Current Issue : January - March Volume : 2014 Issue Number : 1 Articles : 5 Articles
The Pareto distribution is a heavy-tailed distribution with many applications in the real world. The tail of the distribution is\r\nimportant, but the threshold of the distribution is difficult to determine in some situations. In this paper we consider two realworld\r\nexamples with heavy-tailed observations, which leads us to propose a mixture truncated Pareto distribution (MTPD) and\r\nstudy its properties.We construct a cluster truncated Pareto distribution (CTPD) by using a two-point slope technique to estimate\r\nthe MTPD from a random sample.We apply the MTPD and CTPD to the two examples and compare the proposed method with\r\nexisting estimation methods. The results of log-log plots and goodness-of-fit tests show that the MTPD and the cluster estimation\r\nmethod produce very good fitting distributions with real-world data....
The paper refers to the evaluation of the unavailability of systems made by repairable binary independent components subjected\r\nto aging phenomena. Exponential, exponential-linear, and Weibull distributions are assumed for the components failure times.\r\nWe assume that components failure rate increases only slightly during the maintenance period, but we recognize the effectiveness\r\nof preventive maintenance only in presence of aging phenomena. Importance measures allow the ranking of the input variables.\r\nWe propose analytical equations that allow the estimation of the first-order Differential Importance Measure (DIM) on the basis\r\nof the Birnbaum measures of components, under the hypothesis of uniform percentage changes of parameters. Without further\r\ninformation than that used for the estimation of ââ?¬Å?DIM for components,ââ?¬Â ââ?¬Å?DIM for parametersââ?¬Â allows considering separately the\r\nimportance of random failures, aging phenomena, and preventive and corrective maintenance. A two-step process is proposed for\r\nthe system improvement, by increasing the components reliability and maintainability performance asmuch as possible (within the\r\napplicable technological limits) and then by optimizing preventive maintenance on them. Some examples taken from the scientific\r\nliterature are solved in order to verify the correctness of the analytical equations and to show their use....
The statistical application considered here arose in epigenomics, linking the DNA methylation proportions measured at specific\r\ngenomic sites to characteristics such as phenotype or birth order. It was found that the distribution of errors in the proportions\r\nof chemical modification (methylation) on DNA, measured at CpG sites, may be successfully modelled by a Laplace distribution\r\nwhich is perturbed by a Hermite polynomial.We use a linear model with such a response function. Hence, the response function is\r\nknown, or assumed well estimated, but fails to be differentiable in the classical sense due to themodulus function. Our problem was\r\nto estimate coefficients for the linear model and the corresponding covariance matrix and to compare models with varying numbers\r\nof coefficients. The linear model coefficients may be found using the (derivative-free) simplex method, as in quantile regression.\r\nHowever, this theory does not yield a simple expression for the covariance matrix of the coefficients of the linear model. Assuming\r\nresponse functions which are C2 except where the modulus function attains zero, we derive simple formulae for the covariance\r\nmatrix and a log-likelihood ratio statistic, using generalized calculus. These original formulae enable a generalized analysis of\r\nvariance and further model comparisons....
For a Bi-Exponentiated Weibull model, the authors obtain a general AUC formula and derive the maximum likelihood estimator\r\nof AUC and its asymptotic property. A simulation study is carried out to illustrate the finite sample size performance....
We prove Shao and Yu�s tightness criterion for the generalized empirical process in the space ??[0, 1] with ??1 topology. Covariance\r\ninequalities are used in applying the criterion to particular types of the empirical processes.We weaken the assumptions imposed\r\non the covariance structure as well as the properties of the underlying sequence of r.v.�s, under which presented processes converge\r\nweakly....
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