Showing papers in "Communications in Statistics-theory and Methods in 2005"
TL;DR: In this paper, the authors propose a new similarity index which includes the species proportions of both the shared and non shared species in each population, and also propose a Nonparametric Maximum Likelihood Estimator (NPMLE) for this index.
Abstract: There are several indices for measuring the similarity of two populations, including the ratio of the number of shared species to the number of distinct species (Jaccard's index) and the conditional probability of observing a shared species (Smith et al., 1996). However, these indices only take into account the number of species and species proportions of shared species. In this article, we propose a new similarity index which includes the species proportions of both the shared and non shared species in each population, and also propose a Nonparametric Maximum Likelihood Estimator (NPMLE) for this index. Bootstrap and delta methods are used to evaluate the standard errors of the NPMLE. Based on a loss function, we also compare a class of nonparametric estimators for the proposed index in various situations.
477 citations
TL;DR: In this paper, a new three-parameter asymmetric Laplace distribution and its extension are introduced, which has established a direct link to estimation of quantile and quantile regression.
Abstract: In this article, a new three-parameter asymmetric Laplace distribution and its extension are introduced. This includes as special case the symmetric Laplace double-exponential distribution. The distribution has established a direct link to estimation of quantile and quantile regression. Properties of the new distribution are presented. Application is made to a flood data modeling example.
237 citations
TL;DR: In this paper, a new approach for choosing the ridge parameter (K), when multicollinearity among the columns of the design matrix exists, is suggested and evaluated by simulation techniques, in terms of mean squared errors.
Abstract: Hoerl and Kennard (1970a) introduced the ridge regression estimator as an alternative to the ordinary least squares estimator in the presence of multicollinearity. In this article, a new approach for choosing the ridge parameter (K), when multicollinearity among the columns of the design matrix exists, is suggested and evaluated by simulation techniques, in terms of mean squared errors (MSE). A number of factors that may affect the properties of these methods have been varied. The MSE from this approach has shown to be smaller than using Hoerl and Kennard (1970a) in almost all situations.
221 citations
TL;DR: In this paper, a new ratio estimator in stratified random sampling based on the Prasad (1989) estimator was proposed. But the proposed estimator is more efficient than combined ratio estimate in all conditions.
Abstract: In this article, we suggest a new ratio estimator in stratified random sampling based on the Prasad (1989) estimator. Theoretically, we obtain the mean square error (MSE) for this estimator and compare it with the MSE of traditional combined ratio estimate. By this comparison, we demonstrate that proposed estimator is more efficient than combined ratio estimate in all conditions. In addition, this theoretical result is supported by a numerical example.
102 citations
TL;DR: In this paper, a Bayesian estimation for the two parameters of the exponential distribution are obtained based on k-record values under Linear-Exponential LINEX loss function, and the admissibility of some estimators are discussed.
Abstract: There are many situations where experimental outcomes are a sequence of record-breaking observations. In this article, Bayesian estimation for the two parameters of the exponential distribution are obtained based on k-record values under Linear-Exponential LINEX loss function. The admissibility of some estimators are discussed. Prediction, either point or interval, for future k-record values are also presented from a Bayesian view point. Numerical computations are given for an empirical comparison.
85 citations
TL;DR: In this paper, Bayes estimates of the two shape parameters, reliability, and failure rate functions of the exponentiated Weibull lifetime model are derived from complete and type II censored samples.
Abstract: In this article, Bayes estimates of the two shape parameters, reliability, and failure rate functions of the exponentiated Weibull lifetime model are derived from complete and type II censored samples. When the Bayesian aproach is considered, conjugate priors for either the one or the two shape parameters cases are considered. An approximation form due to Lindely [Lindely, D. V. (1980). Approximate Bayesian method. Trabajos de Estadistica 31:223–237] is used for obtaining the Bayes estimates under the squared error loss and LINEX loss functions. The root mean square errors of the estimates are computed. Comparisons are made between these estimators and the maximum likelihood ones using Monte Carlo simulation study.
