Physical Sciences and Mathematics Commons^™

Exact Asymptotic Errors Of The Hazard Conditional Rate Kernel For Functional Random Fields, Abbes Rabhi, Sara Soltani

Applications and Applied Mathematics: An International Journal (AAM)

We consider the problem of nonparametric estimation of the kernel type estimators for the conditional cumulative distribution function and the successive derivatives of the conditional density for spatial data. More precisely, given a strictly stationary random field Z = (X, Y), we investigate a kernel estimate of the conditional hazard function of univariate response variable Y given the functional variable X. The principal aim of this paper is to give the mean squared convergence rate of the proposed estimator. Finally, we apply these theoretical results to the estimation of the conditional hazard function where we give the mean squared convergence …

Markov Chain Profit Modelling And Evaluation Between Two Dissimilar Systems Under Two Types Of Failures, Saminu I. Bala, Ibrahim Yusuf

Applications and Applied Mathematics: An International Journal (AAM)

No abstract provided.

Applying Ahp And Clustering Approaches For Public Transportation Decisionmaking: A Case Study Of Isfahan City, Alireza Salavati, Hossein Haghshenas, Bahador Ghadirifaraz, Jamshid Laghaei, Ghodrat Eftekhari

Journal of Public Transportation

The main purpose of this paper is to define appropriate criteria for the systematic approach to evaluate and prioritize multiple candidate corridors for public transport investment simultaneously to serve travel demand, regarding supply of current public transportation system and road network conditions of Isfahan, Iran. To optimize resource allocation, policymakers need to identify proper corridors to implement a public transportation system. In fact, the main question is to adopt the best public transportation system for each main corridor of Isfahan. In this regard, 137 questionnaires were completed by experts, directors, and policymakers of Isfahan to identify goals and objectives in …

Non Markovian Queue With Two Types Service Optional Re-Service And General Vacation Distribution, K. Sathiya, G. Ayyappan

Applications and Applied Mathematics: An International Journal (AAM)

We consider a single server batch arrival queueing system, where the server provides two types of heterogeneous service. A customer has the option of choosing either type 1 service with probability p1 or type 2 service with probability p2 with the service times follow general distribution. After the completion of either type 1 or type 2 service a customer has the option to repeat or not to repeat the type 1 or type 2 service. As soon as the customer service is completed, the server will take a vacation with probability θ or may continue staying in the system with …

Gathering Steam In Health Care: A Student History, Michael J. Leach

The STEAM Journal

In this reflection, I demonstrate STEAM in health care by outlining my 15 years as a university student engaged in formal education, extracurricular learning, research, and employment.

Efficient And Unbiased Estimation Procedure Of Population Mean In Two-Phase Sampling, Reba Maji, Arnab Bandyopadhyay, G. N. Singh

Journal of Modern Applied Statistical Methods

In this paper, an unbiased regression-ratio type estimator has been developed for estimating the population mean using two auxiliary variables in double sampling. Its properties are studied under two different cases. Empirical studies and graphical simulation have been done to demonstrate the efficiency of the proposed estimator over other estimators.

Developing Bayesian-Based Confidence Bounds For Non-Identically Distributed Observations Using The Lyapunov Condition, Garry M. Jacyna, Scott L. Rosen

Journal of Modern Applied Statistical Methods

The purpose of this paper is to establish a direct method for assessing the confidence in the detection and identification probabilities for segmented observations that are not identically distributed across assigned segments within a region. This paper arrives at easily computable confidence intervals by showing through mathematical analysis that:

I. The probability of successful detection within each test segment can be characterized by a Beta distribution;
II. The distribution of a weighted sum of independent but non-identically distributed sample means is asymptotically Normally distributed by the Lyapunov variant of the Central Limit Theorem, i.e., the approximation improves as the number …

E-Bayesian Estimation Of The Parameter Of The Logarithmic Series Distribution, Parviz Nasiri, Hassan Esfandyarifar

Journal of Modern Applied Statistical Methods

E-Bayesian estimation is introduced to estimate the parameter of logarithmic series distribution. In addition, E-Bayesian, Bayesian and maximum likelihood estimation with through applying mean squared error.

