Journal of Data Science

The so-called Kumaraswamy distribution is a special probability distribution developed to model doubled bounded random processes for which the mode do not necessarily have to be within the bounds. In this article, a generalization of the Kumaraswamy distribution called the T-Kumaraswamy family is defined using the T-R {Y} family of distributions framework. The resulting T-Kumaraswamy family is obtained using the quantile functions of some standardized distributions. Some general mathematical properties of the new family are studied. Five new generalized Kumaraswamy distributions are proposed using the T-Kumaraswamy method. Real data sets are further used to test the applicability of the new family.

Subsampling the data is used in this paper as a learning method about the influence of the data points for drawing inference on the parameters of a fitted logistic regression model. The alternative, alternative regularized, alternative regularized lasso, and alternative regularized ridge estimators are proposed for the parameter estimation of logistic regression models and are then compared with the maximum likelihood estimators. The proposed alternative regularized estimators are obtained by using a tuning parameter but the proposed alternative estimators are not regularized. The proposed alternative regularized lasso estimators are the averaged standard lasso estimators and the alternative regularized ridge estimators are also the averaged standard ridge estimators over subsets of groups where the number of subsets could be smaller than the number of parameters. The values of the tuning parameters are obtained to make the alternative regularized estimators very close to the maximum likelihood estimators and the process is explained with two real data as well as a simulated study. The alternative and alternative regularized estimators always have the closed form expressions in terms of observations that the maximum likelihood estimators do not have. When the maximum likelihood estimators do not have the closed form expressions, the alternative regularized estimators thus obtained provide the approximate closed form expressions for them.

The Power function distribution is a flexible life time distribution that has applications in finance and economics. It is, also, used to model reliability growth of complex systems or the reliability of repairable systems. A new weighted Power function distribution is proposed using a logarithmic weight function. Statistical properties of the weighted power function distribution are obtained and studied. Location measures such as mode, median and mean, reliability measures such as reliability function, hazard and reversed hazard functions and the mean residual life are derived. Shape indices such as skewness and kurtosis coefficients and order statistics are obtained. Parametric estimation is performed to obtain estimators for the parameters of the distribution using three different estimation methods; namely: the maximum likelihood method, the L-moments method and the method of moments. Numerical simulation is carried out to validate the robustness of the proposed distribution.

In this paper Zografos Balakrishnan Power Lindley (ZB-PL) distribution has been obtained through the generalization of Power Lindley distribution using Zografos and Balakrishnan (2009) technique. For this technique, density of upper record values exists as their special case. Probability density (pdf), cumulative distribution (cdf) and hazard rate function (hrf) of the proposed distribution are obtained. The probability density and cumulative distribution function are expanded as linear combination of the density and distribution function of Exponentiated Power Lindley (EPL) distribution. This expansion is further used to study different properties of the new distribution. Some mathematical and statistical properties such as asymptotes, quantile function, moments, mgf, mean deviation, renyi entropy and reliability are also discussed. Probability density (pdf), cumulative distribution (cdf) and hazard rate (hrf) functions are graphically presented for different values of the parameters. In the end Maximum Likelihood Method is used to estimate the unknown parameters and application to a real data set is provided a. It has been observed that the proposed distribution provides superior fit than many useful distributions for given data set.

We propose a lifetime distribution with flexible hazard rate called cubic rank transmuted modified Burr III (CRTMBIII) distribution. We develop the proposed distribution on the basis of the cubic ranking transmutation map. The density function of CRTMBIII is symmetrical, right-skewed, left-skewed, exponential, arc, J and bimodal shaped. The flexible hazard rate of the proposed model can accommodate almost all types of shapes such as unimodal, bimodal, arc, increasing, decreasing, decreasing-increasing-decreasing, inverted bathtub and modified bathtub. To show the importance of proposed model, we present mathematical properties such as moments, incomplete moments, inequality measures, residual life function and stress strength reliability measure. We characterize the CRTMBIII distribution via techniques. We address the maximum likelihood method for the model parameters. We evaluate the performance of the maximum likelihood estimates (MLEs) via simulation study. We establish empirically that the proposed model is suitable for strengths of glass fibers. We apply goodness of fit statistics and the graphical tools to examine the potentiality and utility of the CRTMBIII distribution.

In this paper, a new four parameter zero truncated Poisson Frechet distribution is defined and studied. Various structural mathematical properties of the proposed model including ordinary moments, incomplete moments, generating functions, order statistics, residual and reversed residual life functions are investigated. The maximum likelihood method is used to estimate the model parameters. We assess the performance of the maximum likelihood method by means of a numerical simulation study. The new distribution is applied for modeling two real data sets to illustrate empirically its flexibility.

The paper presents an investigation of estimating treatment effect using differ- ent matching methods through Monte Carlo simulation. The study proposed a new method which is computationally efficient and convenient in implication—largest caliper matching and compared the performance with other five popular matching methods. The bias, empirical standard deviation and the mean square error of the estimates in the simulation are checked under different treatment prevalence and different distributions of covariates. It is shown that largest caliper matching improves estimation of the population treatment effect in a wide range of settings compare to other methods. It reduces the bias if the data contains the selection on observables and treatment imbalances. Also, findings about the relative performance of the different matching methods are provided to help practitioners determine which method should be used under certain situations. An application of these methods is implemented on the Study to Understand Prognoses and Preferences for Outcomes and Risks of Treatments (SUPPORT) data and, important demographic and socioeconomic factors that may affect the clinical outcome are also reported in this paper.

In this paper, the geometric process model is used for analyzing constant stress accelerated life testing. The generalized half logistic lifetime distribution is considered under progressive type-II censoring. Statistical inference is developed on the basis of maximum likelihood approach for estimating the unknown parameters and getting both the asymptotic and bootstrap confidence intervals. Besides, the predictive values of the reliability function under usual conditions are found. Moreover, the method of finding the optimal value of the ratio of the geometric process is presented. Finally, a simulation study is presented to illustrate the proposed procedures and to evaluate the performance of the geometric process model.

In this article, the maximum likelihood estimators of the k independent exponential populations parameters are obtained based on joint progressive type- I censored (JPC-I) scheme. The Bayes estimators are also obtained by considering three different loss functions. The approximate confidence, two Bootstrap confidence and the Bayes credible intervals for the unknown parameters are discussed. A simulated and real data sets are analyzed to illustrate the theoretical results.

Factor analysis (FA) is the most commonly used pattern recognition methodology in social and health research. A technique that may help to better retrieve true information from FA is the rotation of the information axes. The purpose of this study was to evaluate whether the selection of rotation type affects the repeatability of the patterns derived from FA, under various scenarios of random error introduced, based on simulated data from the Standard Normal distribution. It was observed that when applying promax non - orthogonal rotation, the results were more repeatable as compared to the orthogonal rotation, irrespective of the level of random error introduced in the model.