85 citations
TL;DR: In this article, a Laguerre expansion for inverse Laplace transform is derived based on the estimation problem in the gamma distribution, which is used to obtain the density and distribution functions of a sum of positive weighted central chi-square variables as a series in Laguero polynomials.
Abstract: We derive a Laguerre expansion for the inverse Laplace transform, based on the estimation problem in the gamma distribution. This procedure is used to obtain the density and distribution functions of a sum of positive weighted central chi-square variables as a series in Laguerre polynomials. The formulas so obtained will depend on certain parameters which adequately chosen will give some expressions already known in the literature and some new ones. Finally, we obtain bounds for the truncation error in the numerical approximations.
85 citations
TL;DR: In this article, the authors derived a more general expression for the nth moment of the beta normal distribution, which is the first moment for some particular values of the parameters of the distribution.
Abstract: Eugene et al. [Eugene, N., Lee, C., Famoye, F. (2002). Beta-normal distribution and its applications. Commun. Stat. Theory Meth. 31:497–512] introduced the beta normal distribution, generated from the logit of a beta random variable. The only properties of the distribution studied by them are its first moments for some particular values of the parameters. In this article, we derive a more general expression for the nth moment of the beta normal distribution. We also consider several particular cases (including those cases considered by Eugene et al.). Apart from being more general, the proof of our results are simpler and avoid the differential equations approach taken by Eugene et al.
81 citations
TL;DR: In this article, a zero adjusted generalized Poisson distribution is studied and a score test is developed, with and without covariates, to determine whether such an adjustment is necessary or not.
Abstract: In certain applications involving count data, it is sometimes found that zeros are observed with a frequency significantly higher (lower) than predicted by the assumed model. Examples of such applications are cited in the literature from engineering, manufacturing, economics, public health, epidemiology, psychology, sociology, political science, agriculture, road safety, species abundance, use of recreational facilities, horticulture and criminology. In this article, a zero adjusted generalized Poisson distribution is studied and a score test is developed, with and without covariates, to determine whether such an adjustment is necessary. Examples, with and without covariates, are provided to illustrate the results.
75 citations
TL;DR: The proposed definition measures the mean residual life function of a parallel system consisting of n identical and independent components under the condition that n - i, i = 0, 2, …, n - 1, components of the system are working and other components have already failed.
Abstract: One of the most important types of system structures is the parallel structure. In the present article, we propose a definition for the mean residual life function of a parallel system and obtain some of its properties. The proposed definition measures the mean residual life function of a parallel system consisting of n identical and independent components under the condition that n - i, i = 0, 2, …, n - 1, components of the system are working and other components of the system have already failed. It is shown that, for the case where the components of the system have increasing hazard rate, the mean residual life function of the system is a nonincreasing function of time. Finally, we will obtain an upper bound for the proposed mean residual life function.
74 citations
TL;DR: In this paper, the reliability of a system is discussed when both the strength of the system and the stress imposed on it are independent, non identical Burr Type III distributed random variables.
Abstract: In this article, the reliability of a system is discussed when both the strength of the system and the stress imposed on it are independent, non identical Burr Type III distributed random variables. Different methods for estimating the reliability are applied. The point estimators obtained are maximum likelihood, uniformly minimum variance unbiased, and Bayesian estimators based on conjugate and non informative prior distributions. A comparison of the estimates obtained is performed. Interval estimators of the reliability are also discussed.
TL;DR: In this paper, the concept of directional dependence in bivariate regression was defined and studied by using copulas, and two cases of directional dependency were considered: one originating from marginals and the other originating from the joint behavior of variables.
Abstract: In this article, we define and study the concept of directional dependence in bivariate regression setting by using copulas. We consider two cases of directional dependence; one originating from marginals and the other originating from the joint behavior of variables. We also generalize and clarify the results given by Dodge and Rousson (2000) and Muddapur (2003).
