Open Access. Powered by Scholars. Published by Universities.®

Statistical Theory Commons

Open Access. Powered by Scholars. Published by Universities.®

1,639 Full-Text Articles 2,109 Authors 1,182,386 Downloads 58 Institutions

All Articles in Statistical Theory

Faceted Search

1,639 full-text articles. Page 1 of 44.

Parametric And Reliability Estimation Of The Kumaraswamy Generalized Distribution Based On Record Values, Mohd. Arshad, Qazi J. Azhad 2022 Indian Institute of Technology Indore, Madhya Pradesh, India

Parametric And Reliability Estimation Of The Kumaraswamy Generalized Distribution Based On Record Values, Mohd. Arshad, Qazi J. Azhad

Journal of Modern Applied Statistical Methods

A general family of distributions, namely Kumaraswamy generalized family of (Kw-G) distribution, is considered for estimation of the unknown parameters and reliability function based on record data from Kw-G distribution. The maximum likelihood estimators (MLEs) are derived for unknown parameters and reliability function, along with its confidence intervals. A Bayesian study is carried out under symmetric and asymmetric loss functions in order to find the Bayes estimators for unknown parameters and reliability function. Future record values are predicted using Bayesian approach and non Bayesian approach, based on numerical examples and a monte carlo simulation.


Does The Type Of Records Affect The Estimates Of The Parameters?, Ayush Tripathi, Umesh Singh, Sanjay Kumar Singh 2022 Banaras Hindu University

Does The Type Of Records Affect The Estimates Of The Parameters?, Ayush Tripathi, Umesh Singh, Sanjay Kumar Singh

Journal of Modern Applied Statistical Methods

The maximum likelihood estimation of the unknown parameters of inverse Rayleigh and exponential distributions are discussed based on lower and upper records. The aim is to study the effect of the type of records on the behavior of the corresponding estimators. Mean squared errors are calculated through simulation to study the behavior of the estimators. The results shall be of interest to those situations where the data can be obtained in the form of either of the two types of records and the experimenter must decide between these two for estimation of the unknown parameters of the distribution.


Design Of Sksp-R Plan For Popular Statistical Distributions, Jaffer Hussain, S. Balamurali, Muhammad Aslam 2022 GC University, Lahore, Pakistan

Design Of Sksp-R Plan For Popular Statistical Distributions, Jaffer Hussain, S. Balamurali, Muhammad Aslam

Journal of Modern Applied Statistical Methods

The design of a Skip-lot sampling plan of type SkSP-R is presented for time truncated life test for the Weibull, Exponentiated Weibull, and Birnbaum-Saunders lifetime distributions. The plan parameters of the SkSP-R plan under these three distributions are determined through a nonlinear optimization problem. Tables are also constructed for each distribution. The advantages of the proposed plan over the existing sampling schemes are discussed. Application of the proposed plan is explained with the help of an example. The Birnbaum-Saunders distribution is economically superior to other two distributions in terms of minimum average sample number.


Parameter Estimation Based On Double Ranked Set Samples With Applications To Weibull Distribution, Mohamed Abd Elhamed Sabry, Hiba Zeyada Muhammed, Mostafa Shaaban, Abd El Hady Nabih 2022 Cairo University, Cairo, Egypt

Parameter Estimation Based On Double Ranked Set Samples With Applications To Weibull Distribution, Mohamed Abd Elhamed Sabry, Hiba Zeyada Muhammed, Mostafa Shaaban, Abd El Hady Nabih

Journal of Modern Applied Statistical Methods

In this paper, the likelihood function for parameter estimation based on double ranked set sampling (DRSS) schemes is introduced. The proposed likelihood function is used for the estimation of the Weibull distribution parameters. The maximum likelihood estimators (MLEs) are investigated and compared to the corresponding ones based on simple random sampling (SRS) and ranked set sampling (RSS) schemes. A Monte Carlo simulation is conducted and the absolute relative biases, mean square errors, and efficiencies are compared for the different schemes. It is found that, the MLEs based on DRSS is more efficient than MLE using SRS and RSS for estimating ...


