Showing papers in "Journal of Statistical Computation and Simulation in 2011"
TL;DR: In this paper, a new family of generalized distributions for double-bounded random processes with hydrological applications is described, including Kw-normal, Kw-Weibull and Kw-Gamma distributions.
Abstract: Kumaraswamy [Generalized probability density-function for double-bounded random-processes, J. Hydrol. 462 (1980), pp. 79–88] introduced a distribution for double-bounded random processes with hydrological applications. For the first time, based on this distribution, we describe a new family of generalized distributions (denoted with the prefix ‘Kw’) to extend the normal, Weibull, gamma, Gumbel, inverse Gaussian distributions, among several well-known distributions. Some special distributions in the new family such as the Kw-normal, Kw-Weibull, Kw-gamma, Kw-Gumbel and Kw-inverse Gaussian distribution are discussed. We express the ordinary moments of any Kw generalized distribution as linear functions of probability weighted moments (PWMs) of the parent distribution. We also obtain the ordinary moments of order statistics as functions of PWMs of the baseline distribution. We use the method of maximum likelihood to fit the distributions in the new class and illustrate the potentiality of the new model with a...
742 citations
TL;DR: In this article, the power of eight selected normality tests: the Shapiro-Wilk test, Kolmogorov-Smirnov test, Lilliefors test, Cramer-von Mises test, Anderson-Darling test, D'Agostino-Pearson test, the Jarque-Bera test and chi-squared test were compared.
Abstract: Normality tests can be classified into tests based on chi-squared, moments, empirical distribution, spacings, regression and correlation and other special tests. This paper studies and compares the power of eight selected normality tests: the Shapiro–Wilk test, the Kolmogorov–Smirnov test, the Lilliefors test, the Cramer–von Mises test, the Anderson–Darling test, the D'Agostino–Pearson test, the Jarque–Bera test and chi-squared test. Power comparisons of these eight tests were obtained via the Monte Carlo simulation of sample data generated from alternative distributions that follow symmetric short-tailed, symmetric long-tailed and asymmetric distributions. Our simulation results show that for symmetric short-tailed distributions, D'Agostino and Shapiro–Wilk tests have better power. For symmetric long-tailed distributions, the power of Jarque–Bera and D'Agostino tests is quite comparable with the Shapiro–Wilk test. As for asymmetric distributions, the Shapiro–Wilk test is the most powerful test followed b...
545 citations
TL;DR: A simple and efficient Gibbs sampling algorithm for fitting the quantile regression model based on a location-scale mixture representation of the asymmetric Laplace distribution is developed and it is shown that the resulting Gibbs sampler can be accomplished by sampling from either normal or generalized inverse Gaussian distribution.
Abstract: This paper considers quantile regression models using an asymmetric Laplace distribution from a Bayesian point of view. We develop a simple and efficient Gibbs sampling algorithm for fitting the quantile regression model based on a location-scale mixture representation of the asymmetric Laplace distribution. It is shown that the resulting Gibbs sampler can be accomplished by sampling from either normal or generalized inverse Gaussian distribution. We also discuss some possible extensions of our approach, including the incorporation of a scale parameter, the use of double exponential prior, and a Bayesian analysis of Tobit quantile regression. The proposed methods are illustrated by both simulated and real data.
392 citations
TL;DR: The Weibull-geometric (WG) distribution as mentioned in this paper is a generalization of the extended exponential geometric (EG) distribution introduced by Adamidis et al. The hazard function of the EG distribution is monotone decreasing but the hazard function can take more general forms.
Abstract: For the first time, we propose the Weibull-geometric (WG) distribution which generalizes the extended exponential-geometric (EG) distribution introduced by Adamidis et al. [K. Adamidis, T. Dimitrakopoulou, and S. Loukas, On a generalization of the exponential-geometric distribution, Statist. Probab. Lett. 73 (2005), pp. 259–269], the exponential-geometric distribution discussed by Adamidis and Loukas [K. Adamidis and S. Loukas, A lifetime distribution with decreasing failure rate, Statist. Probab. Lett. 39 (1998), pp. 35–42] and the Weibull distribution. We derive many of its standard properties. The hazard function of the EG distribution is monotone decreasing, but the hazard function of the WG distribution can take more general forms. Unlike the Weibull distribution, the new distribution is useful for modelling unimodal failure rates. We derive the cumulative distribution and hazard functions, moments, density of order statistics and their moments. We provide expressions for the Renyi and Shannon entrop...