TL;DR: In this paper, the authors consider multiple linear regression models under nonnormality and derive modified maximum likelihood estimators (MMLEs) of the parameters and show that they are efficient and robust.
Abstract: We consider multiple linear regression models under nonnormality We derive modified maximum likelihood estimators (MMLEs) of the parameters and show that they are efficient and robust We show that the least squares esimators are considerably less efficient We compare the efficiencies of the MMLEs and the M estimators for symmetric distributions and show that, for plausible alternatives to an assumed distribution, the former are more efficient We provide real-life examples
TL;DR: In this article, the authors presented maximum likelihood, Bayes, and empirical Bayes estimators of the truncated first moment and hazard function of the Maxwell distribution and compared the relative efficiency of these estimators via a Monte Carlo simulation study.
Abstract: This article presents maximum likelihood, Bayes, and empirical Bayes estimators of the truncated first moment and hazard function of the Maxwell distribution. A comparison of the relative efficiency of these three estimators is performed via a Monte Carlo simulation study.
TL;DR: In this article, a simple method of deriving an explicit estimator by approximating the likelihood function is presented, and the bias and variance of this estimator is examined through simulations.
Abstract: For the half-logistic distribution, the maximum likelihood method does not provide an explicit estimator for the scale parameter based on a progressively Type-II censored sample In this article, we first present a simple method of deriving an explicit estimator by approximating the likelihood function We then examine through simulations the bias and variance of this estimator and show that this estimator is as efficient as the maximum likelihood estimator (MLE) Next, we show that the probability coverages of the pivotal quantities (for the scale parameter) based on asymptotic normality are unsatisfactory, especially when the effective sample size is small Therefore, we suggest using unconditional simulated percentage points of these pivotal quantities for the construction of confidence intervals A wide range of sample sizes and progressive censoring schemes have been considered in this study Finally, we present a numerical example to illustrate all the methods of inference discussed here
TL;DR: In this paper, an empirical estimator of the stationary distribution of the embedded Markov chain and the mean sojourn time is presented for semi-Markov processes, and the main results given here are the asymptotic properties of these estimators, as well as the strong consistency and the normality.
Abstract: The problem of statistical inference for semi-Markov processes is of increasing interest in recent literature. The aim of this article is to present an empirical estimator of the stationary distribution for semi-Markov processes. We use the empirical estimators for the stationary distribution of the embedded Markov chain and for the mean sojourn time. The main results given here are the asymptotic properties of these estimators, as the strong consistency and the asymptotic normality.
TL;DR: In this article, the authors derived various closed-form representations for the moments of the Weibull distribution with no restrictions imposed on the parameters of the distribution, and these representations involve only the gamma junction and its derivatives.
Abstract: This article concerns the exponentiated Weibull distribution introduced by Mudholkar et al. (1995). The moments of this distribution have been of some interest, Mudholkar and Hutson (1996) provided a non closed form integral representatior, for the moments while, most recently, Nassar and Eissa (2003) derived a finite sum representation by restricting one of the parameters of the distribution to be c positive integer. In this article, we derive various closed-form representations for the moments with no restrictions imposed on the parameters of the distribution. These representations involve only the (standard) gamma junction and its derivatives.
TL;DR: In this article, the authors used the maximum likelihood and Bayes methods of estimation for the parameters of the Burr type XII distribution, and compared the results of AL-Hussaini and Jaheen (1992) which are based on ordinary order statistics.
Abstract: The concept of generalized order statistics was introduced by Kamps (1995) to unify several concepts that have been used in statistics such as order statistics, record values, and sequential order statistics. Estimation of the parameters of the Burr type XII distribution are obtained based on generalized order statistics. The maximum likelihood and Bayes methods of estimation are used for this purposes. The Bayes estimates are derived by using the approximation form of Lindley (1980). Estimation based on upper records from the Burr model is obtained and compared by using Monte Carlo simulation study. Our results are specialized to the results of AL-Hussaini and Jaheen (1992) which are based on ordinary order statistics.