A New Goodness Of Fit Measure Based On Income Inequality Curves, Shahryar Mirzaei, S. M. A. Jahanshahi 2022 Payam Noor University, Tehran, Iran

A New Goodness Of Fit Measure Based On Income Inequality Curves, Shahryar Mirzaei, S. M. A. Jahanshahi

Journal of Modern Applied Statistical Methods

This paper uses inequality-measurement techniques to assess goodness of fit in income distribution models. It exposes the shortcomings of the use of conventional goodness of fit criteria in face of the big income data and proposes a new set of metrics, based on income inequality curves. In this note, we mentioned that the distance between theoretical and empirical inequality curves can be considered as a goodness of fit criterion. We demonstrate certain advantages of this measure over the other general goodness of fit criteria. Unlike other goodness of fit measures, this criterion is bounded. It is 0 in minimum difference ...


Non-Parametric Tests For Testing Of Scale Parameters, Manish Goyal, Narinder Kumar 2021 Panjab University, Chandigarh

Non-Parametric Tests For Testing Of Scale Parameters, Manish Goyal, Narinder Kumar

Journal of Modern Applied Statistical Methods

One of the fundamental problems in testing of equality of populations is of testing the equality of scale parameters. The subsequent usages for scale are dispersion, spread and variability. In this paper, we proposed non-parametric tests based on U-Statistics for the testing of equality of scale parameters. The null distribution of proposed tests is developed and its Pitman efficiency is worked out to compare proposed tests with respect to some existing tests. Simulation study is carried out to compute the asymptotic power of proposed tests. An illustrative example is also provided.


Confidence Interval For The Mean Of A Beta Distribution, Sean Rangel 2021 Stephen F Austin State University

Confidence Interval For The Mean Of A Beta Distribution, Sean Rangel

Electronic Theses and Dissertations

Statistical inference for the mean of a beta distribution has become increasingly popular in various fields of academic research. In this study, we developed a novel statistical model from likelihood-based techniques to evaluate various confidence interval techniques for the mean of a beta distribution. Simulation studies will be implemented to compare the performance of the confidence intervals. In addition to the development and study involving confidence intervals, we will also apply the confidence intervals to real biological data that was gathered by the Department of Biology at Stephen F. Austin State University and provide recommendations on the best practice.


Comparative Study Of New And Traditional Estimators Of A New Lifetime Model, Sandeep Kumar Maurya, Sanjay Kumar Singh, Umesh Singh 2021 Central University of South Bihar, Bihar, India

Comparative Study Of New And Traditional Estimators Of A New Lifetime Model, Sandeep Kumar Maurya, Sanjay Kumar Singh, Umesh Singh

Journal of Modern Applied Statistical Methods

In this article, we have studied the behavior of estimators of parameter of a new lifetime model, suggested by Maurya et al. (2016), obtained by using methods of moments, maximum likelihood, maximum product spacing, least squares, weighted least squares, percentile, Cramer-von-Mises, Anderson-Darling and Right-tailed Anderson-Darling. Comparison of the estimators has been done on the basis of their mean square errors, biases, absolute and maximum absolute differences between empirical and estimated distribution function and a newly proposed criterion. We have also obtained the asymptomatic confidence interval and associated coverage probability for the parameter.


On The Extension Of Exponentiated Pareto Distribution, Amal S. Hassan, Saeed Elsayed Hemeda, Said G. Nassr 2021 Cairo University, Giza, Egypt

On The Extension Of Exponentiated Pareto Distribution, Amal S. Hassan, Saeed Elsayed Hemeda, Said G. Nassr

Journal of Modern Applied Statistical Methods

In this study, an extended exponentiated Pareto distribution is proposed. Some statistical properties are derived. We consider maximum likelihood, least squares, weighted least squares and Bayesian estimators. A simulation study is implemented for investigating the accuracy of different estimators. An application of the proposed distribution to a real data is presented.


