigma }_W^2$ and ${\sigma }_B^2$ , respectively), there is sometimes a need to monitor for a shift in the mean of time-ordered data. Uncertainty in the estimates ${\widehat{\sigma }}_W^2$ and ${\widehat{\sigma }}_B^2$ should be accounted for when setting alarm thresholds to check for a mean shift as both ${\sigma }_W^2$ and ${\sigma }_B^2$ must be estimated. One-way random effects analysis of variance (ANOVA) is the main tool for analysing such grouped data. Nearly all of the ANOVA applications assume that both the within-group and between-group components are normally distributed. However, depending on the application, the within-group and/or between-group probability distributions might not be well approximated by a normal distribution. This review paper uses the same example throughout to illustrate the possible approaches to setting alarm limits in grouped data, depending on what is assumed about the within-group and between-group probability distributions. The example involves measurement data, for which systematic errors are assumed to remain constant within a group, and to change between groups. The false alarm probability depends on the assumed measurement error model and its within-group and between-group error variances, which are estimated while using historical data, usually with ample within-group data, but with a small number of groups (three to 10 typically). This paper illustrates the parametric, semi-parametric, and non-parametric options to setting alarm thresholds in such grouped data. Full article

A new one-parameter distribution is proposed in this paper. The new distribution allows for the occurrence of instantaneous failures (inliers) that are natural in many areas. Closed-form expressions are obtained for the moments, mean, variance, a coefficient of variation, skewness, kurtosis, and mean residual life. The relationship between the new distribution with the exponential and Lindley distributions is presented. The new distribution can be viewed as a combination of a reparametrized version of the Zakerzadeh and Dolati distribution with a particular case of the gamma model and the occurrence of zero value. The parameter estimation is discussed under the method of moments and the maximum likelihood estimation. A simulation study is performed to verify the efficiency of both estimation methods by computing the bias, mean squared errors, and coverage probabilities. The superiority of the proposed distribution and some of its concurrent distributions are tested by analyzing four real lifetime datasets. Full article

We introduce new equivalence tests for approximate independence in two-way contingency tables. The critical values are calculated asymptotically. The finite sample performance of the tests is improved by means of the bootstrap. An estimator of boundary points is developed to make the bootstrap based tests statistically efficient and computationally feasible. We compare the performance of the proposed tests for different table sizes by simulation. Then we apply the tests to real data sets. Full article

In this paper, we use a Bayesian methodology to analyze the outcome of a hockey game using different sources of information, such as points in previous games, home advantage, and specialists’ opinions. Two different models to predict the number of goals are considered, taking into account that it is the nature of hockey that goals are infrequent and rarely exceed six per team per game. A Bayesian predictive density to predict the number of the goals using each model will be used and the possible winner of the game will be predicted. The corresponding prediction error for each model will be addressed. Full article

Extrapolations of future market forward rates are a better predictor of the 30-days ahead BRL-USD exchange rate than forecasts from the Central Bank Focus survey of Brazilian market participants. This is puzzling because market participants observe forward rates as they submit predictions, and thus these agents perform biased forecasts even though they have access to a set of unbiased forecasts, consistent with a martingale process for the exchange rate. We argue that this rational conundrum can be explained by a mechanism through which new information enlarges the information set (a filtration), changing the underlying measure and inducing a drift into the martingale process, turning the process into a strict local martingale and generating a forecast bias. Empirical results suggest that Focus survey forecasts indeed display characteristics of a strict local martingale, while spot exchange rates and forward rates are consistent with a martingale process. Full article

Discipline is an important component of human behavior, and one could assert that without it, an organization cannot function well toward the achievement of its goals. The aim of this study was to assess the impact of school rules and regulations on students’ perception toward promoting good behavior. The data were obtained from 438 respondents through a mailed questionnaire instrument. The data were tabulated, and Pearson’s chi-square test was applied for inferential analysis. Around 33.1% of the students had a negative perception of school rules and regulations about promoting good behavior, whereas 66.9% of them had a positive perception. A p-value of 0.015 (<5% significance level) indicated that there is a significant association between students’ awareness on school rules and regulations and their perception toward promoting good behavior. Students’ attitudes on school rules and regulations and perception toward promoting good behavior were statistically associated at a p-value of 0.012. Parents’ educational levels had a significant effect on students’ perception toward promoting good behavior. Generally, students’ awareness on school rules and regulations, parents’ education levels, civics and ethical education scores, and students’ attitudes toward promoting good behavior were found as significant effects on perception toward promoting good behavior. Full article