195 citations
TL;DR: In this article, a new probability mass function is introduced by discretizing the continuous failure model of the Lindley distribution, which is suitable to be applied in the collective risk model when both number of claims and size of a single claim are implemented into the model.
Abstract: Modelling count data is one of the most important issues in statistical research. In this paper, a new probability mass function is introduced by discretizing the continuous failure model of the Lindley distribution. The model obtained is over-dispersed and competitive with the Poisson distribution to fit automobile claim frequency data. After revising some of its properties a compound discrete Lindley distribution is obtained in closed form. This model is suitable to be applied in the collective risk model when both number of claims and size of a single claim are implemented into the model. The new compound distribution fades away to zero much more slowly than the classical compound Poisson distribution, being therefore suitable for modelling extreme data.
168 citations
TL;DR: In this paper, a new generalized p-value method is proposed for testing the equality of coefficients of variation in k normal populations, and the proposed test is also compared with likelihood ratio test, modified Bennett's test and score test through Monte Carlo simulation, the results demonstrate that the generalized pvalue method has satisfactory performance in terms of sizes and powers.
Abstract: A new generalized p-value method is proposed for testing the equality of coefficients of variation in k normal populations. Simulation studies show that the type I error probabilities are close to the nominal level. The proposed test is also compared with likelihood ratio test, modified Bennett's test and score test through Monte Carlo simulation, the results demonstrate that the generalized p-value method has satisfactory performance in terms of sizes and powers.
82 citations
TL;DR: In this paper, a four-parameter extension of the generalized gamma distribution capable of modeling a bathtub-shaped hazard rate function is defined and studied, and the density of the order statistics and two expansions for their moments are derived.
Abstract: A four-parameter extension of the generalized gamma distribution capable of modelling a bathtub-shaped hazard rate function is defined and studied. The beauty and importance of this distribution lies in its ability to model monotone and non-monotone failure rate functions, which are quite common in lifetime data analysis and reliability. The new distribution has a number of well-known lifetime special sub-models, such as the exponentiated Weibull, exponentiated generalized half-normal, exponentiated gamma and generalized Rayleigh, among others. We derive two infinite sum representations for its moments. We calculate the density of the order statistics and two expansions for their moments. The method of maximum likelihood is used for estimating the model parameters and the observed information matrix is obtained. Finally, a real data set from the medical area is analysed.
81 citations
TL;DR: In this article, the estimation of parameters of log-normal distribution based on hybrid censored data is considered and the parameters are estimated by the maximum likelihood method, which can be used as initial estimates for any iterative procedure.
Abstract: The two most common censoring schemes used in life-testing experiments are Type-I and Type-II censoring schemes. The hybrid censoring scheme is mixture of Type-I and Type-II censoring schemes. In this work, we consider the estimation of parameters of log-normal distribution based on hybrid censored data. The parameters are estimated by the maximum likelihood method. It is observed that the maximum likelihood estimates cannot be obtained in a closed form. We obtain the maximum likelihood estimates of the unknown parameters using EM algorithm. We also propose approximate maximum likelihood estimates and these can be used as initial estimates for any iterative procedure. The Fisher information matrix has been obtained and it can be used for constructing asymptotic confidence intervals. The method of obtaining optimum censoring scheme is discussed. One data set is analysed for illustrative purposes.
63 citations
TL;DR: This article forms interval-valued variables as bivariate random vectors and introduces the bivariate symbolic regression model based on the generalized linear models theory which provides much-needed exibility in practice.
