Madhuri S. Mulekar Pengarang

A New Generalization of the Exponentiated Pare to Distribution With an Application M azen N assar,a Sanku Dey,b and Devendra Kumarc aDepartment of Statistics, Faculty of Commerce, Zagazig University, Egypt; bDepartment of Statistics, St. Anthony’s College, Shillong, Meghalaya, India; cDepartment of Statistics, Central University of Haryana, Haryana, India SYNOPTIC ABSTR AC T We introduce for the fist time a new lifetime distribution, namely, transmuted exponentiated Pareto (TEP) distribution, which generalizes the exponentiated Pareto distribution proposed by Gupta, Gupta, and Gupta (1998) with an additional parameter using the quadratic rank transmutation map which was studied by Shaw and Buckley (2009) to provide greater flxibility in modeling data from a practical point of view. In this article, our main focus is on estimation from a frequentist point of view, yet, some statistical and reliability characteristics for the model are derived. We briefl describe diffrent estimation procedures, namely, the method of maximum likelihood estimation, moment estimation, L-moment estimation, least square and weighted least squares estimation, maximum product of spacings estimation, and Cramér-vonMises estimation. Monte Carlo simulations are performed to compare the performances of the proposed methods of estimation for both small and large samples. Finally, the potentiality of the model is analyzed by means of one real data set. KEYWO RDS AND PHR ASES Hazard rate function; maximum likelihood estimation; method of maximum product spacing; transmuted exponentiated Pareto distribution Information Theoritic Approaches to Principa l Component Selection At i k ur R. K hana and Rahmatullah Imonb aAmerican International University, Bangladesh; bDepartment of Mathematical Sciences, Ball State University, USA SYNOPTIC ABSTR AC T Component selection in principal component analysis is the main step for dimension reduction and working further with extracted factors. A range of component selection methods include hypothesis testing and subjective judgement of graphical representation of eigenvalues, and most of them are not suitable for automatic selection of number of principal components. Though several versions of description length criteria have been developed for automatic selection of principal components, each of the criteria has its own methodological advantages and disadvantages, and no single method always performs the best in all datasets. With the lack of general guidance and criteria for using a particular method, component selection procedures largely depend on personal preferences rather than real statistics. In this article, we survey theoretical grounds of three commonly used minimum description length criteria based on the inherent Karhunen-Loève expansion of the observed process, and examine their performances by employing a series of simulation experiments. Finally, we present some empirical results to demonstrate that the theoretical properties of these criteria are reflcted in simulation experiments, and results obtained in simulation experiments are also reflcted in real data analysis. KEY WO RDS AND PHR ASES Minimum description length; principal component analysis; Karhunen-Loève decomposition; factor analysis Jonckheere Type Test Procedure with Optimal Criterion Under Order Restric tions Narinder Kumar and M anish G oyal D epar t ment of Stat istics, Panjab U niversit y, Chandigarh, I ndia SYNOPTIC ABSTR AC T I n many practical applications, there is a need for testing of an hypothesis under orderrestrictions. We propose a general class of test swhich generalizes the tests proposed by Jonckheere (1954), Kumar et al. (1994a, b), and Patil (2007). The asymptotic distribution of test statistic under null hypothesis, as well as under an equally spaced sequence of local alternatives, is derived. Pitman asymptotic relative effiency comparisons with respect to competing tests are made to evaluate the performance of the proposed class of tests. An example is provided in Hundal (1969) data for implementing the proposed test procedure. Furthermore, a simulation study is carried out to estimate the power and level of signifiance of the proposed class of tests. KEY WORDS AND PHR ASES Asymptotic power; o p t i m a l i t y c r i te r i o n ; restric ted alternat ives; s i m u l at i o n s t u d y ; su b - s a m p l e On Rescheduling for Two - Machine Flow Shop Syste m with the Ar r i va l o f N e w J o b s Jun Yang and Wenchang Luo Facult y of S cience, N ingbo U niversit y, N ingbo, PR China SYNOPTIC ABSTR AC T In this paper, we consider the rescheduling problem for a t wo – machine fow shop system wi th the arrival of new jobs, in which aset of original jobs has been given a planned s chedule (but has not been executed) on a two - machine fow shop system to minimize the makes pan , when a set of new jobs arrives. The production planner needs to insert the new jobs into the planneds chedule without excessively disrupting it to minimize the makesapn on the original and the new jobs. The disruption is measured by the maximum time deviation for any given original job, between the original and new schedules. We examine two special models and a general model. I n the first special model, the m aximum time deviation appears as a constraint. In the second special model, the maximum time deviation appears as the part of the cost objective. In the general model, the m aximum time deviation appears both as a constraint and as the part of the cost objective. For the two special models, we prove that they are NP- hard and accordingly he general model is also N P- hard. Further more we propose three heuristical gorithms to solve t he general model followed by a numerical example. KEY WO RDS AND PHR ASES R e s c h e d u l i n g ; t wo - m a c h i n e fl ow sh o p ; co m p l ex i t y; h e u r i s t i c a l g o r i t h m s Paramete r Estimation for the Kumaraswamy Distribution Based on Hybrid Censoring Far ha Sult ana,a Yogesh Mani Tripathi,a Manoj Kumar Rastogi,b and Shuo-Jye Wu c aDepartment of Mathematics, Indian Institute of Technology Patna, Bihta, India; bNational Institute of Pharmaceutical Education and Research, Hajipur, India; cDepartment of Statistics, Tamkang University, Tamsui, New Taipei City, Taiwan SYNOPTIC ABSTR AC T We consider estimation of unknown parameters of a two-parameter Kumaraswamy distribution with hybrid censored samples. We obtain maximum likelihood estimates using an expectation-maximization algorithm. Bayes estimates are derived under the squared error loss function using diffrent approximation methods. In addition, an importance sampling technique is also discussed. Interval estimation is considered as well. We conduct a simulation study to compare the performance of diffrent estimates, and based on this study, recommendations are made. A real data set and a simulated data set are analyzed for illustration purposes. KEY WO RDS AND PHR ASES Bayes estimates; EM algorithm; importance sampling; Lindley method; Tierney and Kadane method The Excess Formulation and Related Dynamic Results for the Consistent Value Yu-Hsien Liao Department of Applied Mathematics, National Pingtung University, Pingtung, Taiwan SYNOPTIC ABSTR AC T Diffrent from the results of H wang and Liao (2009) and Liao ( 2016), we propose alternative fo rmulation and related d ynamic processes for the consistent value by applying excess func tions. B ased on the contraction mapping theorem, we provide an alternative viewpoint for t hese dynamic results. KEY WO RDS AND PHR ASES Co nsistent value; excess f u n c t i o n ; dy n a m i c s p ro ce s s