This paper is concerned with estimating the ratio of two distributions with different parameters and common supports. We consider a Bayesian approach based on the log–Huber loss function, which is resistant to outliers and useful for finding robust M-estimators. We propose two different types of Bayesian density ratio estimators and compare their performance in terms of frequentist risk function. Some applications, such as classification and divergence function estimation, are addressed. Full article

The mixed-effects model for repeated measures (MMRM) approach has been widely applied for longitudinal clinical trials. Many of the standard inference methods of MMRM could possibly lead to the inflation of type I error rates for the tests of treatment effect, when the longitudinal dataset is small and involves missing measurements. We propose two improved inference methods for the MMRM analyses, (1) the Bartlett correction with the adjustment term approximated by bootstrap, and (2) the Monte Carlo test using an estimated null distribution by bootstrap. These methods can be implemented regardless of model complexity and missing patterns via a unified computational framework. Through simulation studies, the proposed methods maintain the type I error rate properly, even for small and incomplete longitudinal clinical trial settings. Applications to a postnatal depression clinical trial are also presented. Full article

In this article, we propose approaches for constructing confidence intervals for the single signal-to-noise ratio (SNR) of a log-normal distribution and the difference in the SNRs of two log-normal distributions. The performances of all of the approaches were compared, in terms of the coverage probability and average length, using Monte Carlo simulations for varying values of the SNRs and sample sizes. The simulation studies demonstrate that the generalized confidence interval (GCI) approach performed well, in terms of coverage probability and average length. As a result, the GCI approach is recommended for the confidence interval estimation for the SNR and the difference in SNRs of two log-normal distributions. Full article

The Birnbaum-Saunders (BS) distribution, with its generalizations, has been successfully applied in a wide variety of fields. One generalization, type-II generalized BS (denoted as GBS-II), has been developed and attracted considerable attention in recent years. In this article, we propose a new simple and convenient procedure of inference approach for GBS-II distribution. An extensive simulation study is carried out to assess performance of the methods under various settings of parameter values with different sample sizes. Real data are analyzed for illustrative purposes to display the efficiency of the proposed method. Full article

This article provides a review of the saddlepoint approximation for a M-statistic of a sample of nonnegative random variables with fixed sum. The sample vector follows the multinomial, the multivariate hypergeometric, the multivariate Polya or the Dirichlet distributions. The main objective is to provide a complete presentation in terms of a single and unambiguous notation of the common mathematical framework of these four situations: the simplex sample space and the underlying general urn model. Some important applications are reviewed and special attention is given to recent applications to models of circular data. Some novel applications are developed and studied numerically. Full article

We construct a point and interval estimation using a Bayesian approach for the difference of two population proportion parameters based on two independent samples of binomial data subject to one type of misclassification. Specifically, we derive an easy-to-implement closed-form algorithm for drawing from the posterior distributions. For illustration, we applied our algorithm to a real data example. Finally, we conduct simulation studies to demonstrate the efficiency of our algorithm for Bayesian inference. Full article

Research papers represent an important and rich source of comparative data. The change is to extract the information of interest. Herein, we look at the possibilities to construct confidence intervals for sample averages when only ranges are available with maximum likelihood estimation with order statistics (MLEOS). Using Monte Carlo simulation, we looked at the confidence interval coverage characteristics for likelihood ratio and Wald-type approximate 95% confidence intervals. We saw indication that the likelihood ratio interval had better coverage and narrower intervals. For single parameter distributions, MLEOS is directly applicable. For location-scale distribution is recommended that the variance (or combination of it) to be estimated using standard formulas and used as a plug-in. Full article