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Ratio-Cum-Product Estimator Using Multiple Auxiliary Attributes in Two-Phase Sampling

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Open Journal of Statistics 2014年第4期4卷 246-257页

作者： John Kung’u leo odongo Department of Mathematics Kenyatta University Nairobi Kenya

In this paper, we have proposed three classes of ratio-cum-product estimators for estimating population mean of study variable for two-phase sampling using multi-auxiliary attributes for full information, partial information and no information cases. The expressions for mean square errors are derived. An empirical study is given to compare the performance of the estimator with the existing estimator that utilizes auxiliary attribute or multiple auxiliary attributes. The ratio-cum-product estimator in two-phase sampling for full information case has been found to be more efficient than existing estimators and also ratio-cum-product estimator in two-phase sampling for both partial and no information case. Finally, ratio-cum-product estimator in two-phase sampling for partial information case has been found to be more efficient than ratio-cum-product estimator in two-phase sampling for no information case.

关键词： Ratio-Cum-Product Estimator Multiple Auxiliary Attributes Two-Phase Sampling and Bi-Serial Correlation Coefficient

Maximum Likelihood Estimation of the Parameters of Exponentiated Generalized Weibull Based on Progressive Type II Censored Data

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Open Journal of Statistics 2017年第6期7卷 956-963页

作者： Ibrahim Sawadogo leo odongo Ibrahim Ly Pan African University Institute of Science Technology and Innovation Nairobi Kenya Department of Statistics and Actuarial Science Kenyatta University (KU) Nairobi Kenya Department of Mathematics University of Ouagadougou Ouagadougou Burkina Faso Department of Mathematics University of Potsdam Potsdam Germany

Exponentiated Generalized Weibull distribution is a probability distribution which generalizes the Weibull distribution introducing two more shapes parameters to best adjust the non-monotonic shape. The parameters of the new probability distribution function are estimated by the maximum likelihood method under progressive type II censored data via expectation maximization algorithm.

关键词： Maximum Likelihood Type II Censored Data Exponentiated Generalized Weibull EM-Algorithm

A New Regression Type Estimator with Two Auxiliary Variables for Single-Phase Sampling

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Open Journal of Statistics 2014年第9期4卷 789-796页

作者： Everline Chemutai Tum John Kung’u leo odongo Department of Statistics and Actuarial Science Kenyatta University Nairobi Kenya

In this paper, we have proposed an estimator of finite population mean using a new regression type estimator with two auxiliary variables for single-phase sampling and investigated its finite sample properties. An empirical study has been carried out to compare the performance of the proposed estimator with the existing estimators that utilize auxiliary variables for finite population mean. It has been found that the new regression type estimator with two auxiliary variables for to be more efficient than mean per unit, ratio and product estimator and exponential ratio and exponential product estimators and exponential ratio-product estimator.

关键词： Regression Estimator Exponential Ratio-Product Estimator Auxiliary Variables Mean Squared Error

The Modi Exponentiated Exponential Distribution

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Journal of Data Analysis and Information Processing 2023年第4期11卷 341-359页

作者： Antoine Dieudonné Ndayisaba leo Odiwuor odongo Anthony Ngunyi Department of Mathematics Pan African University Institute for Basic Sciences Technology and Innovation (PAUSTI) Nairobi Kenya Department of Mathematics and Actuarial Science Kenyatta University (KU) Nairobi Kenya Department of Mathematics Statistics and Actuarial Sciences Dedan Kimathi University of Technology (De KUT) Nairobi Kenya

In this study, a new four-parameter distribution called the Modi Exponentiated Exponential distribution was proposed and studied. The new distribution has three shape and one scale parameters. Its mathematical and statistical properties were investigated. The parameters of the new model were estimated using the method of Maximum Likelihood Estimation. Monte Carlo simulation was used to evaluate the performance of the MLEs through average bias and RMSE. The flexibility and goodness-of-fit of the proposed distribution were demonstrated by applying it to two real data sets and comparing it with some existing distributions.

关键词： Modi Family Exponentiated Exponential Distribution Maximum Likelihood Estimation Order Statistics Moments Quantile Function

A Bayesian Approach for Penalized Splines with Hierarchical Penalty

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Open Journal of Statistics 2022年第5期12卷 623-633页

作者： Anne Wanjira Ndung’u Samuel Musili Mwalili leo odongo Pan African University Nairobi Kenya Department of Mathematics Statistics and Actuarial Sciences JKUAT University Nairobi Kenya Department of Mathematics and Actuarial Sciences Kenyatta University Nairobi Kenya

Penalized spline has largely been applied in many research studies not limited to disease modeling and epidemiology. However, due to spatial heterogeneity of the data because different smoothing parameter leads to different amount of smoothing in different regions the penalized spline has not been exclusively appropriate to fit the data. The study assessed the properties of penalized spline hierarchical model;the hierarchy penalty improves the fit as well as the accuracy of inference. The simulation demonstrates the potential benefits of using the hierarchical penalty, which is obtained by modelling the global smoothing parameter as another spline. The results showed that mixed model with penalized hierarchical penalty had a better fit than the mixed model without hierarchy this was demonstrated by the rapid convergence of the model posterior parameters and the smallest DIC value of the model. Therefore hierarchical model with fifteen sub-knots provides a better fit of the data.

