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Mathematics
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Statistical Simulation and Computation: 3rd Edition
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Statistical Simulation and Computation: 3rd Edition

A special issue of Mathematics (ISSN 2227-7390). This special issue belongs to the section "Probability and Statistics".

Deadline for manuscript submissions: 31 January 2025 | Viewed by 3820

Special Issue Editor

Prof. Dr. Yuhlong Lio

E-Mail Website
Guest Editor
Department of Mathematical Sciences, University of South Dakota, Vermillion, SD 57069, USA
Interests: reliability analysis; quality control; kernel-smooth estimation; mathematical modeling
Special Issues, Collections and Topics in MDPI journals

Special Issue Information

Dear Colleagues,

Recently, the need to solve real-world problems has increased the need for skills in mathematics. Moreover, real-world problems are usually not determinate, but are affected by random phenomena. Therefore, the statistical modeling of environments often plays an important role in mathematically solving real-world applications. Due to the complicities of models, closed forms of solutions cannot usually be established. Therefore, computation and simulation technologies are needed. In this Special Issue, articles concerning mathematical or statistical modeling that require computation and simulation skills are particularly welcome. Topics of interest include, but are not limited to, the following:

  1. Industrial applications;
  2. Medical sciences applications;
  3. Environment applications;
  4. Biological science applications.

Prof. Dr. Yuhlong Lio
Guest Editor

Manuscript Submission Information

Manuscripts should be submitted online at www.mdpi.com by registering and logging in to this website. Once you are registered, click here to go to the submission form. Manuscripts can be submitted until the deadline. All submissions that pass pre-check are peer-reviewed. Accepted papers will be published continuously in the journal (as soon as accepted) and will be listed together on the special issue website. Research articles, review articles as well as short communications are invited. For planned papers, a title and short abstract (about 100 words) can be sent to the Editorial Office for announcement on this website.

Submitted manuscripts should not have been published previously, nor be under consideration for publication elsewhere (except conference proceedings papers). All manuscripts are thoroughly refereed through a single-blind peer-review process. A guide for authors and other relevant information for submission of manuscripts is available on the Instructions for Authors page. Mathematics is an international peer-reviewed open access semimonthly journal published by MDPI.

Please visit the Instructions for Authors page before submitting a manuscript. The Article Processing Charge (APC) for publication in this open access journal is 2600 CHF (Swiss Francs). Submitted papers should be well formatted and use good English. Authors may use MDPI's English editing service prior to publication or during author revisions.

Keywords

  • Bayesian estimation
  • dynamic system
  • maximum likelihood estimate
  • Monte Carlo simulation
  • reliability
  • stress strength
  • survival analysis

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Related Special Issue

Published Papers (5 papers)

