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981.
Ying-zi Fu 《统计学通讯:理论与方法》2013,42(20):5918-5932
ABSTRACTIn this article, a finite mixture model of hurdle Poisson distribution with missing outcomes is proposed, and a stochastic EM algorithm is developed for obtaining the maximum likelihood estimates of model parameters and mixing proportions. Specifically, missing data is assumed to be missing not at random (MNAR)/non ignorable missing (NINR) and the corresponding missingness mechanism is modeled through probit regression. To improve the algorithm efficiency, a stochastic step is incorporated into the E-step based on data augmentation, whereas the M-step is solved by the method of conditional maximization. A variation on Bayesian information criterion (BIC) is also proposed to compare models with different number of components with missing values. The considered model is a general model framework and it captures the important characteristics of count data analysis such as zero inflation/deflation, heterogeneity as well as missingness, providing us with more insight into the data feature and allowing for dispersion to be investigated more fully and correctly. Since the stochastic step only involves simulating samples from some standard distributions, the computational burden is alleviated. Once missing responses and latent variables are imputed to replace the conditional expectation, our approach works as part of a multiple imputation procedure. A simulation study and a real example illustrate the usefulness and effectiveness of our methodology. 相似文献
982.
AbstractA Marshall–Olkin variant of the Provost type gamma–Weibull probability distribution is being introduced in this paper. Some of its statistical functions and numerical characteristics among others characteristics function, moment generalizing function, central moments of real order are derived in the computational series expansion form and various illustrative special cases are discussed. This density function is utilized to model two real data sets. The new distribution provides a better fit than related distributions as measured by the Anderson–Darling and Cramér–von Mises statistics. The proposed distribution could find applications for instance in the physical and biological sciences, hydrology, medicine, meteorology, engineering, etc. 相似文献
983.
Katarzyna Budny 《统计学通讯:理论与方法》2013,42(17):5220-5223
ABSTRACTWe extend Chebyshev's inequality to a random vector with a singular covariance matrix. Then we consider the case of a multivariate normal distribution for this generalization. 相似文献
984.
Inferential analysis for the reliability parameter based on the three-parameter Lindley distribution
ABSTRACTIn this article, we consider the estimation of R = P(Y < X), when Y and X are two independent three-parameter Lindley (LI) random variables. On the basis of two independent samples, the modified maximum likelihood estimator along its asymptotic behavior and conditional likelihood-based estimator are used to estimate R. We also propose sample-based estimate of R and the associated credible interval based on importance sampling procedure. A real life data set involving the times to breakdown of an insulating fluid is presented and analyzed for illustrative purposes. 相似文献
985.
ABSTRACTThis paper studies a cold standby repairable system with two identical components and one repairman having multiple vacations applying matrix-analytic methods. The lifetime of the component follows a phase-type distribution. The repair times and the vacation times of the repairman are governed by different phase-type distributions, respectively. For this system, the Markov process governing the system is constructed. The system is studied in a transient and stationary regime, the availability, the reliability, the rates of occurrence of the different types of failures, and the working probability of the repairman are calculated, respectively. A numerical application is performed to illustrate the calculations. 相似文献
986.
AbstractIn this article, we proposed a new three parameter lifetime distribution motivated mainly by lifetime issues, which generalizes the Exponential Poisson distribution proposed by Cancho et al. (2011). We derive various standard mathematical properties of the proposed model including a formal proof of its probability density function and hazard rate function. The inference via the maximum likelihood approach is discussed. The performance of the maximum likelihood estimators, the likelihood ratio test and its power are studied by simulation. Finally, the proposed model is fitted to two real data sets and it is compared with several models. 相似文献
987.
AbstractWe propose a unified approach for multilevel sample selection models using a generalized result on skew distributions arising from selection. If the underlying distributional assumption is normal, then the resulting density for the outcome is the continuous component of the sample selection density and has links with the closed skew-normal distribution (CSN). The CSN distribution provides a framework which simplifies the derivation of the conditional expectation of the observed data. This generalizes the Heckman’s two-step method to a multilevel sample selection model. Finite-sample performance of the maximum likelihood estimator of this model is studied through a Monte Carlo simulation. 相似文献
988.
AbstractWe introduce here the truncated version of the unified skew-normal (SUN) distributions. By considering a special truncations for both univariate and multivariate cases, we derive the joint distribution of consecutive order statistics X(r, ..., r + k) = (X(r), ..., X(r + K))T from an exchangeable n-dimensional normal random vector X. Further we show that the conditional distributions of X(r + j, ..., r + k) given X(r, ..., r + j ? 1), X(r, ..., r + k) given (X(r) > t)?and X(r, ..., r + k) given (X(r + k) < t) are special types of singular SUN distributions. We use these results to determine some measures in the reliability theory such as the mean past life (MPL) function and mean residual life (MRL) function. 相似文献
989.
ABSTRACTEarly detection with a low false alarm rate (FAR) is the main aim of outbreak detection as used in public health surveillance or in regard to bioterrorism. Multivariate surveillance is preferable to univariate surveillance since correlation between series (CBS) is recognized and incorporated. Sufficient reduction has proved a promising method for handling CBS, but has not previously been used when correlation within series (CWS) is present. Here we develop sufficient reduction methods for reducing a p-dimensional multivariate series to a univariate series of statistics shown to be sufficient to monitor a sudden, but persistent, shift in the multivariate series mean. Correlation both within and between series is taken into account, as public health data typically exhibit both forms of association. Simultaneous and lagged changes and different shift sizes are investigated. A one-sided exponentially weighted moving average chart is used as a tool for detection of a change. The performance of the proposed method is compared with existing sufficient reduction methods, the parallel univariate method and both VarR and Z charts. A simulation study using bivariate normal autoregressive data shows that the new method gives shorter delays and a lower FAR than other methods, which have high FARs when CWS is clearly present. 相似文献
990.
AbstractThe most commonly studied generalized normal distribution is the well-known skew-normal by Azzalini. In this paper, a new generalized normal distribution is defined and studied. The distribution is unimodal and it can be skewed right or left. The relationships between the parameters and the mean, variance, skewness, and kurtosis are discussed. It is observed that the new distribution has a much wider range of skewness and kurtosis than the skew-normal distribution. The method of maximum likelihood is proposed to estimate the distribution parameters. Two real data sets are applied to illustrate the flexibility of the distribution. 相似文献