Regularized Neural Network To Identify Potential Breast Cancer: A Bayesian Approach, Hansapani S. Rodrigo, Chris P. Tsokos, Taysseer Sharaf

Journal of Modern Applied Statistical Methods

In the current study, we have exemplified the use of Bayesian neural networks for breast cancer classification using the evidence procedure. The optimal Bayesian network has 81% overall accuracy in correctly classifying the true status of breast cancer patients, 59% sensitivity in correctly detecting the malignancy and 83% specificity in correctly detecting the non-malignancy. The area under the receiver operating characteristic curve (0.7940) shows that this is a moderate classification model.

Longitudinal Stability Of Effect Sizes In Education Research, Joshua Stephens

Journal of Modern Applied Statistical Methods

Educators use meta-analyses to decide best practices. It has been suggested that effect sizes have declined over time due to various biases. This study applies an established methodological framework to educational meta-analyses and finds that effect sizes have increased from 1970–present. Potential causes for this phenomenon are discussed.

Latent Variable Model For Weight Gain Prevention Data With Informative Intermittent Missingness, Li Qin, Lisa Weissfeld, Michele Levine, Marsha Marcus, Feng Dai

Journal of Modern Applied Statistical Methods

Missing data is a common problem in longitudinal studies because of the characteristics of repeated measurements. Herein is proposed a latent variable model for nonignorable intermittent missing data in which the latent variables are used as random effects in modeling and link longitudinal responses and missingness process. In this methodology, the latent variables are assumed to be normally distributed with zero-mean, and the values of variance-covariance are calculated through maximum likelihood estimations. Parameter estimates and standard errors of the proposed method are compared with the mixed model and the complete-case analysis in the simulations and the application to the weight …

Evaluation Of The Addition Of Firth’S Penalty Term To The Bradley-Terry Likelihood, Paul Meyvisch

Journal of Modern Applied Statistical Methods

A major shortcoming of the Bradley-Terry model is that the maximum likelihood estimates are infinite-valued in the presence of separation and may be unreliable when data are nearly separated. A well-known solution consists of the addition of Firth' s penalty term to the log-likelihood function, and solve this penalized likelihood through logistic regression.The maximum likelihood estimates with and without Firth's penalty are compared in a large and heterogeneous population of table-tennis players. We additionally show that exact penalized maximum likelihood estimates can be reasonably approximated using a well-chosen Minorization-Maximization (MM) algorithm.

Optimal Estimation And Sampling Allocation In Survey Sampling Under A General Correlated Superpopulation Model, Ioulia Papageorgiou

Journal of Modern Applied Statistical Methods

Sampling from a finite population with correlated units is addressed. The proposed methodology applies to any type of correlation function and provides the sample allocation that ensures optimal efficiency of the population parameters estimates. The expressions of the estimate and its MSE are also provided.

The Application Of Legendre Multiwavelet Functions In Image Compression, Elham Hashemizadeh, Sohrab Rahbar

Journal of Modern Applied Statistical Methods

Legendre multiwavelets are introduced. These functions can be designed in such a way that the properties of orthogonality, polynomial approximation, and symmetry hold at the same time. In this way, they can be effectively deployed in image compression.

Estimation Of Population Mean On Recent Occasion Under Non-Response In H-Occasion Successive Sampling, Anup Kumar Sharma, Garib Nath Singh

Journal of Modern Applied Statistical Methods

In this article, an attempt has been made to study on general estimation procedures of population mean on recent occasion when non-response occurs in h-occasion successive sampling. Suggested estimators have advantageously influenced the estimation procedures in the presence of non-response. Detailed properties of the suggested estimation procedures have been examined and compared with the estimation process of the same circumstances but in the absence of non-response. Empirical studies have been carried out to demonstrate the performances of the estimates and suitable recommendations have been made.

Fitting Flexible Parametric Regression Models With Gldreg In R, Steve Su

Journal of Modern Applied Statistical Methods

This article outlines the functionality of the GLDreg package in R which fits parametric regression models using generalized lambda distributions via maximum likelihood estimation and L moment matching. The main advantage of GLDreg is the provision of robust regression lines and smooth regression quantiles beyond the capabilities of existing known methods.