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Research

17 pages, 2171 KiB  
Article
A Ratio Estimator for the Mean Using a Mixture Optional Enhance Trust (MOET) Randomized Response Model
by Sat Gupta, Michael Parker and Sadia Khalil
Mathematics 2024, 12(22), 3617; https://doi.org/10.3390/math12223617 - 20 Nov 2024
Viewed by 324
Abstract
When researchers conduct surveys seeking sensitive, socially stigmatized information, respondents, on average, modify their answers to represent themselves favorably. To overcome this issue, researchers may use Randomized Response Technique (RRT) models. Recently, Parker et al. proposed a model that incorporates some of the [...] Read more.
When researchers conduct surveys seeking sensitive, socially stigmatized information, respondents, on average, modify their answers to represent themselves favorably. To overcome this issue, researchers may use Randomized Response Technique (RRT) models. Recently, Parker et al. proposed a model that incorporates some of the most critical recent quantitative RRT advancements—mixture, optionality, and enhanced trust—into a single model, which they called a Mixture Optional Enhanced (MOET) model. We now improve upon the MOET model by incorporating auxiliary information into the analysis. Positively correlated auxiliary information can improve the mean response estimation through use of a ratio estimator. In this study, we propose just such an estimator for the MOET model. Further, we investigate the conditions under which the ratio estimator outperforms the basic MOET estimator proposed by Parker et al. in 2024. We also consider the possibility that the collection of auxiliary information may compromise privacy; and we study the impact of privacy reduction on the overall model performance as assessed by the unified measure (UM) proposed by Gupta et al. in 2018. Full article
(This article belongs to the Special Issue Statistical Simulation and Computation: 3rd Edition)
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44 pages, 786 KiB  
Article
New Statistical Residuals for Regression Models in the Exponential Family: Characterization, Simulation, Computation, and Applications
by Raydonal Ospina, Patrícia L. Espinheira, Leilo A. Arias, Cleber M. Xavier, Víctor Leiva and Cecilia Castro
Mathematics 2024, 12(20), 3196; https://doi.org/10.3390/math12203196 - 12 Oct 2024
Viewed by 748
Abstract
Residuals are essential in regression analysis for evaluating model adequacy, validating assumptions, and detecting outliers or influential data. While traditional residuals perform well in linear regression, they face limitations in exponential family models, such as those based on the binomial and Poisson distributions, [...] Read more.
Residuals are essential in regression analysis for evaluating model adequacy, validating assumptions, and detecting outliers or influential data. While traditional residuals perform well in linear regression, they face limitations in exponential family models, such as those based on the binomial and Poisson distributions, due to heteroscedasticity and dependence among observations. This article introduces a novel standardized combined residual for linear and nonlinear regression models within the exponential family. By integrating information from both the mean and dispersion sub-models, the new residual provides a unified diagnostic tool that enhances computational efficiency and eliminates the need for projection matrices. Simulation studies and real-world applications demonstrate its advantages in efficiency and interpretability over traditional residuals. Full article
(This article belongs to the Special Issue Statistical Simulation and Computation: 3rd Edition)
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10 pages, 259 KiB  
Article
Modified Cox Models: A Simulation Study on Different Survival Distributions, Censoring Rates, and Sample Sizes
by Iketle Aretha Maharela, Lizelle Fletcher and Ding-Geng Chen
Mathematics 2024, 12(18), 2903; https://doi.org/10.3390/math12182903 - 18 Sep 2024
Viewed by 852
Abstract
The classical Cox model is the most popular procedure for studying right-censored data in survival analysis. However, it is based on the fundamental assumption of proportional hazards (PH). Modified Cox models, stratified and extended, have been widely employed as solutions when the PH [...] Read more.
The classical Cox model is the most popular procedure for studying right-censored data in survival analysis. However, it is based on the fundamental assumption of proportional hazards (PH). Modified Cox models, stratified and extended, have been widely employed as solutions when the PH assumption is violated. Nevertheless, prior comparisons of the modified Cox models did not employ comprehensive Monte-Carlo simulations to carry out a comparative analysis between the two models. In this paper, we conducted extensive Monte-Carlo simulation to compare the performance of the stratified and extended Cox models under varying censoring rates, sample sizes, and survival distributions. Our results suggest that the models’ performance at varying censoring rates and sample sizes is robust to the distribution of survival times. Thus, their performance under Weibull survival times was comparable to that of exponential survival times. Furthermore, we found that the extended Cox model outperformed other models under every combination of censoring, sample size and survival distribution. Full article
(This article belongs to the Special Issue Statistical Simulation and Computation: 3rd Edition)
33 pages, 530 KiB  
Article
Imputing Missing Data in One-Shot Devices Using Unsupervised Learning Approach
by Hon Yiu So, Man Ho Ling and Narayanaswamy Balakrishnan
Mathematics 2024, 12(18), 2884; https://doi.org/10.3390/math12182884 - 15 Sep 2024
Viewed by 726
Abstract
One-shot devices are products that can only be used once. Typical one-shot devices include airbags, fire extinguishers, inflatable life vests, ammo, and handheld flares. Most of them are life-saving products and should be highly reliable in an emergency. Quality control of those productions [...] Read more.
One-shot devices are products that can only be used once. Typical one-shot devices include airbags, fire extinguishers, inflatable life vests, ammo, and handheld flares. Most of them are life-saving products and should be highly reliable in an emergency. Quality control of those productions and predicting their reliabilities over time is critically important. To assess the reliability of the products, manufacturers usually test them in controlled conditions rather than user conditions. We may rely on public datasets that reflect their reliability in actual use, but the datasets often come with missing observations. The experimenter may lose information on covariate readings due to human errors. Traditional missing-data-handling methods may not work well in handling one-shot device data as they only contain their survival statuses. In this research, we propose Multiple Imputation with Unsupervised Learning (MIUL) to impute the missing data using Hierarchical Clustering, k-prototype, and density-based spatial clustering of applications with noise (DBSCAN). Our simulation study shows that MIUL algorithms have superior performance. We also illustrate the method using datasets from the Crash Report Sampling System (CRSS) of the National Highway Traffic Safety Administration (NHTSA). Full article
(This article belongs to the Special Issue Statistical Simulation and Computation: 3rd Edition)
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18 pages, 1921 KiB  
Article
Predicting Pump Inspection Cycles for Oil Wells Based on Stacking Ensemble Models
by Hua Xin, Shiqi Zhang, Yuhlong Lio and Tzong-Ru Tsai
Mathematics 2024, 12(14), 2231; https://doi.org/10.3390/math12142231 - 17 Jul 2024
Viewed by 688
Abstract
Beam pumping is currently the broadly used method for oil extraction worldwide. A pumpjack shutdown can be incurred by failures from the load, corrosion, work intensity, and downhole working environment. In this study, the duration of uninterrupted pumpjack operation is defined as the [...] Read more.
Beam pumping is currently the broadly used method for oil extraction worldwide. A pumpjack shutdown can be incurred by failures from the load, corrosion, work intensity, and downhole working environment. In this study, the duration of uninterrupted pumpjack operation is defined as the pump inspection cycle. Accurate prediction of the pump inspection cycle can extend the lifespan, reduce unexpected pump accidents, and significantly enhance the production efficiency of the pumpjack. To enhance the prediction performance, this study proposes an improved two-layer stacking ensemble model, which combines the power of the random forests, light gradient boosting machine, support vector regression, and Adaptive Boosting approaches, for predicting the pump inspection cycle. A big pump-related oilfield data set is used to demonstrate the proposed two-layer stacking ensemble model can significantly enhance the prediction quality of the pump inspection cycle. Full article
(This article belongs to the Special Issue Statistical Simulation and Computation: 3rd Edition)
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