BURR CRITICAL VALUE APPROXIMATIONS FOR TESTS OF AUTOCORRELATION AND HETEROSCEDASTICITY

The paper evaluates the accuracy of Burr approximations of critical values and p-values for test a of autocorrelation and heteroscedasticity in the linear regression model.     

A Score Test for the Multivariate Burr and Other Weibull Mixture Distributions

The p -variate Burr distribution has been derived, developed, discussed and deployed by various authors. In this paper a score statistic for testing independence of the components, equivalent to testing for p independent Weibull against a p -variate Burr alternative, is obtained. Its null and non-null properties are investigated with and without nuisance parameters and including the possibility of censoring. Two applications to real data are described. The test is also discussed in the context of other Weibull mixture models.     

Modelling the diameter distribution of forest stands using the Burr distribution

SUMMARY For the past 20 years, forest modellers have largely used the Weibull distribution to summarize diameter distributions and to predict timber volume in a forest at clearfell time. The wider family of Burr distributions is investigated here as an alternative to the Weibull distribution. Using data from 20 permanent sample plots of Pinus radiata, we compare Burr and Weibull fits, showing that the Burr distribution enhances precision by roughly 13 . The effectiveness of the Burr distribution for prediction is found to be similar to that of the Weibull distribution.     

Attribute control chart for some popular distributions

The binomial distribution is often used to display attribute control data. In this paper, a statistical model is settled for attribute control chart under truncated life test. By Burr X & XII, inverse Gaussian (IG), and exponential lifetime-truncated distributions, a Shewhart-type attribute control chart is built to display the data. The performance of attributed control chart constructed on truncated life test is evaluated by average run length, which compares the performance of all distributions. Our study arranges that IG is better distribution among all.     

Discrete Burr and discrete Pareto distributions

In this paper we obtain discrete Burr and Pareto distributions using the general approach of discretizing a continuous distribution and propose them as suitable lifetime models. It may be worth exploring the possibility of developing discrete versions of the Burr and Pareto distributions, so that, the same can be used for modeling discrete data. The equivalence of continuous and discrete Burr distributions has been established. Some important distributional properties and estimation of reliability characteristics are discussed. An application in reliability estimation in series system and a real data example on dentistry using this distribution is also discussed.     

Another extended Burr III model: some properties and applications

We introduce an extended Burr III distribution as an important model for problems in survival analysis and reliability. The new distribution can be expressed as a linear combination of Burr III distributions and then it has tractable properties for the ordinary and incomplete moments, generating and quantile functions, mean deviations and reliability. The density of its order statistics can be given in terms of an infinite linear combination of Burr III densities. The estimation of the model parameters is approached by maximum likelihood and the observed information matrix is derived. The proposed model is applied to a real data set to illustrate its potentiality.     

A characterization of the Burr Type III and Type XII distributions through the method of percentiles and the Spearman correlation

A characterization of Burr Type III and Type XII distributions based on the method of percentiles (MOP) is introduced and contrasted with the method of (conventional) moments (MOM) in the context of estimation and fitting theoretical and empirical distributions. The methodology is based on simulating the Burr Type III and Type XII distributions with specified values of medians, inter-decile ranges, left-right tail-weight ratios, tail-weight factors, and Spearman correlations. Simulation results demonstrate that the MOP-based Burr Type III and Type XII distributions are substantially superior to their (conventional) MOM-based counterparts in terms of relative bias and relative efficiency.     

Recurrence relations for moments of progressive type-II right censored order statstics from burr distribution

In this paper some recurrence relations between moments of progressive Type-II right censored order statistics from doubly truncated Burr distribution are established. These recurrence relations would enable one to obtain all the single and product moments of Burr progressive Type-II right censored order statistics in a simple recursive manner.     

Robust regression for estimating the Burr XII parameters with outliers

The Burr XII distribution offers a more flexible alternative to the lognormal, log-logistic and Weibull distributions. Outliers can occur during reliability life testing. Thus, we need an efficient method to estimate the parameters of the Burr XII distribution for censored data with outliers. The objective of this paper is to present a robust regression (RR) method called M-estimator to estimate the parameters of a two-parameter Burr XII distribution based on the probability plotting procedure for both the complete and multiply-censored data with outliers. The simulation results show that the RR method outperforms the unweighted least squares and maximum likelihood methods in most cases in terms of bias and errors in the root mean square.     

Bayesian nonparametric survival analysis using mixture of Burr XII distributions

ABSTRACT

Recently, the Bayesian nonparametric approaches in survival studies attract much more attentions. Because of multimodality in survival data, the mixture models are very common. We introduce a Bayesian nonparametric mixture model with Burr distribution (Burr type XII) as the kernel. Since the Burr distribution shares good properties of common distributions on survival analysis, it has more flexibility than other distributions. By applying this model to simulated and real failure time datasets, we show the preference of this model and compare it with Dirichlet process mixture models with different kernels. The Markov chain Monte Carlo (MCMC) simulation methods to calculate the posterior distribution are used.     

