Journal of Data Science

We propose a varying coefficient Susceptible-Infected-Removal (vSIR) model that allows changing infection and removal rates for the latest corona virus (COVID-19) outbreak in China. The vSIR model together with proposed estimation procedures allow one to track the reproductivity of the COVID-19 through time and to assess the effectiveness of the control measures implemented since Jan 23 2020 when the city of Wuhan was lockdown followed by an extremely high level of self-isolation in the population. Our study finds that the reproductivity of COVID-19 had been significantly slowed down in the three weeks from January 27th to February 17th with 96.3% and

Abstract: This paper introduces a new four parameters model called the Weibull Generalized Flexible Weibull extension (WGFWE) distribution which exhibits bathtub-shaped hazard rate. Some of it’s statistical properties are obtained including ordinary and incomplete moments, quantile and generating functions, reliability and order statistics. The method of maximum likelihood is used for estimating the model parameters and the observed Fisher’s information matrix is derived. We illustrate the usefulness of the proposed model by applications to real data.

Abstract: Mosaic plots are state-of-the-art graphics for multivariate categor ical data in statistical visualization. Knowledge structures are mathematical models that belong to the theory of knowledge spaces in psychometrics. This paper presents an application of mosaic plots to psychometric data arising from underlying knowledge structure models. In simulation trials and with empirical data, the scope of this graphing method in knowledge space theory is investigated.

Abstract: Considering the importance of science and mathematics achieve ments of young students, one of the most well known observed phenomenon is that the performance of U.S. students in mathematics and sciences is undesirable. In order to deal with the problem of declining mathematics and science scores of American high school students, many strategies have been implemented for several decades. In this paper, we give an in-depth longitudinal study of American youth using a double-kernel approach of non parametric quantile regression. Two of the advantages of this approach are: (1) it guarantees that a Nadaraya-Watson estimator of the conditional func tion is a distribution function while, in some cases, this kind of estimator being neither monotone nor taking values only between 0 and 1; (2) it guar antees that quantile curves which are based on Nadaraya-Watson estimator not absurdly cross each other. Previous work has focused only on mean re gression and parametric quantile regression. We obtained many interesting results in this study.

Abstract: We compare two linear dimension-reduction methods for statisti cal discrimination in terms of average probabilities of misclassification in re duced dimensions. Using Monte Carlo simulation we compare the dimension reduction methods over several different parameter configurations of multi variate normal populations and find that the two methods yield very different results. We also apply the two dimension-reduction methods examined here to data from a study on football helmet design and neck injuries.

Abstract: Longitudinal studies represent one of the principal research strategies employed in medical and social research. These studies are the most appropriate for studying individual change over time. The prematurely withdrawal of some subjects from the study (dropout) is termed nonrandom when the probability of missingness depends on the missing value. Nonrandom dropout is common phenomenon associated with longitudinal data and it complicates statistical inference. Linear mixed effects model is used to fit longitudinal data in the presence of nonrandom dropout. The stochastic EM algorithm is developed to obtain the model parameter estimates. Also, parameter estimates of the dropout model have been obtained. Standard errors of estimates have been calculated using the developed Monte Carlo method. All these methods are applied to two data sets.

The choice of an appropriate bivariate parametrical probability distribution for pairs of lifetime data in presence of censored observations usually is not a simple task in many applications. Each existing bivariate lifetime probability distribution proposed in the literature has different dependence structure. Commonly existing classical or Bayesian discrimination methods could be used to discriminate the best among different proposed distributions, but these techniques could not be appropriate to say that we have good fit of some particular model to the data set. In this paper, we explore a recent dependence measure for bivariate data introduced in the literature to propose a graphical and simple criterion to choose an appropriate bivariate lifetime distribution for data in presence of censored data.

Abstract: The power law process (PLP) (i.e., the nonhomogeneous Poisson process with power intensity law) is perhaps the most widely used model for analyzing failure data from reliability growth studies. Statistical inferences and prediction analyses for the PLP with left-truncated data with classical methods were extensively studied by Yu et al. (2008) recently. However, the topics discussed in Yu et al. (2008) only included maximum likelihood estimates and confidence intervals for parameters of interest, hypothesis testing and goodness-of-fit test. In addition, the prediction limits of future failure times for failure-truncated case were also discussed. In this paper, with Bayesian method we consider seven totally different prediciton issues besides point estimates and prediction limits for xn+k. Specifically, we develop estimation and prediction methods for the PLP in the presence of left-truncated data by using the Bayesian method. Bayesian point and credible interval estimates for the parameters of interest are derived. We show how five single-sample and three two-sample issues are addressed by the proposed Bayesian method. Two real examples from an engine development program and a repairable system are used to illustrate the proposed methodologies.