Abstract: Interval-valued variables have become very common in data analysis. Up until now, symbolic regression mostly approaches this type of data from an optimization point of view, considering neither the probabilistic aspects of the models nor the nonlinear relationships between the interval response and the interval predictors. In this article, we formulate interval-valued variables as bivariate random vectors and introduce the bivariate symbolic regression model based on the generalized linear models theory which provides much-needed exibility in practice. Important inferential aspects are investigated. Applications to synthetic and real data illustrate the usefulness of the proposed approach.
61 citations
TL;DR: In this article, seven different tests of normality were compared by using Monte Carlo computations under various alternatives, and the results of the results were discussed and interpreted separately, and power comparisons were made by making use of Monte Carlo computation under different alternatives.
Abstract: This article studies seven different tests of normality. The tests in question are Kolmogorov–Smirnov, Anderson–Darling, Kuiper, Jarque–Bera, Cramer von Mises, Shapiro–Wilk, and Vasicek. Each test is described and power comparisons are made by using Monte Carlo computations under various alternatives. The results are discussed and interpreted separately.
55 citations
TL;DR: In this paper, the Gibbs sampling technique was used to generate samples from the posterior density function, and the Bayes estimates of the unknown parameters were computed using Lindley's approximation under the assumption of gamma priors of the shape parameter.
Abstract: In this article, the Bayes estimates of two-parameter gamma distribution are considered. It is well known that the Bayes estimators of the two-parameter gamma distribution do not have compact form. In this paper, it is assumed that the scale parameter has a gamma prior and the shape parameter has any log-concave prior, and they are independently distributed. Under the above priors, we use Gibbs sampling technique to generate samples from the posterior density function. Based on the generated samples, we can compute the Bayes estimates of the unknown parameters and can also construct HPD credible intervals. We also compute the approximate Bayes estimates using Lindley's approximation under the assumption of gamma priors of the shape parameter. Monte Carlo simulations are performed to compare the performances of the Bayes estimators with the classical estimators. One data analysis is performed for illustrative purposes. We further discuss the Bayesian prediction of future observation based on the observed s...
TL;DR: In this article, a variable repetitive group sampling plan is proposed to deal with process loss, which can be used to determine whether the products meet the desired levels of protection for both producers and consumers.
Abstract: Traditionally, most acceptance sampling plans considering the fraction defective do not distinguish among the products that fall within the specification limits. However, products that fall within the specification limits may not be good if their mean is far away from the target. So, developing an acceptance sampling plan with process loss consideration is essential. In this paper, a variable repetitive group sampling plan is proposed to deal with process loss. The design parameters of the proposed plan are tabulated for various combinations of acceptance quality levels. The proposed methodology can be used to determine whether the products meet the desired levels of protection for both producers and consumers.
TL;DR: This work derives small-sample adjustments to the likelihood ratio statistic in beta regression models, which are useful for modelling continuous proportions that are affected by independent variables, and presents Monte Carlo simulations showing that inference based on the adjusted statistics it proposes is much more reliable than thatbased on the usual likelihood Ratio statistic.
Abstract: We consider the issue of performing accurate small-sample likelihood-based inference in beta regression models, which are useful for modelling continuous proportions that are affected by independent variables. We derive small-sample adjustments to the likelihood ratio statistic in this class of models. The adjusted statistics can be easily implemented from standard statistical software. We present Monte Carlo simulations showing that inference based on the adjusted statistics we propose is much more reliable than that based on the usual likelihood ratio statistic. A real data example is presented.
TL;DR: It is shown that exchangeable Marshall–Olkin survival copulas coincide with a parametric family of copulas studied in [J.-F. Mai and M. Scherer, Lévy-Frailty copulas], which implies an alternative probabilistic interpretation in many cases and allows the transfer of known results from one family to the other.
Abstract: It is shown that exchangeable Marshall–Olkin survival copulas coincide with a parametric family of copulas studied in [J.-F. Mai and M. Scherer, Levy-Frailty copulas, J. Multivariate Anal. 100 (2009), pp. 1567–1585]. This observation implies an alternative probabilistic interpretation in many cases and allows the transfer of known results from one family to the other. For instance, using the classical construction of [A.W. Marshall and I. Olkin, A multivariate exponential distribution, J. Am. Stat. Assoc. 62 (1967), pp. 30–44], sampling an n-dimensional Marshall–Olkin copula requires 2 n −1 exponentially distributed random variables, which is inefficient in large dimensions. Applying the alternative construction, sampling an exchangeable n-dimensional copula boils down to generating n independent exponentially distributed random variables and one path of a certain Levy subordinator, which is highly efficient in many cases. Furthermore, the alternative model and sampling methodology is generalized to high-...