Optimal B-robust estimators for the parameters of the Burr XII distribution

The Burr XII distribution offers a flexible alternative to the distributions that play important role for modelling data in reliability, risk and process capability. However, estimating the shape parameters of the Burr XII distribution is a challenging problem. The classical estimation methods such as maximum likelihood and least squares are often used to estimate the parameters of the Burr XII distribution, but these methods are very sensitive to the outliers in the data. Thus, a robust estimation method alternative to the classical methods is needed to find robust estimators that are less sensitive to the outliers in the data. The purpose of this paper is to use the optimal B-robust estimation method [Hampel FR, Ronchetti EM, Rousseeuw PJ, Stahel WA. Robust statistics: the approach based on influence functions. New York: Wiley; 1986] to obtain robust estimators for the shape parameters of the Burr XII distribution. The simulation results show that the optimal B-robust estimators generally outperform the classical estimators in terms of the bias and root mean square errors when there are outliers in data.     

The four-parameter Burr XII distribution: Properties,regression model,and applications

This paper introduces a new four-parameter lifetime model called the Weibull Burr XII distribution. The new model has the advantage of being capable of modeling various shapes of aging and failure criteria. We derive some of its structural properties including ordinary and incomplete moments, quantile and generating functions, probability weighted moments, and order statistics. The new density function can be expressed as a linear mixture of Burr XII densities. We propose a log-linear regression model using a new distribution so-called the log-Weibull Burr XII distribution. The maximum likelihood method is used to estimate the model parameters. Simulation results to assess the performance of the maximum likelihood estimation are discussed. We prove empirically the importance and flexibility of the new model in modeling various types of data.     

中国上市公司企业规模分布规律研究——基于1997—2008年全部上市公司数据的研究

针对1997-2008年全部上市公司企业规模进行研究,选取企业资产总值作为变量,数据来源于Wind数据库。分别通过对Burr分布、广义极值分布的研究,发现中国企业规模服从Burr分布。在各显著性水平下,均通过K-S检验,验证了结果的有效性。     

Recurrence relations for single and product moments of k-th record values from pareto,generalized pareto and burr distributions

In this note we give recurrence relations satisfied by single and product momenrs of k-th upper-record values from the Pareto, generalized Pareto and Burr distributions. From these relations one can obtain all the single and product moments of all k-th record values and at the same time all record values ( k=1). Moreover, we see that the single and product moment of all k-th record values from these distributions can be exprrssed in terms of the moments of the minimal statistic of a k-sample from the exponential distribution may be deduced by letting the shape parameter deptend to 0. At the end we give characterizations of the three distributions considered. These results generalize, among other things, those given by Balakrishnan and Abuamllah (1994).     

A new lifetime model with regression models,characterizations and applications

In this article, we introduce a new extension of Burr XII distribution called Topp Leone Generated Burr XII distribution. We derive some of its properties. Useful characterizations are presented. Simulation study is performed to assess the performance of the maximum likelihood estimators. Censored maximum likelihood estimation is presented in the general case of multi-censored data. The new location-scale regression model based on the proposed distribution is introduced. The usefulness of the proposed models is illustrated empirically by means of three real datasets.     

Some properties of a scaled Burr type X distribution

Properties of a scaled Burr type X distribution are given. Closed-form expressions for the moments only exist for certain special cases, so upper and lower bounds for the first moment are given, as well as an approximation based on these bounds. Maximum likelihood estimation is considered, and the asymptotic properties of these estimators are discussed for i.i.d. samples, as well as for Types I and II censoring. Finally, an extension to a multivariate Burr type X distribution is introduced.     

Moments of order statistics from doubly truncated continuous distributions and characterizations

In this paper, recurrence relations from a general class of doubly truncated continuous distributions which are satisfied by single as well as product moments of order statistics are obtained. Recurrence relations from doubly truncated generalized Weibull, exponential, Raleigh and logistic distributions have been derived as special cases of our result, Some previous results for doubly truncated Weibull, standard exponential, power function and Burr type XII distributions are obtained as special cases. The general recurrence relation of single moments has been used in the case of the left and right truncation to characterize the Weibull, Burr type XII and Pareto distributions.     

An extension of Banerjee and Rahim model in economic and economic statistical designs for multivariate quality characteristics under Burr XII distribution

The design parameters of the economic and economic statistical designs of control charts depend on the distribution of process failure mechanism or shock model. So far, only a small number of failure distributions, such as exponential, gamma, and Weibull with fixed or increasing hazard rates, have been used as a shock model in the economic and economic statistical designs of the Hotelling T² control charts. Due to both theoretical and practical aspects, the lifetime of the process under study may not follow a distribution with fixed or increasing hazard rate. A proper alternative for this situation may be the Burr distribution, in which the hazard rate can be fixed, increasing, decreasing, single mode, or even U-shaped. In this research article, economic and economic statistical designs of the Hotelling T² control charts under the Burr XII shock models under two uniform and non uniform sampling schemes were proposed, constructed, and compared. The obtained design models were implemented by a numerical example, and a sensitivity analysis was conducted to evaluate the effect of changing parameters of shock model distribution on the optimum values of the proposed design models. The results showed that first the proposed designs under non uniform sampling scheme perform better and second the optimum values of the designs are not significantly sensitive to changing of the Burr XII distribution parameters. We showed that the obtained design models are also true for the beta Burr XII shock model.     

Odd-Burr generalized family of distributions with some applications

We study a new family of continuous distributions with two extra shape parameters called the Burr generalized family of distributions. We investigate the shapes of the density and hazard rate function. We derive explicit expressions for some of its mathematical quantities. The estimation of the model parameters is performed by maximum likelihood. We prove the flexibility of the new family by means of applications to two real data sets. Furthermore, we propose a new extended regression model based on the logarithm of the Burr generalized distribution. This model can be very useful to the analysis of real data and provide more realistic fits than other special regression models.