Physical Sciences and Mathematics Commons^™

The Gelfand Problem For The Infinity Laplacian, Fernando Charro, Byungjae Son, Peiyong Wang

Mathematics Faculty Research Publications

We study the asymptotic behavior as p → ∞ of the Gelfand problem

−Δ_pu = λe^u in Ω ⊂ Rⁿ, u = 0 on ∂Ω.

Under an appropriate rescaling on u and λ, we prove uniform convergence of solutions of the Gelfand problem to solutions of

min{|∇_u|−Λe^u, −Δ_∞u} = 0 in Ω, u = 0 on ∂Ω.

We discuss existence, non-existence, and multiplicity of solutions of the limit problem in terms of Λ.

Asymptotic Mean-Value Formulas For Solutions Of General Second-Order Elliptic Equations, Pablo Blanc, Fernando Charro, Juan J. Manfredi, Julio D. Rossi

Mathematics Faculty Research Publications

We obtain asymptotic mean-value formulas for solutions of second-order elliptic equations. Our approach is very flexible and allows us to consider several families of operators obtained as an infimum, a supremum, or a combination of both infimum and supremum, of linear operators. The families of equations that we consider include well-known operators such as Pucci, Issacs, and k-Hessian operators.

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

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

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

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

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

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.

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

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

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

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

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

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.

From Mathematics To Medicine: A Practical Primer On Topological Data Analysis (Tda) And The Development Of Related Analytic Tools For The Functional Discovery Of Latent Structure In Fmri Data, Andrew Salch, Adam Regalski, Hassan Abdallah, Raviteja Suryadevara, Michael J. Catanzaro, Vaibhav A. Diwadkar

Mathematics Faculty Research Publications

fMRI is the preeminent method for collecting signals from the human brain in vivo, for using these signals in the service of functional discovery, and relating these discoveries to anatomical structure. Numerous computational and mathematical techniques have been deployed to extract information from the fMRI signal. Yet, the application of Topological Data Analyses (TDA) remain limited to certain sub-areas such as connectomics (that is, with summarized versions of fMRI data). While connectomics is a natural and important area of application of TDA, applications of TDA in the service of extracting structure from the (non-summarized) fMRI data itself are heretofore nonexistent ...

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

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

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

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 ...

How To Apply Multiple Imputation In Propensity Score Matching With Partially Observed Confounders: A Simulation Study And Practical Recommendations, Albee Ling, Maria Montez-Rath, Maya Mathur, Kris Kapphahn, Manisha Desai

Journal of Modern Applied Statistical Methods

Propensity score matching (PSM) has been widely used to mitigate confounding in observational studies, although complications arise when the covariates used to estimate the PS are only partially observed. Multiple imputation (MI) is a potential solution for handling missing covariates in the estimation of the PS. However, it is not clear how to best apply MI strategies in the context of PSM. We conducted a simulation study to compare the performances of popular non-MI missing data methods and various MI-based strategies under different missing data mechanisms. We found that commonly applied missing data methods resulted in biased and inefficient estimates ...

Jmasm 57: Bayesian Survival Analysis Of Lomax Family Models With Stan (R), Mohammed H. A. Abujarad, Athar Ali Khan

Journal of Modern Applied Statistical Methods

An attempt is made to fit three distributions, the Lomax, exponential Lomax, and Weibull Lomax to implement Bayesian methods to analyze Myeloma patients using Stan. This model is applied to a real survival censored data so that all the concepts and computations will be around the same data. A code was developed and improved to implement censored mechanism throughout using rstan. Furthermore, parallel simulation tools are also implemented with an extensive use of rstan.

Pairwise Balanced Designs From Cyclic Pbib Designs, D. K. Ghosh, N. R. Desai, Shreya Ghosh

Journal of Modern Applied Statistical Methods

A pairwise balanced designs was constructed using cyclic partially balanced incomplete block designs with either (λ1 – λ2) = 1 or (λ2 – λ1) = 1. This method of construction of Pairwise balanced designs is further generalized to construct it using cyclic partially balanced incomplete block design when |(λ1 – λ2)| = p. The methods of construction of pairwise balanced designs was supported with examples. A table consisting parameters of Cyclic PBIB designs and its corresponding constructed pairwise balanced design is also included.