TL;DR: A way to construct copulas based on periodic functions is introduced, study the two-dimensional case based on one dependence parameter and then provide a way to extend the construction to the n-dimensional framework, implying possibly asymmetric relations.
Abstract: Although there exists a large variety of copula functions, only a few are practically manageable, and often the choice in dependence modeling falls on the Gaussian copula. Furthermore most copulas are exchangeable, thus implying symmetric dependence. We introduce a way to construct copulas based on periodic functions. We study the two-dimensional case based on one dependence parameter and then provide a way to extend the construction to the n-dimensional framework. We can thus construct families of copulas in dimension n and parameterized by n − 1 parameters, implying possibly asymmetric relations. Such “periodic” copulas can be simulated easily.
TL;DR: In this article, the authors deal with various mixed Poisson distributions in order to analyze count data characterized by their long tails and over dispersion when the Poisson distribution and negative binomial distribution are found to be inadequate.
Abstract: This article deals with various mixed Poisson distributions in order to analyze count data characterized by their long tails and over dispersion when the Poisson distribution and negative binomial distribution are found to be inadequate. Several mixed Poisson distributions are presented and their structural properties are investigated. Three well-known data sets, having long tails, are analyzed and the results of fitting by various models are provided.
TL;DR: In this article, a new estimator of extreme quantiles dedicated to Weibull tail distributions is presented, based on the regular variation coefficient of the inverse cumulative hazard function (RDC).
Abstract: We present a new estimator of extreme quantiles dedicated to Weibull tail distributions. This estimate is based on a consistent estimator of the Weibull tail coefficient. This parameter is defined as the regular variation coefficient of the inverse cumulative hazard function. We give conditions in order to obtain the weak consistency and the asymptotic distribution of the extreme quantiles estimator. Its asymptotic as well as its finite sample performances are compared to classical ones.
TL;DR: In this paper, the authors considered a multivariate Laplace distribution and provided a test with its asymptotic null and non-null distributions, for testing that the skewness is zero.
Abstract: In this article, we consider a multivariate Laplace distribution. When its skewness is zero, the distribution becomes a member of the elliptical family of distributions. We provide a test with its asymptotic null and nonnull distributions, for testing that the skewness is zero. Characteristics of the Laplace distribution such as mean, covariance matrix, third and fourth cumulants, and moments are given. Mardia's real-valued measures of skewness β1p and kurtosis β2p are defined in terms of cumulants, and an inequality between the skewness and kurtosis—namely, β2p ≥ p 2 + β1p , where p is the dimension of the random vector—is given. When p = 1, this reduces to the well-known inequality in the univariate case.
TL;DR: In this paper, pointwise best-possible bounds on the bivariate distribution function of continuous random variables with given margins and a given value of the medial correlation coefficient were obtained.
Abstract: We find pointwise best-possible bounds on the bivariate distribution function of continuous random variables with given margins and a given value of the medial correlation coefficient, and compare those bounds to those obtained from a given value of Kendall’s tau and Spearman’s rho.
TL;DR: In this article, the Rayleigh distribution is proposed to be the underlying model from which observables are to be predicted by using Bayesian approach and the two-sample prediction technique is used.
Abstract: The Rayleigh distribution is proposed to be the underlying model from which observables are to be predicted by using Bayesian approach. Progressively Type-II censored data from the Rayleigh distribution is considered and the two-sample prediction technique is used. Numerical computations and a simulation are given to illustrate the performance of the procedures.
TL;DR: Borders for a multivariate distribution function H with given univariate margins when the value of H is known at a single point whose coordinates are percentiles of the variables X 1, X 2,…, X n , respectively are investigated.
