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1.
The Fisher information matrix for a mixture of two Laplace distributions is derived. Numerical tabulations of the matrix and
a computer program are provided for practical purposes. The work is motivated by two real–life examples discussed in Hsu (Appl
Stat 28:62–72, 1979) and Bhowmick et al. (Biostatistics 7:630–641, 2006).
相似文献
2.
Steven G. From 《统计学通讯:理论与方法》2013,42(6):2201-2223
Methods for estimating the mixing parameters in a mixture of two exponential distributions are proposed. The estimators proposed are consistent and BAN(best asymptotically normal). The optimal spacings for estimating these mixture parameters are calculated. 相似文献
3.
Deepak Singh 《统计学通讯:理论与方法》2020,49(17):4162-4177
AbstractWe construct a new bivariate mixture of negative binomial distributions which represents over-dispersed data more efficiently. This is an extension of a univariate mixture of beta and negative binomial distributions. Characteristics of this joint distribution are studied including conditional distributions. Some properties of the correlation coefficient are explored. We demonstrate the applicability of our proposed model by fitting to three real data sets with correlated count data. A comparison is made with some previously used models to show the effectiveness of the new model. 相似文献
4.
A partially adaptive estimator for the censored regression model based on a mixture of normal distributions 总被引:1,自引:0,他引:1
Steven B. Caudill 《Statistical Methods and Applications》2012,21(2):121-137
The goal of this paper is to introduce a partially adaptive estimator for the censored regression model based on an error
structure described by a mixture of two normal distributions. The model we introduce is easily estimated by maximum likelihood
using an EM algorithm adapted from the work of Bartolucci and Scaccia (Comput Stat Data Anal 48:821–834, 2005). A Monte Carlo study is conducted to compare the small sample properties of this estimator to the performance of some common
alternative estimators of censored regression models including the usual tobit model, the CLAD estimator of Powell (J Econom
25:303–325, 1984), and the STLS estimator of Powell (Econometrica 54:1435–1460, 1986). In terms of RMSE, our partially adaptive estimator performed well. The partially adaptive estimator is applied to data
on wife’s hours worked from Mroz (1987). In this application we find support for the partially adaptive estimator over the usual tobit model. 相似文献
5.
In this paper, Fisher information matrix about the five parameters ρ, μ:1, μ2, λ1and λ2of a mixture of two Inverse Gaussian density functions is obtained. The Leguerre-Gauss quadrature formula is used to evaluate the essential integral on which the twenty five elements of the information matrix are based. Results involving the computation of the information about p are compared with those involving both the power series expansion and Simpson's method of integration. Laguerre-Gauss quadra-ture was found to lead to good approximations as compared with other methods. It was therefore chosen for the computations of the elements of the information matrix. 相似文献
6.
In the present article we suggest two new methods for calculating approximate confidence limits for the differences of the two binomial parameters. Different methods for determining the confidence interval are compared. 相似文献
7.
P. Elliott 《Journal of applied statistics》2015,42(1):27-36
The negative binomial distribution offers an alternative view to the binomial distribution for modeling count data. This alternative view is particularly useful when the probability of success is very small, because, unlike the fixed sampling scheme of the binomial distribution, the inverse sampling approach allows one to collect enough data in order to adequately estimate the proportion of success. However, despite work that has been done on the joint estimation of two binomial proportions from independent samples, there is little, if any, similar work for negative binomial proportions. In this paper, we construct and investigate three confidence regions for two negative binomial proportions based on three statistics: the Wald (W), score (S) and likelihood ratio (LR) statistics. For large-to-moderate sample sizes, this paper finds that all three regions have good coverage properties, with comparable average areas for large sample sizes but with the S method producing the smaller regions for moderate sample sizes. In the small sample case, the LR method has good coverage properties, but often at the expense of comparatively larger areas. Finally, we apply these three regions to some real data for the joint estimation of liver damage rates in patients taking one of two drugs. 相似文献
8.
Dipak K. Dey 《Revue canadienne de statistique》1990,18(2):171-178
Simultaneous estimation of scale parameters is considered in mixture distributions under squared-error loss. A general class of estimators is obtained which dominates the componentwise best multiple estimators and the moment estimators. As special cases, improved estimators are obtained for the multivariate t-distribution and the p-variate Lomax distribution. 相似文献
9.
R.M. Korwar 《统计学通讯:理论与方法》2013,42(2):355-361
In this note we derive sharp lower and upper bounds for the variance of the Graybill-Deal estimator of the common mean of two normal distributions with unknown variances when the sample sizes are not necessarily equal. We also derive similar bounds for the variance of the Brown-Cohen (1974) T a(1) class of unbiased es-timators to which the Graybill-Deal estimator belongs. Further, we illustrate the sharpness of the bounds by numerical computations in the case of the Graybill-Deal estimator. 相似文献
10.
Khalaf S. Sultan A. S. Al-Moisheer 《Journal of Statistical Computation and Simulation》2013,83(10):1900-1914
The main goal of this paper is to develop the approximate Bayes estimation of the five-dimensional vector of the parameters and reliability function of a mixture of two inverse Weibull distributions (MTIWD) under Type-2 censoring. Usually, the posterior distribution is complicated under the scheme of Type-2 censoring and the integrals that are involved cannot be obtained in a simple explicit form. In this study, we use Lindley's [Approximate Bayesian method, Trabajos Estadist. 31 (1980), pp. 223–237] approximate form of Bayes estimation in the case of an MTIWD under Type-2 censoring. Later, we calculate the estimated risks (ERs) of the Bayes estimates and compare them with the corresponding ERs of the maximum-likelihood estimates through Monte Carlo simulation. Finally, we analyse a real data set using the findings. 相似文献
11.
