On some dynamic generalized information measures for bivariate lifetimes

Several generalizations to the concept of Kullback-Leibler divergence measure and Kerridge inaccuracy measure are available in the literature. In a recent paper Kundu (Metrika, 78:415–435, 2015 Kundu, C. 2015. Generalized measures of information for truncated random variables. Metrika 78:415–35.[Crossref], [Web of Science ®] , [Google Scholar]) considered a generalized K-L divergence measure of order (α, β). Nath (Metrika, 13:123–135, 1968 Nath, P. 1968. Inaccuracy and coding theory. Metrika 13:123–35.[Crossref] , [Google Scholar]) has also proposed generalized inaccuracy measure of order α. Here we address the question of extending these measures to higher dimensions with reference to residual lifetimes. In the present work, the generalized divergence and inaccuracy measures are extended for conditional lifetimes of two components having possibly different ages. Several properties, including monotonicity, and bounds of these measures are obtained for conditional random variables. Moreover, we study the effect of (increasing) monotone transformation on these generalized measures.     

On constructing almost unbiased estimators of finite population mean using transformed auxiliary variable

${\overline y}$ , ratio _R and Tracy et al. (1999) estimators. Received: October 12, 1999; revised version: April 25, 2000     

Improved Exponential Type Estimators of the Mean of a Sensitive Variable in the Presence of Nonsensitive Auxiliary Information

Recently, Koyuncu et al. (2013 Koyuncu, N., Gupta, S., Sousa, R. (2014). Exponential type estimators of the mean of a sensitive variable in the presence of non-sensitive auxiliary information. Communications in Statistics- Simulation and Computation[PubMed], [Web of Science ®] , [Google Scholar]) proposed an exponential type estimator to improve the efficiency of mean estimator based on randomized response technique. In this article, we propose an improved exponential type estimator which is more efficient than the Koyuncu et al. (2013 Koyuncu, N., Gupta, S., Sousa, R. (2014). Exponential type estimators of the mean of a sensitive variable in the presence of non-sensitive auxiliary information. Communications in Statistics- Simulation and Computation[PubMed], [Web of Science ®] , [Google Scholar]) estimator, which in turn was shown to be more efficient than the usual mean estimator, ratio estimator, regression estimator, and the Gupta et al. (2012 Gupta, S., Shabbir, J., Sousa, R., Corte-Real, P. (2012). Regression estimation of the mean of a sensitive variable in the presence of auxiliary information. Communications in Statistics – Theory and Methods 41:2394–2404.[Taylor &; Francis Online], [Web of Science ®] , [Google Scholar]) estimator. Under simple random sampling without replacement (SRSWOR) scheme, bias and mean square error expressions for the proposed estimator are obtained up to first order of approximation and comparisons are made with the Koyuncu et al. (2013 Koyuncu, N., Gupta, S., Sousa, R. (2014). Exponential type estimators of the mean of a sensitive variable in the presence of non-sensitive auxiliary information. Communications in Statistics- Simulation and Computation[PubMed], [Web of Science ®] , [Google Scholar]) estimator. A simulation study is used to observe the performances of these two estimators. Theoretical findings are also supported by a numerical example with real data. We also show how to, extend the proposed estimator to the case when more than one auxiliary variable is available.     

On Improvement in Variance Estimation Using Auxiliary Information

Kadilar and Cingi (2006 Kadilar , C. , Cingi , H. ( 2006 ). Improvement in variance estimation using auxiliary information . Hacett. J. Math. Statist. 35 ( 1 ): 111 – 115 . [Google Scholar]) have introduced an estimator for the population variance using an auxiliary variable in simple random sampling. We propose a new ratio-type exponential estimator for population variance which is always more efficient than usual ratio and regression estimators suggested by Isaki (1983 Isaki , C. T. ( 1983 ). Variance estimation using auxiliary information . J. Amer. Statist. Assoc. 78 : 117 – 123 .[Taylor & Francis Online], [Web of Science ®] , [Google Scholar]) and by Kadilar and Cingi (2006 Kadilar , C. , Cingi , H. ( 2006 ). Improvement in variance estimation using auxiliary information . Hacett. J. Math. Statist. 35 ( 1 ): 111 – 115 . [Google Scholar]). Efficiency comparison is carried out both mathematically and numerically.     

On a new positive dependence concept based on the conditional mean inactivity time order

In this paper, we introduce a new positive dependence concept between two non negative random variables which is related to a conditional version of the mean inactivity time order. A number of properties and relationship between the new notion and the concept of positive likelihood ratio dependence (PLRD) is discussed. Some results in terms of proposed notions for the Archimedean family of copulas are provided.     

Construction of some mixed two- and four-level regular designs with GMC criterion

General minimum lower-order confounding (GMC) criterion is to choose optimal designs, which are based on the aliased effect-number pattern (AENP). The AENP and GMC criterion have been developed to form GMC theory. Zhang et al. (2015 Zhang, T.F., Yang, J.F., Li, Z.M., Zhang, R.C. (2015). Construction of regular 2ⁿ4¹ designs with general minimum lower-order confounding. Commun. Stat. - Theory Methods 46:2724–2735.[Taylor &; Francis Online], [Web of Science ®] , [Google Scholar]) introduced GMC 2ⁿ4^m criterion for choosing optimal designs and constructed all GMC 2ⁿ4¹ designs with N/4 + 1 ? n + 2 ? 5N/16. In this article, we analyze the properties of 2ⁿ4¹ designs and construct GMC 2ⁿ4¹ designs with 5N/16 + 1 ? n + 2 < N ? 1, where n and N are, respectively, the numbers of two-level factors and runs. Further, GMC 2ⁿ4¹ designs with 16-run, 32-run are tabulated.     

On the three-way equivalence of AUC in credit scoring with tied scores

In credit scoring, it is well known that AUC (the area under curve) can be calculated geometrically, by the probability of a correct ranking of a good and bad pair, and by the Wilcoxon Rank-Sum statistic. This three-way equivalence was first present by Hanley and McNeil in 1982 without considering tied scores and without giving analytical proofs. In this paper, we extend the three-way equivalence to the case with tied scores and provide analytic proofs for the three-way equivalence.     

On a stochastic process with a heavy-tailed distributed component describing inventory model type of (s,S)

In the present study, the stochastic process X(t) describing inventory model type of (s, S) with a heavy-tailed distributed demands is considered. The asymptotic expansions at sufficiently large values of parameter β = S ? s for the ergodic distribution and nth-order moment of the process X(t) based on the main results of the studies Teugels (1968 Teugels, J.L. (1968). Renewal theorems when the first or the second moment is infinite. Ann. Math. Stat. 39(4):1210–1219.[Crossref] , [Google Scholar]) and Geluk and Frenk (2011 Geluk, J.L., Frenk, J.B.G. (2011). Renewal theory for random variables with a heavy tailed distribution and finite variance. Stat. Probab. Lett. 81:77–82.[Crossref], [Web of Science ®] , [Google Scholar]) are obtained.