A New Right-Skewed Upside Down Bathtub Shaped Heavy-Tailed Distribution And Its Applications, Sandeep Kumar Maurya, Sanjay K. Singh, Umesh Singh

Journal of Modern Applied Statistical Methods

A one parameter right skewed, upside down bathtub type, heavy-tailed distribution is derived. Various statistical properties and maximum likelihood approaches for estimation purpose are studied. Five different real data sets with four different models are considered to illustrate the suitability of the proposed model.

Penalized Likelihood Estimation Of Gamma Distributed Response Variable Via Corrected Solution Of Regression Coefficients, Rasaki Olawale Olanrewaju

Journal of Modern Applied Statistical Methods

A Gamma distributed response is subjected to regression penalized likelihood estimations of Least Absolute Shrinkage and Selection Operator (LASSO) and Minimax Concave Penalty via Generalized Linear Models (GLMs). The Gamma related disturbance controls the influence of skewness and spread in the corrected path solutions of the regression coefficients.

Two Different Classes Of Shrinkage Estimators For The Scale Parameter Of The Rayleigh Distribution, Talha Omer, Zawar Hussain, Muhammad Qasim, Said Farooq Shah, Akbar Ali Khan

Journal of Modern Applied Statistical Methods

Shrinkage estimators are introduced for the scale parameter of the Rayleigh distribution by using two different shrinkage techniques. The mean squared error properties of the proposed estimator have been derived. The comparison of proposed classes of the estimators is made with the respective conventional unbiased estimators by means of mean squared error in the simulation study. Simulation results show that the proposed shrinkage estimators yield smaller mean squared error than the existence of unbiased estimators.

On The Level Of Precision Of A Heterogeneous Transfer Function In A Statistical Neural Network Model, Christopher Godwin Udomboso

Journal of Modern Applied Statistical Methods

A heterogeneous function of the statistical neural network is presented from two transfer functions: symmetric saturated linear and hyperbolic tangent sigmoid. The precision of the derived heterogeneous model over their respective homogeneous forms are established, both at increased sample sizes hidden neurons. Results further show the sensitivity of the heterogeneous model to increase in hidden neurons.

A Simple Random Sampling Modified Dual To Product Estimator For Estimating Population Mean Using Order Statistics, Sanjay Kumar, Priyanka Chhaparwal

Journal of Modern Applied Statistical Methods

Bandopadhyaya (1980) developed a dual to product estimator using robust modified maximum likelihood estimators (MMLE’s). Their properties were obtained theoretically and supported through simulations studies with generated as well as one real data set. Robustness properties in the presence of outliers and confidence intervals were studied.

Inference For Step-Stress Partially Accelerated Life Test Model With An Adaptive Type-I Progressively Hybrid Censored Data, Showkat Ahmad Lone, Ahmadur Rahman, Tanveer A. Tarray

Journal of Modern Applied Statistical Methods

Consider estimating data of failure times under step-stress partially accelerated life tests based on adaptive Type-I hybrid censoring. The mathematical model related to the lifetime of the test units is assumed to follow Rayleigh distribution. The point and interval maximum-likelihood estimations are obtained for distribution parameter and tampering coefficient. Also, the work is conducted under a traditional Type-I hybrid censoring plan (scheme). A Monte Carlo simulation algorithm is used to evaluate and compare the performances of the estimators of the tempering coefficient and model parameters under both progressively hybrid censoring plans. The comparison is carried out on the basis of ...

Vif-Regression Screening Ultrahigh Dimensional Feature Space, Hassan S. Uraibi

Journal of Modern Applied Statistical Methods

Iterative Sure Independent Screening (ISIS) was proposed for the problem of variable selection with ultrahigh dimensional feature space. Unfortunately, the ISIS method transforms the dimensionality of features from ultrahigh to ultra-low and may result in un-reliable inference when the number of important variables particularly is greater than the screening threshold. The proposed method has transformed the ultrahigh dimensionality of features to high dimension space in order to remedy of losing some information by ISIS method. The proposed method is compared with ISIS method by using real data and simulation. The results show this method is more efficient and more reliable ...

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.