Kristofer Månsson 《Journal of Statistical Computation and Simulation》2013,83(9):1773-1780
This paper introduces a new shrinkage estimator for the negative binomial regression model that is a generalization of the estimator proposed for the linear regression model by Liu [A new class of biased estimate in linear regression, Comm. Stat. Theor. Meth. 22 (1993), pp. 393–402]. This shrinkage estimator is proposed in order to solve the problem of an inflated mean squared error of the classical maximum likelihood (ML) method in the presence of multicollinearity. Furthermore, the paper presents some methods of estimating the shrinkage parameter. By means of Monte Carlo simulations, it is shown that if the Liu estimator is applied with these shrinkage parameters, it always outperforms ML. The benefit of the new estimation method is also illustrated in an empirical application. Finally, based on the results from the simulation study and the empirical application, a recommendation regarding which estimator of the shrinkage parameter that should be used is given. 相似文献
12.
K. S. Sultan A. S. Al-Moisheer 《Journal of Statistical Computation and Simulation》2013,83(3):405-416
The classification of a random variable based on a mixture can be meaningfully discussed only if the class of all finite mixtures is identifiable. In this paper, we find the maximum-likelihood estimates of the parameters of the mixture of two inverse Weibull distributions by using classified and unclassified observations. Next, we estimate the nonlinear discriminant function of the underlying model. Also, we calculate the total probabilities of misclassification as well as the percentage bias. In addition, we investigate the performance of all results through a series of simulation experiments by means of relative efficiencies. Finally, we analyse some simulated and real data sets through the findings of the paper. 相似文献
13.
Cátia R. Gonçalves Cira E. G. Otiniano Evelyn C. Cruvinel 《Journal of Statistical Computation and Simulation》2018,88(6):1147-1171
In this paper, the identifiability of finite mixture of generalized extreme value (GEV) distributions is proved. Next, a procedure for finding maximum likelihood estimates (MLEs) of the parameters of a finite mixture of two generalized extreme value (MGEV) distributions is presented by using classified and unclassified observations. Then, a nonlinear discriminant function for a mixture of two GEV distributions is derived and the performance of the corresponding estimated discriminant function is investigated through a series of simulation experiments. Finally, the methodology is applied to real data. 相似文献
14.
《Journal of Statistical Computation and Simulation》2012,82(1):124-134
In this article, a two-parameter estimator is proposed to combat multicollinearity in the negative binomial regression model. The proposed two-parameter estimator is a general estimator which includes the maximum likelihood (ML) estimator, the ridge estimator (RE) and the Liu estimator as special cases. Some properties on the asymptotic mean-squared error (MSE) are derived and necessary and sufficient conditions for the superiority of the two-parameter estimator over the ML estimator and sufficient conditions for the superiority of the two-parameter estimator over the RE and the Liu estimator in the asymptotic mean-squared error (MSE) matrix sense are obtained. Furthermore, several methods and three rules for choosing appropriate shrinkage parameters are proposed. Finally, a Monte Carlo simulation study is given to illustrate some of the theoretical results. 相似文献
15.
Kai F. Yu 《统计学通讯:理论与方法》2013,42(2):595-609
Various classical methods of estimation are compared with those proposed by From (1989) for the estimation of the mixing parameter in a mixture of two distributions. Emphasis is put on the actual implementation of the estimation methods. 相似文献
16.
This paper addresses the admissibility of the maximum-likelihood estimator (MLE) of the variance of a binomial distribution with parameters n and p under squared-error loss. We show that the MLE is admissible for n ≤ 5 and inadmissible for n≥ 6. 相似文献
17.
The zero-inflated binomial (ZIB) regression model was proposed to account for excess zeros in binomial regression. Since then, the model has been applied in various fields, such as ecology and epidemiology. In these applications, maximum-likelihood estimation (MLE) is used to derive parameter estimates. However, theoretical properties of the MLE in ZIB regression have not yet been rigorously established. The current paper fills this gap and thus provides a rigorous basis for applying the model. Consistency and asymptotic normality of the MLE in ZIB regression are proved. A consistent estimator of the asymptotic variance–covariance matrix of the MLE is also provided. Finite-sample behavior of the estimator is assessed via simulations. Finally, an analysis of a data set in the field of health economics illustrates the paper. 相似文献
18.
Using the likelihood equations, a method based on the generalized inverse of matrices is proposed to derive closed-form estimates for the mixing proportions in a finite mixture, when the component distributions are known. 相似文献
19.
In this paper, we investigate the problem of updating a discriminant function on the basis of data of unknown origin. We consider the updating procedure for the nonlinear discriminant function on the basis of two inverse Weibull distributions in situations when the additional observations are mixed or classified. Then, we introduce the nonlinear discriminant function of the underlying model. Also, we calculate the total probabilities of misclassification. In addition, we investigate the performance of the updating procedures through series of simulation experiments by means of the relative efficiencies. Finally, we analyze a simulated data set by using the findings of the paper. 相似文献
20.
The estimation δ = μ1 ? μ2 and of the common μ when ?=0 is exhibited separately for ρ = σ2/σ1 specified, and unspecified, for two Type II censored samples from exponential distributions (μ i , σ i ). The problem is treated as a special case of the general location-scale family. As such, it presents a useful parallel to the well known results for the normal distribution. 相似文献