TL;DR: In this paper, the authors proposed a simple and effective procedure to design a CQC chart coupled with runs rules that can yield average run length (ARL)-unbiased performance and meet the required in-control ARL.
Abstract: In this paper, we consider incorporating the runs rules into the cumulative quantity control (CQC) chart for monitoring time-between-events data. We propose a simple and effective procedure to design a CQC chart coupled with runs rules that can yield average run length (ARL)-unbiased performance and meet the required in-control ARL. The proposed design involves determining a relation between the upper side and lower side false alarm probabilities. A Markov chain approach is used to evaluate the ARL performance of various control schemes studied in this paper. An extensive numerical comparison shows that the proposed design approach can result in a significant reduction in ARL for detecting increases in the occurrence rate of the event in comparison with the basic CQC charts.
TL;DR: In this article, the authors considered the Birnbaum-Saunders distribution as a life model to develop various acceptance sampling schemes based on the truncated life tests and developed the double sampling plan and determine the design parameters satisfying both the producer's and consumer's risks simultaneously for the specified reliability levels in terms of the mean ratio to the specified life.
Abstract: In this paper, we consider the Birnbaum–Saunders distribution as a life model to develop various acceptance sampling schemes based on the truncated life tests. We develop the double sampling plan and determine the design parameters satisfying both the producer's and consumer's risks simultaneously for the specified reliability levels in terms of the mean ratio to the specified life. We also propose a group sampling plan and determine the parameters by the above-mentioned two-point method. Tables are constructed for the proposed sampling plans and results are explained with examples.
TL;DR: In this article, the authors present two characterizations of the exponential distribution and next introduce three exact goodness-of-fit test for exponentiality, and compare the powers of the proposed tests under various alternatives.
Abstract: In this paper, we first present two characterizations of the exponential distribution and next introduce three exact goodness-of-fit test for exponentiality. By simulation, the powers of the proposed tests under various alternatives are compared with the existing tests.
TL;DR: In this paper, double robust extreme ranked set sampling (DRERSS) and its properties for estimating the population mean are considered and it turns out that, when the underlying distribution is symmetric, DRERSS gives unbiased estimators.
Abstract: In this paper, double robust extreme ranked set sampling (DRERSS) and its properties for estimating the population mean are considered. It turns out that, when the underlying distribution is symmetric, DRERSS gives unbiased estimators of the population mean. Also, it is found that DRERSS is more efficient than the simple random sampling (SRS), ranked set sampling (RSS), and extreme ranked set sampling (ERSS) methods. For asymmetric distributions considered in this study, the DRERSS has a small bias and it is more efficient than SRS, RSS, and ERSS. A real data set is used to illustrate the DRERSS method.
TL;DR: In this paper, the authors studied the so-called beta modified Weibull distribution and derived the moments and moment generating function of the new distribution, as well as the asymptotic distributions of the extreme values.
Abstract: We study in detail the so-called beta-modified Weibull distribution, motivated by the wide use of the Weibull distribution in practice, and also for the fact that the generalization provides a continuous crossover towards cases with different shapes. The new distribution is important since it contains as special sub-models some widely-known distributions, such as the generalized modified Weibull, beta Weibull, exponentiated Weibull, beta exponential, modified Weibull and Weibull distributions, among several others. It also provides more flexibility to analyse complex real data. Various mathematical properties of this distribution are derived, including its moments and moment generating function. We examine the asymptotic distributions of the extreme values. Explicit expressions are also derived for the chf, mean deviations, Bonferroni and Lorenz curves, reliability and entropies. The estimation of parameters is approached by two methods: moments and maximum likelihood. We compare by simulation the perform...