Abstract: If H denotes the joint distribution function of n random variables X 1, X 2,…, X n whose margins are F 1, F 2,…, F n , respectively, then the fundamental best-possible bounds inequality for H is F 2(x 2),…, F n (x n )) for all x 1, x 2,…, x n in [−∞, ∞]. In this paper we employ n-copulas and n-quasi-copulas to find similar bounds on arbitrary sets of multivariate distribution functions with given margins. We discuss bounds for an n-quasi-copula Q when a value of Q at a single point is known. As an application, we investigate about bounds for a multivariate distribution function H with given univariate margins when the value of H is known at a single point whose coordinates are percentiles of the variables X 1, X 2,…, X n , respectively.
TL;DR: In this article, a confidence interval and test are obtained for the mean of an asymmetric distribution using a random sample of size n. The method is based on N. J. Johnson's (1978) modified t-test, where terms of Cornish-Fisher expansions involving the third moment are used to adjust the conventional statistic to have more closely a Student's t-distribution with n − 1 degrees of freedom.
Abstract: A confidence interval and test are obtained for the mean of an asymmetric distribution using a random sample of size n. The method is based on N. J. Johnson's (1978) modified t-test, where terms of Cornish–Fisher expansions involving the third moment are used to adjust the conventional statistic to have more closely a Student's t-distribution with n − 1 degrees of freedom. Johnson's (1978) test cannot be inverted uniquely, so a corresponding confidence interval for the mean may be disjointed. However, an artificial term of small order can be added to make inversion of the test a uniquely defined operation, which prevents such disjointedness. The resulting one-sided and two-sided intervals perform better than others in the literature with skewed distributions, and have good performance with a normal distribution. The two-sided interval may be recommended for general use if the sample size is 10 or more and the nominal confidence coefficient is 95% or less, or if the sample size is 30 or more and t...
TL;DR: An alternative way of looking at regression analysis by using copulas is introduced, its properties are studied, and advantages that will come out from the approach are discussed.
Abstract: The main objective of this article is to introduce an alternative way of looking at regression analysis by using copulas. To achieve our objective we work on copula regression function, study its properties, and discuss advantages that will come out from our approach.
TL;DR: In this paper, a class of goodness-of-fit tests for the Laplace distribution is proposed, based on a weighted integral involving the empirical characteristic function, and the consistency of the tests as well as their asymptotic distribution under the null hypothesis are investigated.
Abstract: In this paper a class of goodness-of-fit tests for the Laplace distribution is proposed. The tests are based on a weighted integral involving the empirical characteristic function. The consistency of the tests as well as their asymptotic distribution under the null hypothesis are investigated. As the decay of the weight function tends to infinity the test statistics approach limit values. In a particular case the resulting limit statistic is related to the first nonzero component of Neyman's smooth test for this distribution. The new tests are compared with other omnibus tests for the Laplace distribution.
TL;DR: In this article, the authors present a partition of the numerator of the tau statistic, or equivalently, the BSS measure in the CATANOVA framework, into location, dispersion, and higher order components.
Abstract: The analysis of variance of cross-classified (categorical) data (CATANOVA) is a technique designed to identify the variation between treatments of interest to the researcher. There are well-established links between CATANOVA and the Goodman and Kruskal tau statistic as well as the Light and Margolin R 2 for the purposes of the graphical identification of this variation. The aim of this article is to present a partition of the numerator of the tau statistic, or equivalently, the BSS measure in the CATANOVA framework, into location, dispersion, and higher order components. Even if a CATANOVA identifies an overall lack of variation, by considering this partition and calculations derived from them, it is possible to identify hidden, but statistically significant, sources of variation.
TL;DR: In this article, the authors discuss the estimation of a multiple state model under several scenarios when only a single survey of cross-sectional data is available, and the conclusions are used to discuss the disability level of the Spanish elderly population and are helpful to develop welfare programs and insurance products.
Abstract: We split the components corresponding to the disability-free survival probability, and the disability survival probability. Our analysis is conducted for men and women separately, for age groups over 64 years. We discuss the estimation of a multiple state model under several scenarios when only a single survey of cross-sectional data is available. The conclusions are used to discuss the disability level of the Spanish elderly population and are helpful to develop welfare programs and insurance products.