A New Generating Family Of Distributions: Properties And Applications To The Weibull Exponential Model, El-Sayed A. El-Sherpieny, Salwa Assar, Tamer Helal 2021 Cairo University

A New Generating Family Of Distributions: Properties And Applications To The Weibull Exponential Model, El-Sayed A. El-Sherpieny, Salwa Assar, Tamer Helal

Journal of Modern Applied Statistical Methods

A new method for generating family of distributions was proposed. Some fundamental properties of the new proposed family include the quantile, survival function, hazard rate function, reversed hazard and cumulative hazard rate functions are provided. This family contains several new models as sub models, such as the Weibull exponential model which was defined and discussed its properties. The maximum likelihood method of estimation is using to estimate the model parameters of the new proposed family. The flexibility and the importance of the Weibull-exponential model is assessed by applying it to a real data set and comparing it with other known ...


Jmasm 55: Matlab Algorithms And Source Codes Of 'Cbnet' Function For Univariate Time Series Modeling With Neural Networks (Matlab), Cagatay Bal, Serdar Demir 2021 Muğla Sitki Kocman University, Turkey

Jmasm 55: Matlab Algorithms And Source Codes Of 'Cbnet' Function For Univariate Time Series Modeling With Neural Networks (Matlab), Cagatay Bal, Serdar Demir

Journal of Modern Applied Statistical Methods

Artificial Neural Networks (ANN) can be designed as a nonparametric tool for time series modeling. MATLAB serves as a powerful environment for ANN modeling. Although Neural Network Time Series Tool (ntstool) is useful for modeling time series, more detailed functions could be more useful in order to get more detailed and comprehensive analysis results. For these purposes, cbnet function with properties such as input lag generator, step-ahead forecaster, trial-error based network selection strategy, alternative network selection with various performance measure and global repetition feature to obtain more alternative network has been developed, and MATLAB algorithms and source codes has been ...


Bayesian Sensitivity-Specificity And Roc Analysis For Finding Key Drivers, Stan Lipovetsky, Michael W. Conklin 2021 GfK North America

Bayesian Sensitivity-Specificity And Roc Analysis For Finding Key Drivers, Stan Lipovetsky, Michael W. Conklin

Journal of Modern Applied Statistical Methods

Finding key drivers in regression modeling via Bayesian Sensitivity-Specificity and Receiver Operating Characteristic is suggested, and clearly interpretable results are obtained. Numerical comparisons with other techniques show that this methodology can be useful in practical statistical modeling and analysis helping to researchers and managers in making meaningful decisions.


Performance Of The Beta-Binomial Model For Clustered Binary Responses: Comparison With Generalized Estimating Equations, Seongah Im 2021 University of Hawai’i at Mānoa

Performance Of The Beta-Binomial Model For Clustered Binary Responses: Comparison With Generalized Estimating Equations, Seongah Im

Journal of Modern Applied Statistical Methods

This study examined performance of the beta-binomial model in comparison with GEE using clustered binary responses resulting in non-normal outcomes. Monte Carlo simulations were performed under varying intracluster correlations and sample sizes. The results showed that the beta-binomial model performed better for small sample, while GEE performed well under large sample.


Model-Free Descriptive Modeling For Multivariate Categorical Data With An Ordinal Dependent Variable, Li Wang 2021 University of Massachusetts Amherst

Model-Free Descriptive Modeling For Multivariate Categorical Data With An Ordinal Dependent Variable, Li Wang

Doctoral Dissertations

In the process of statistical modeling, the descriptive modeling plays an essential role in accelerating the formulation of plausible hypotheses in the subsequent explanatory modeling and facilitating the selection of potential variables in the subsequent predictive modeling. Especially, for multivariate categorical data analysis, it is desirable to use the descriptive modeling methods for uncovering and summarizing the potential association structure among multiple categorical variables in a compact manner. However, many classical methods in this case either rely on strong assumptions for parametric models or become infeasible when the data dimension is higher. To this end, we propose a model-free method ...