Doubly Censored Data From Two-Component Mixture Of Inverse Weibull Distributions: Theory And Applications, Tabassum Sindhu, Navid Feroze, Muhammad Aslam

Journal of Modern Applied Statistical Methods

Finite mixture distributions consist of a weighted sum of standard distributions and are a useful tool for reliability analysis of a heterogeneous population. They provide the necessary flexibility to model failure distributions of components with multiple failure models. The analysis of the mixture models under Bayesian framework has received sizable attention in the recent years. However, the Bayesian estimation of the mixture models under doubly censored samples has not yet been introduced in the literature. The main objective of this paper is to discuss the Bayes estimation of the inverse Weibull mixture distributions under doubly censoring. Different priors and loss …

A Comparison Of Usual T-Test Statistic And Modified T-Test Statistics On Skewed Distribution Functions, Wooi K. Lim, Alice W. Lim

Journal of Modern Applied Statistical Methods

When the sample size n is small, the random variable T= √n(\overline{X} – μ)/S is said to follow a central t distribution with degrees of freedom (n – 1), where \overline{X} is the sample mean and S is the sample standard deviation, provided that the data X ~ N (μ, σ²). The random variable T can be used as a test statistic to hypothesize the population mean μ. Some argue that the t-test statistic is robust against the normality of the distribution and claim that the normality assumption is not necessary. In this …

Monte Carlo Simulation Design For Evaluating Normal-Based Control Chart Properties, John N. Dyer

Journal of Modern Applied Statistical Methods

The advent of more complicated control charting schemes has necessitated the use of Monte Carlo simulation (MCS) methods. Unfortunately, few sources exist to study effective design and validation of MCS methods related to control charting. This paper describes the design, issues, considerations and limitations for conducting normal-based control chart MCS studies, including choice of random number generator, simulation size requirements, and accuracy/error in simulation estimation. This paper also describes two design strategies for MCS for control chart evaluations and provides the programming code. As a result, this paper hopes to establish de facto MCS schemes aimed at guiding researchers and …

Bayesian Analysis Of Discrete Skewed Laplace Distribution, A. Hossianzadeh, K Zare

Journal of Modern Applied Statistical Methods

The discrete skewed Laplace distribution is a flexible distribution with integer domain and simple closed form that can be applied to model count data. Parameters are estimated under empirical Bayes (EB) analysis and comparison are made between the Bayesian parameter estimation and classical parameter estimation, i.e. the maximum likelihood (ML) approach. The results show that the Bayesian parameter estimations are preferable.

Multicollinearity And A Ridge Parameter Estimation Approach, Ghadban Khalaf, Mohamed Iguernane

Journal of Modern Applied Statistical Methods

One of the main goals of the multiple linear regression model, Y = Xβ + u, is to assess the importance of independent variables in determining their predictive ability. However, in practical applications, inference about the coefficients of regression can be difficult because the independent variables are correlated and multicollinearity causes instability in the coefficients. A new estimator of ridge regression parameter is proposed and evaluated by simulation techniques in terms of mean squares error (MSE). Results of the simulation study indicate that the suggested estimator dominates ordinary least squares (OLS) estimator and other ridge estimators with respect to …

Designing Of Bayesian Skip Lot Sampling Plan Under Destructive Testing, K. K. Suresh, S. Umamaheswari

Journal of Modern Applied Statistical Methods

Skip-lot sampling plan serves as a cost-effective technique to manage the cost of performing frequent product inspections. As a powerful tool within a real-time quality management system, the ability to collect data which an optimize skip-lot sampling parameters affords manufacturers the luxury of lowering inspection expenses in various manufacturing units. The good quality of product can be produced in continuous improvement of production process in excellent quality history for suppliers. The procedures and necessary tables are provided for finding the respective plans for which sum of producer and consumer risks are minimized with acceptable and limiting quality levels which accounts …

An Improved Generalized Estimation Procedure Of Current Population Mean In Two-Occasion Successive Sampling, G. N. Singh, Alok Kumar Singh, Anup Kumar Sharma

Journal of Modern Applied Statistical Methods

The present work is an attempt to make use of several auxiliary variables on both occasions for improving the precision of estimates for the current population mean in two-occasion successive sampling. A generalized exponential-cum-regression type estimator of the current population mean is proposed and its optimum replacement strategy has been discussed. Empirical studies are carried out to show the dominance of the proposed estimation procedure over the sample mean estimator and natural successive sampling estimator. Empirical results have been interpreted and suitable recommendations are put forward to survey practitioners.