关键词： Penalized Splines Mixed Model Hierarchical Penalty

Mixture Regression Estimators Using Multi-Auxiliary Variables and Attributes in Two-Phase Sampling

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Open Journal of Statistics 2014年第5期4卷 355-366页

作者： John John Kung’u Grace Chumba leo odongo Department of Mathematics Kenyatta University Nairobi Kenya

In this paper, we have developed estimators of finite population mean using Mixture Regression estimators using multi-auxiliary variables and attributes in two-phase sampling and investigated its finite sample properties in full, partial and no information cases. An empirical study using natural data is given to compare the performance of the proposed estimators with the existing estimators that utilizes either auxiliary variables or attributes or both for finite population mean. The Mixture Regression estimators in full information case using multiple auxiliary variables and attributes are more efficient than mean per unit, Regression estimator using one auxiliary variable or attribute, Regression estimator using multiple auxiliary variable or attributes and Mixture Regression estimators in both partial and no information case in two-phase sampling. A Mixture Regression estimator in partial information case is more efficient than Mixture Regression estimators in no information case.

关键词： Regression Estimator Multiple Auxiliary Variables Multiple Auxiliary Attributes Two-Phase Sampling Bi-Serial Correlation Coefficient

Marshall-Olkin Exponentiated Fréchet Distribution

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Journal of Data Analysis and Information Processing 2023年第3期11卷 262-292页

作者： Aurise Niyoyunguruza leo Odiwuor odongo Euna Nyarige Alexis Habineza Abdisalam Hassan Muse Department of Mathematics Pan African University Institute for Basic Sciences Technology and Innovation (PAUSTI) Nairobi Kenya Department of Mathematics and Actuarial Science Kenyatta University (KU) Nairobi Kenya Department of Mathematics and Statistics Machakos University Machakos Kenya

In this paper, a new distribution called Marshall-Olkin Exponentiated Fréchet distribution (MOEFr) is proposed. The goal is to increase the flexibility of the existing Exponentiated Fréchet distribution by including an extra shape parameter, resulting into a more flexible distribution that can provide a better fit to various data sets than the baseline distribution. A generator method introduced by Marshall and Olkin is used to develop the new distribution. Some properties of the new distribution such as hazard rate function, survival function, reversed hazard rate function, cumulative hazard function, odds function, quantile function, moments and order statistics are derived. The maximum likelihood estimation is used to estimate the model parameters. Monte Carlo simulation is used to evaluate the behavior of the estimators through the average bias and root mean squared error. The new distribution is fitted and compared with some existing distributions such as the Exponentiated Fréchet (EFr), Marshall-Olkin Fréchet (MOFr), Beta Exponential Fréchet (BEFr), Beta Fréchet (BFr) and Fréchet (Fr) distributions, on three data sets, namely Bladder cancer, Carbone and Wheaton River data sets. Based on the goodness-of-fit statistics and information criteria values, it is demonstrated that the new distribution provides a better fit for the three data sets than the other distributions considered in the study.

关键词： Exponentiated Fréchet Distribution Maximum Likelihood Estimation Marshall-Olkin Family

Longitudinal Survey, Nonmonotone, Nonresponse, Imputation, Nonparametric Regression

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Open Journal of Statistics 2016年第6期6卷 1138-1154页

作者： Sarah Pyeye Charles K. Syengo leo odongo George O. Orwa Romanus O. Odhiambo Pan African University Institute for Basic Sciences Technology and Innovation Nairobi Kenya Department of Statistics and Actuarial Science Kenyatta University Nairobi Kenya Department of Statistics and Actuarial Science Jomo Kenyatta University of Agriculture and Technology Nairobi Kenya

The study focuses on the imputation for the longitudinal survey data which often has nonignorable nonrespondents. Local linear regression is used to impute the missing values and then the estimation of the time-dependent finite populations means. The asymptotic properties (unbiasedness and consistency) of the proposed estimator are investigated. Comparisons between different parametric and nonparametric estimators are performed based on the bootstrap standard deviation, mean square error and percentage relative bias. A simulation study is carried out to determine the best performing estimator of the time-dependent finite population means. The simulation results show that local linear regression estimator yields good properties.

关键词： Longitudinal Survey Nonmonotone Nonresponse Imputation Nonparametric Regression

Extended Lorenz majorization and frequencies of distances in an undirected network

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Journal of Data and Information Science 2024年第1期9卷 1-10页

作者： leo Egghe Hasselt University Diepenbeek 3590Belgium

Purpose:To contribute to the study of networks and ***/methodology/approach:We apply standard mathematical ***:We show that the distance distribution in an undirected network Lorenz majorizes the one of a *** a consequence,the average and median distances in any such network are smaller than or equal to those of a *** limitations:We restricted our investigations to undirected,unweighted *** implications:We are convinced that these results are useful in the study of small worlds and the so-called six degrees of separation ***/value:To the best of our knowledge our research contains new network results,especially those related to frequencies of distances.

关键词： majorization Lorenz curves networks shortest path distance graphs