Calibration-Based Estimators Using Different Distance Measures Under Two Auxiliary Variables: A Comparative Study, Piyush Kant Rai, Alka Singh, Muhammad Qasim 2021 Banaras Hindu University, Varanasi, India

Calibration-Based Estimators Using Different Distance Measures Under Two Auxiliary Variables: A Comparative Study, Piyush Kant Rai, Alka Singh, Muhammad Qasim

Journal of Modern Applied Statistical Methods

This article introduces calibration estimators under different distance measures based on two auxiliary variables in stratified sampling. The theory of the calibration estimator is presented. The calibrated weights based on different distance functions are also derived. A simulation study has been carried out to judge the performance of the proposed estimators based on the minimum relative root mean squared error criterion. A real-life data set is also used to confirm the supremacy of the proposed method.


Pareto Distribution Under Hybrid Censoring: Some Estimation, Gyan Prakash 2021 Moti Lal Nehru Medical College, Allahabad, India

Pareto Distribution Under Hybrid Censoring: Some Estimation, Gyan Prakash

Journal of Modern Applied Statistical Methods

In the present study, the Pareto model is considered as the model from which observations are to be estimated using a Bayesian approach. Properties of the Bayes estimators for the unknown parameters have studied by using different asymmetric loss functions on hybrid censoring pattern and their risks have compared. The properties of maximum likelihood estimation and approximate confidence length have also been investigated under hybrid censoring. The performances of the procedures are illustrated based on simulated data obtained under the Metropolis-Hastings algorithm and a real data set.


Robust Lag Weighted Lasso For Time Series Model, Tahir R. Dikheel, Alaa Q. Yaseen 2021 University of Al-Qadisiyah, Iraq

Robust Lag Weighted Lasso For Time Series Model, Tahir R. Dikheel, Alaa Q. Yaseen

Journal of Modern Applied Statistical Methods

The lag-weighted lasso was introduced to deal with lag effects when identifying the true model in time series. This method depends on weights to reflect both the coefficient size and the lag effects. However, the lag weighted lasso is not robust. To overcome this problem, we propose robust lag weighted lasso methods. Both the simulation study and the real data example show that the proposed methods outperform the other existing methods.


Generalized Ratio-Cum-Product Estimator For Finite Population Mean Under Two-Phase Sampling Scheme, Gajendra Kumar Vishwakarma, Sayed Mohammed Zeeshan 2021 Indian Institute of Technology (ISM) Dhanbad

Generalized Ratio-Cum-Product Estimator For Finite Population Mean Under Two-Phase Sampling Scheme, Gajendra Kumar Vishwakarma, Sayed Mohammed Zeeshan

Journal of Modern Applied Statistical Methods

A method to lower the MSE of a proposed estimator relative to the MSE of the linear regression estimator under two-phase sampling scheme is developed. Estimators are developed to estimate the mean of the variate under study with the help of auxiliary variate (which are unknown but it can be accessed conveniently and economically). The mean square errors equations are obtained for the proposed estimators. In addition, optimal sample sizes are obtained under the given cost function. The comparison study has been done to set up conditions for which developed estimators are more effective than other estimators with novelty. The ...


A New Generalized Family Of Distributions For Lifetime Data, Maha A. D. Aldahlan, Mohamed G. Khalil, Ahmed Z. Afify 2021 King Abdulaziz University

A New Generalized Family Of Distributions For Lifetime Data, Maha A. D. Aldahlan, Mohamed G. Khalil, Ahmed Z. Afify

Journal of Modern Applied Statistical Methods

A new class of continuous distributions called the generalized Burr X-G family is introduced. Some special models of the new family are provided. Some of its mathematical properties including explicit expressions for the quantile and generating functions, ordinary and incomplete moments, order statistics and Rényi entropy are derived. The maximum likelihood is used for estimating the model parameters. The flexibility of the generated family is illustrated by means of two applications to real data sets.


Extending Singh-Maddala Distribution, Mohamed Ali Ahmed 2021 Al Madina Higher Institute of Management and Technology, Giza, Egypt

Extending Singh-Maddala Distribution, Mohamed Ali Ahmed

Journal of Modern Applied Statistical Methods

A new distribution, the exponentiated transmuted Singh-Maddala distribution (ETSM), is presented, and three important special distributions are illustrated. Some mathematical properties are obtained, and parameters estimation method is applied using maximum likelihood. Illustrations based on random numbers and a real data set are given.


Digital Commons powered by bepress