TL;DR: In this paper, the authors developed nearly unbiased estimators for the Kumaraswamy distribution with a bias correction mechanism based on the parametric bootstrap and conduct Monte Carlo simulations to investigate the performance of the corrected estimators.
Abstract: We develop nearly unbiased estimators for the Kumaraswamy distribution proposed by Kumaraswamy [Generalized probability density-function for double-bounded random-processes, J Hydrol 46 (1980), pp 79–88], which has considerable attention in hydrology and related areas We derive modified maximum-likelihood estimators that are bias-free to second order As an alternative to the analytically bias-corrected estimators discussed, we consider a bias correction mechanism based on the parametric bootstrap We conduct Monte Carlo simulations in order to investigate the performance of the corrected estimators The numerical results show that the bias correction scheme yields nearly unbiased estimates
TL;DR: Pan et al. as discussed by the authors considered 10 Levene type tests: the W50, the M50 and L50 tests, and considered the two-sample scale problem and in particular with LevenEve type tests.
Abstract: Tests for the equality of variances are of interest in many areas such as quality control, agricultural production systems, experimental education, pharmacology, biology, as well as a preliminary to the analysis of variance, dose–response modelling or discriminant analysis. The literature is vast. Traditional non-parametric tests are due to Mood, Miller and Ansari–Bradley. A test which usually stands out in terms of power and robustness against non-normality is the W50 Brown and Forsythe [Robust tests for the equality of variances, J. Am. Stat. Assoc. 69 (1974), pp. 364–367] modification of the Levene test [Robust tests for equality of variances, in Contributions to Probability and Statistics, I. Olkin, ed., Stanford University Press, Stanford, 1960, pp. 278–292]. This paper deals with the two-sample scale problem and in particular with Levene type tests. We consider 10 Levene type tests: the W50, the M50 and L50 tests [G. Pan, On a Levene type test for equality of two variances, J. Stat. Comput. Simul. 6...
TL;DR: In this paper, a wavelet filtering approach is proposed to estimate the parameters of a linear regression model where the regressand and the regressors are persistent processes and contain a measurement error.
Abstract: This paper proposes a wavelet (spectral) approach to estimate the parameters of a linear regression model where the regressand and the regressors are persistent processes and contain a measurement error. We propose a wavelet filtering approach which does not require instruments and yields unbiased estimates for the intercept and the slope parameters. Our Monte Carlo results also show that the wavelet approach is particularly effective when measurement errors for the regressand and the regressor are serially correlated. With this paper, we hope to bring a fresh perspective and stimulate further theoretical research in this area.
TL;DR: In this article, an adaptation of the Stahel-Donoho estimator is presented, where separate weights for each variable are used to identify and downweight the contaminated variables such that they avoid losing the information contained in the other variables.
Abstract: The Stahel–Donoho estimator is defined as a weighted mean and covariance, where each observation receives a weight which depends on a measure of its outlyingness. Therefore, all variables are treated in the same way whether they are responsible for the outlyingness or not. We present an adaptation of the Stahel–Donoho estimator, where we allow separate weights for each variable. By using cellwise weights, we aim to only downweight the contaminated variables such that we avoid losing the information contained in the other variables. The goal is to increase the precision and possibly the robustness, of the estimator. We compare several variants of our proposal and show to what extent they succeed in identifying and downweighting precisely those variables which are contaminated. We further demonstrate that in many situations the mean-squared error of the adapted estimators is lower than that of the original Stahel–Donoho estimator and that this results in better outlier detection capabilities. We also consid...
TL;DR: The Encyclopedic of statistics in behavioural science, edited by Brian S. Everitt and David C. Howell as mentioned in this paper, is the most widely used encyclopedia for behavioral science research.
Abstract: Encyclopedia of statistics in behavioural science, edited by Brian S. Everitt and David C. Howell, John Wiley and Sons Inc., 111 River Street, MS 8-01, Hoboken, NJ 07030 – 5774, USA, 2nd ed., Vols ...
TL;DR: A nonlinear integer programming formulation for fitting a spline-based regression to two-dimensional data using an adaptive knot-selection approach, with the number and location of the knots being determined in the solution process.