The Br2 – Weighting Method For Estimating The Effects Of Air Pollution On Population Health, Goran Krstic, Nikolas S. Krstic, Mauricio Zambrano-Bigiarini

Journal of Modern Applied Statistical Methods

Uncertainties, limitations and biases may impede the correct application of concentration-response linear functions to estimate the effects of air pollution exposure on population health. The reliability of a prediction depends largely on the strength of the linear correlation between the studied variables. This work proposes the joint use of the coefficient of determination, r², with the regression slope, b, as an improved measure of the strength of the linear relation between air pollution and its effects on population health. The proposed br²‑weighting method offers more reliable inferences about the potential effects of air pollution on …

An Adjusted Network Information Criterion For Model Selection In Statistical Neural Network Models, Christopher Godwin Udomboso, Godwin Nwazu Amahia, Isaac Kwame Dontwi

Journal of Modern Applied Statistical Methods

In this paper, we derived and investigated the Adjusted Network Information Criterion (ANIC) criterion, based on Kullback’s symmetric divergence, which has been designed to be an asymptotically unbiased estimator of the expected Kullback-Leibler information of a fitted model. The ANIC improves model selection in more sample sizes than does the NIC.

Bayesian Inference For Median Of The Lognormal Distribution, K. Aruna Rao, Juliet Gratia D'Cunha

Journal of Modern Applied Statistical Methods

Lognormal distribution has many applications. The past research papers concentrated on the estimation of the mean of this distribution. This paper develops credible interval for the median of the lognormal distribution. The estimated coverage probability and average length of the credible interval is compared with the confidence interval using Monte Carlo simulation.

Estimating The Parameter Of Exponential Distribution Under Type Ii Censoring From Fuzzy Data, Iman Makhdoom, Parviz Nasiri, Abbas Pak

Journal of Modern Applied Statistical Methods

The problem of estimating the parameter of Exponential distribution on the basis of type II censoring scheme is considered when the available data are in the form of fuzzy numbers. The Bayes estimate of the unknown parameter is obtained by using the approximation forms of Lindley (1980) and Tierney and Kadane (1986) under the assumption of gamma prior. The highest posterior density (HPD) estimate of the parameter of interest is found. A Monte Carlo simulation is used to compare the performances of the different methods. A real data set is investigated to illustrate the applicability of …

On Generalizing Cumulative Ordered Regression Models, Robert W. Walker

Journal of Modern Applied Statistical Methods

We examine models that relax proportionality in cumulative ordered regression models. Something fundamental arising from ordered variables and stochastic ordering implies a partitioning. Efforts to relax proportionality also relax the ability to collapse an inherently multidimensional problem to a partitioning of the (unidimensional) real line. It is surprising and unfortunate to find that deviations from proportionality are sufficient to generate internal contradictions; undecidable propositions must exist by relaxing proportional odds without other relevant and significant changes in the underlying model. We prove a single theorem linking continuous support and partitions of a latent space to show that for these two …

Limited Failure Censored Life Test Sampling Plan In Burr Type X Distribution, R. R. L. Kantam, M. S. Ravikumar

Journal of Modern Applied Statistical Methods

The Burr type X distribution is considered as a life time random variable of a product whose lots are to be decided for acceptance or otherwise on the basis of sample lifetimes drawn from the lot. The sample is divided into various groups in order to develop a group sampling plan in such a way that the life testing experiment is terminated as soon as the first failure in each group is observed. The acceptance criterion based on the theory of order statistics is proposed and is shown to be more economical than a criterion proposed in the earlier similar …

Comparison Of Some Multivariate Nonparametric Tests In Profile Analysis To Repeated Measurements, Mehrdad Vossoughi, Shila Shahvali, Erfan Sadeghi

Journal of Modern Applied Statistical Methods

Through Monte Carlo simulations, the performance of six multivariate nonparametric tests for testing the hypothesis of parallelism in profile analysis was studied. In conclusion, the tests based on ranks were as efficient as Hotelling's T² under multivariate normal distribution. For the heavy tailed distribution, the tests based on signs performed best.