Journal of Data Science

In a Bayesian approach, uncertainty explained by a prior distribution that contains information about an uncertain parameter. Determination of the prior distribution is important in because it impacts the posterior inference. The objective of this study is to use metaanalysis for proportion to obtain prior information about patients with breast cancer stage I who undergoing modified radical mastectomy treatment and applied Bayesian approach. R and WinBUGS programs are performed for meta-analysis and Bayesian approach respectively.

In this article, we introduce an extension referred to as the exponentiated Weibull power function distribution based on the exponentiated Weibull-G family of distributions. The proposed model serves as an extension of the two-parameter power function distribution as well as a generalization to the Weibull power function presented by Tahir et al. (2016 a). Various mathematical properties of the subject distribution are studied. General explicit expressions for the quantile function, expansion of density and distribution functions, moments, generating function, incomplete moments, conditional moments, residual life function, mean deviation, inequality measures, Rényi and q – entropies, probability weighted moments and order statistics are obtained. The estimation of the model parameters is discussed using maximum likelihood method. Finally, the practical importance of the proposed distribution is examined through three real data sets. It has been concluded that the new distribution works better than other competing models.

Factor Analysis is one of the data mining methods that can be used to analyse, mainly large-scale, multi-variable datasets. The main objective of this method is to derive a set of uncorrelated variables for further analysis when the use of highly inter-correlated variables may give misleading results in regression analysis. In the light of the vast and broad advances that have occurred in factor analysis due largely to the advent of electronic computers, this article attempt to provide researchers with a simplified approach to comprehend how exploratory factors analysis work, and to provide a guide of application using R. This multivariate mathematical method is an important tool which very often used in the development and evaluation of tests and measures that can be used in biomedical research. The paper comes to the conclusion that the factor analysis is a proper method used in biomedical research, just because clinical readers can better interpret and evaluate their goal and results.

Inferences about the ratio of two lognormal means δ can depend on plausible values of ρ, the ratio of the normal standard deviations associated to these distributions. This aspect is not usually considered in most of the analyses carried out in some applied sciences. In this paper we propose a profile likelihood approach that allows the comparison of two independent lognormal data sets in a more exhaustive way. Inferences about δ, ρ and (δ, ρ) are jointly analyzed through a simple closed-form expression obtained for the profile likelihood function of the parameter vector (δ, ρ). A similar analysis is done for ψ and ρ, where ψ is the ratio of two lognormal medians, obtaining also a simple closed-form expression for the profile likelihood function of these parameters. These expressions allow us to construct likelihood contour plots that capture most of the information provided by the samples and become valuable to identify if a trade-off between the parameters under study occurs; in case of that, individual inferences should be analyzed carefully. A detailed series of Monte Carlo simulations are included; they illustrate the performance of profile likelihood and parametric bootstrap approaches, for different sample sizes and parameter values.

The analysis of sports data, especially cricket is an interesting field for the statisticians. Every year, a large number of cricket tournaments take place among the cricket playing nations. It is of interest to study their performance when they play with each other in a one-day international (ODI) match or a test match. In this study, we assess the performance of top ten cricket teams in the ODI cricket match and make a comparison among them. The abilities of teams change over time. As a result, not a single team dominates the game over a long period. Therefore, a paired comparison method is more reliable and appropriate to compare more than two teams at the same time based on the outcomes of the matches they play. Arguably, a team’s performance also depends on whether they play at home or away. In this study, we consider Bradley-Terry model, a widely accepted model for pairwise comparison. In that, we consider home and away effect to demonstrate how the home advantages differ among these teams.

A graphical tool for choosing the number of nodes for a neural network is introduced. The idea is to fit the neural network with a range of numbers of nodes at first, and then generate a jump plot using a transformation of the mean square errors of the resulting residuals. A theorem is proven to show that the jump plot will select several candidate numbers of nodes among which one is the true number of nodes. Then a single node only test, which has been theoretically justified, is used to rule out erroneous candidates. The method has a sound theoretical background, yields good results on simulated datasets, and shows wide applicability to datasets from real research.

Marshall and Olkin (1997) introduced a general method for obtaining more flexible distributions by adding a new parameter to an existing one, called the Marshall-Olkin family of distributions. We introduce a new class of distributions called the Marshall - Olkin Log-Logistic Extended Weibull (MOLLEW) family of distributions. Its mathematical and statistical properties including the quantile function hazard rate functions, moments, conditional moments, moment generating function are presented. Mean deviations, Lorenz and Bonferroni curves, R´enyi entropy and the distribution of the order statistics are given. The Maximum likelihood estimation technique is used to estimate the model parameters and a special distribution called the Marshall-Olkin Log Logistic Weibull (MOLLW) distribution is studied, and its mathematical and statistical properties explored. Applications and usefulness of the proposed distribution is illustrated by real datasets.

In this paper, we introduce a new family of continuous distributions called the transmuted Topp-Leone G family which extends the transmuted class pioneered by Shaw and Buckley (2007). Some of its mathematical properties including probability weighted moments, mo- ments, generating functions, order statistics, incomplete moments, mean deviations, stress- strength model, moment of residual and reversed residual life are studied. Some useful char- acterizations results based on two truncated moments as well as based on hazard function are presented. The maximum likelihood method is used to estimate its parameters. The Monte Carlo simulation is used for assessing the performance of the maximum likelihood estimators. The usefulness of the new model is illustrated by means of two real data set.