Abstract: We present a nonlinear integer programming formulation for fitting a spline-based regression to two-dimensional data using an adaptive knot-selection approach, with the number and location of the knots being determined in the solution process. However, the nonlinear nature of this formulation makes its solution impractical, so we also outline a knot selection heuristic inspired by the Remes Exchange Algorithm, to produce good solutions to our formulation. This algorithm is intuitive and naturally accommodates local changes in smoothness. Results are presented for the algorithm demonstrating performance that is as good as, or better than, other current methods on established benchmark functions.
TL;DR: In this paper, five entropy tests of exponentiality using five statistics based on different entropy estimates are compared by simulation, and the power of these five tests for various alternatives and sample sizes.
Abstract: The paper studies five entropy tests of exponentiality using five statistics based on different entropy estimates. Critical values for various sample sizes determined by means of Monte Carlo simulations are presented for each of the test statistics. By simulation, we compare the power of these five tests for various alternatives and sample sizes.
TL;DR: In this paper, the authors derived an explicit expression for the Bayes risk of a sampling plan when a quadratic loss function is used and used the simulated annealing algorithm to determine the optimal sampling plan.
Abstract: From the exact distribution of the maximum likelihood estimator of the average lifetime based on progressive hybrid exponential censored sample, we derive an explicit expression for the Bayes risk of a sampling plan when a quadratic loss function is used. The simulated annealing algorithm is then used to determine the optimal sampling plan. Some optimal Bayes solutions under progressive hybrid and ordinary hybrid censoring schemes are presented to illustrate the effectiveness of the proposed method.
TL;DR: In this article, a multivariate control chart that integrates a support vector machine (SVM) algorithm, a bootstrap method, and a control chart technique to improve multivariate process monitoring is proposed.
Abstract: Statistical process control tools have been used routinely to improve process capabilities through reliable on-line monitoring and diagnostic processes. In the present paper, we propose a novel multivariate control chart that integrates a support vector machine (SVM) algorithm, a bootstrap method, and a control chart technique to improve multivariate process monitoring. The proposed chart uses as the monitoring statistic the predicted probability of class (PoC) values from an SVM algorithm. The control limits of SVM-PoC charts are obtained by a bootstrap approach. A simulation study was conducted to evaluate the performance of the proposed SVM–PoC chart and to compare it with other data mining-based control charts and Hotelling's T 2 control charts under various scenarios. The results showed that the proposed SVM–PoC charts outperformed other multivariate control charts in nonnormal situations. Further, we developed an exponential weighed moving average version of the SVM–PoC charts for increasing sensiti...
TL;DR: This article used Cox regression as the main platform for variable selection, and compared the strength and diversity of the ensembles in terms of their diversity and strength, providing useful insights for how to choose among different ensemble strategies, as well as guidelines for thinking about how to design more effective ensemble strategies.
Abstract: Using Cox regression as the main platform, we study the ensemble approach for variable selection. We use a popular real-data example as well as simulated data with various censoring levels to illustrate the usefulness of the ensemble approach, and study the nature of these ensembles in terms of their strength and diversity. By relating these characteristics to the ensemble's selection accuracy, we provide useful insights for how to choose among different ensemble strategies, as well as guidelines for thinking about how to design more effective ensembles.
TL;DR: In this article, the authors considered the case of constant-stress partially accelerated life testing (CSPALT) when two stress levels are involved under type-I censoring, and the lifetimes of test items were assumed to follow a two-parameter Pareto lifetime distribution.
Abstract: The paper considers the case of constant-stress partially accelerated life testing (CSPALT) when two stress levels are involved under type-I censoring. The lifetimes of test items are assumed to follow a two-parameter Pareto lifetime distribution. Maximum-likelihood method is used to estimate the parameters of CSPALT model. Confidence intervals for the model parameters are constructed. Optimum CSPALT plans that determine the best choice of the proportion of test units allocated to each stress are developed. Such optimum test plans minimize the generalized asymptotic variance of the maximum-likelihood estimators of the model parameters. For illustration, Monte Carlo simulation studies are presented.