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Applied Mathematics 2015年第11期6卷 1902-1912页

作者： O. O. Alabi B. A. Oyejola Department of Statistics Federal University of Technology Akure Nigeria Department of Statistics University of Ilorin Ilorin Nigeria

In each equation of simultaneous Equation model, the exogenous variables need to satisfy all the basic assumptions of linear regression model and be non-negative especially in econometric studies. This study examines the performances of the Ordinary Least Square (OLS), Two Stage Least Square (2SLS), Three Stage Least Square (3SLS) and Full Information Maximum Likelihood (FIML) estimators of simultaneous equation model with both normally and uniformly distributed exogenous variables under different identification status of simultaneous equation model when there is no correlation of any form in the model. Four structural equation models were formed such that the first and third are exact identified while the second and fourth are over identified equations. Monte Carlo experiments conducted 5000 times at different levels of sample size (n = 10, 20, 30, 50, 100, 250 and 500) were used as criteria to compare the estimators. Result shows that OLS estimator is best in the exact identified equation except with normally distributed exogenous variables when . At these instances, 2SLS estimator is best. In over identified equations, the 2SLS estimator is best except with normally distributed exogenous variables when the sample size is small and large, and;and with uniformly distributed exogenous variables when n is very large, , the best estimator is either OLS or FIML or 3SLS.

关键词： Normally Distributed Exogenous Variables Uniformly Distributed Exogenous Variables Identification Status estimators Exact Identified Equation Over Identified Equation

Estimation of Population Ratio in Post-Stratified Sampling Using Variable Transformation

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Open Journal of Statistics 2015年第1期5卷 1-9页

作者： Aloy Chijioke Onyeka Chinyeaka Hostensia Izunobi Iheanyi Sylvester Iwueze Department of Statistics Federal University of Technology Owerri Nigeria

Extending the work carried out by [1], this paper proposes six combined-type estimators of population ratio of two variables in post-stratified sampling scheme, using variable transformation. Properties of the proposed estimators were obtained up to first order approximations,(on–1), both for achieved sample configurations (conditional argument) and over repeated samples of fixed size n (unconditional argument). Efficiency conditions were obtained. Under these conditions the proposed combined-type estimators would perform better than the associated customary combined-type estimator. Furthermore, optimum estimators among the proposed combined-type estimators were obtained both under the conditional and unconditional arguments. An empirical work confirmed the theoretical results.

关键词： Variable Transformation Combined-Type Estimator Ratio Product and Regression-Type estimators Mean Squared Error

Pseudodistance Methods Using Simultaneously Sample Observations and Nearest Neighbour Distance Observations for Continuous Multivariate Models

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Open Journal of Statistics 2019年第4期9卷 445-457页

作者： Andrew Luong école d’actuariat Université Laval Ste Foy Québec Canada

Using the fact that a multivariate random sample of n observations also generates n nearest neighbour distance (NND) univariate observations and from these NND observations, a set of n auxiliary observations can be obtained and with these auxiliary observations when combined with the original multivariate observations of the random sample, a class of pseudodistance?Dh?is allowed to be used and inference methods can be developed using this class of pseudodistances. The Dh?estimators obtained from this class can achieve high efficiencies and have robustness properties. Model testing also can be handled in a unified way by means of goodness-of-fit tests statistics derived from this class which have an asymptotic normal distribution. These properties make the developed inference methods relatively simple to implement and appear to be suitable for analyzing multivariate data which are often encountered in applications.

关键词： Goodness-of-Fit Statistics Robust estimators Multivariate Density Estimate Information Matrix Model Testing

Algorithms of Confidence Intervals of WG Distribution Based on Progressive Type-II Censoring Samples

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Journal of Computer and Communications 2017年第7期5卷 101-116页

作者： Mohamed A. El-Sayed Fathy H. Riad M. A. Elsafty Yarub A. Estaitia Department of Mathematics Faculty of Science Fayoum University Fayoum Egypt Department of Computer Science College of Computers and IT Taif University Taif KSA Department of Mathematics Faculty of Science Minia University Minia Egypt Department of Mathematics Faculty of Science Aljouf University Aljouf KSA Department of Mathematics and Statistics Faculty of Science Taif University Taif KSA

The purpose of this article offers different algorithms of Weibull Geometric (WG) distribution estimation depending on the progressive Type II censoring samples plan, spatially the joint confidence intervals for the parameters. The approximate joint confidence intervals for the parameters, the approximate confidence regions and percentile bootstrap intervals of confidence are discussed, and several Markov chain Monte Carlo (MCMC) techniques are also presented. The parts of mean square error (MSEs) and credible intervals lengths, the estimators of Bayes depend on non-informative implement more effective than the maximum likelihood estimates (MLEs) and bootstrap. Comparing the models, the MSEs, average confidence interval lengths of the MLEs, and Bayes estimators for parameters are less significant for censored models.

关键词： Algorithms Simulations Point Estimation Confidence Intervals Bootstrap Approximate Bayes estimators MCMC MLEs

Generalized Weighted Exponential-Gompertez Distribution

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Applied Mathematics 2020年第2期11卷 97-118页

作者： Abd El-Moneim A. M. Teamah Hanan H. El-Damrawy Shaimaa M. T. Swan Mathematics Department Faculty of Science Tanta University Tanta Egypt

Statistical analysis of lifetime data is a significant topic in social sciences, engineering, reliability, biomedical and others. We use the generalized weighted exponential distribution, as a generator to introduce a new family called generalized weighted exponential-G family, and apply this new generator to provide a new distribution called generalized weighted exponential gombertez distribution. We investigate some of its properties, moment generating function, moments, conditional moments, mean residual lifetime, mean inactivity time, strong mean inactivity time, Rényi entropy, Lorenz curves and Bonferroni. Furthermore, in this model, we estimate the parameters by using maximum likelihood method. We apply this model to a real data-set to show that the new generated distribution can produce a better fit than other classical lifetime models.

关键词： Generalized Weighted Exponential-G Family Gombertez Distribution Bonferroni and Lorenz Curves Conditional Moments Mean Inactivity Time Mean Residual Lifetime Maximum Likelihood estimators

Estimation of Parameter in a New Truncated Distribution

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Open Journal of Statistics 2013年第4期3卷 221-224页

作者： G. Nanjundan Department of Statistics Bangalore University Bangalore India

This paper discusses the estimation of the parameter in a truncated form of a discrete distribution which is analogous to Burr distribution. The maximum likelihood and the moment estimators of the parameter are obtain... 详细信息

关键词： Maximum Likelihood and Moment estimators Fisher Information Asymptotic Relative Efficiency