Special Issue "Statistical Simulation and Computation"

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

Deadline for manuscript submissions: 31 May 2020.

Special Issue Editor

Prof. Yuhlong Lio
Website
Guest Editor
Department of Mathematical Science, University of South Dakota, SD, USA
Interests: survival analysis; reliability; smooth estimation; Bayesian inference

Special Issue Information

Dear Colleagues,

Recently, the need to solve real-world problems has increased the need for mathematics skills. Moreover, real-world problems are usually not determinate but are affected by random phenomonous. Therefore, the statistical modeling of environments often plays an important role in solving real-world applications mathematically. 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. Yuhlong Lio
Guest Editor

Manuscript Submission Information

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Please visit the Instructions for Authors page before submitting a manuscript. The Article Processing Charge (APC) for publication in this open access journal is 1200 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

Published Papers (2 papers)

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Research

Open AccessArticle
On the Smoothing of the Generalized Extreme Value Distribution Parameters Using Penalized Maximum Likelihood: A Case Study on UVB Radiation Maxima in the Mexico City Metropolitan Area
Mathematics 2020, 8(3), 329; https://doi.org/10.3390/math8030329 - 03 Mar 2020
Abstract
This paper concerns the use and implementation of penalized maximum likelihood procedures to fitting smoothing functions of the generalized extreme value distribution parameters to analyze spatial extreme values of ultraviolet B (UVB) radiation across the Mexico City metropolitan area in the period 2000–2018. [...] Read more.
This paper concerns the use and implementation of penalized maximum likelihood procedures to fitting smoothing functions of the generalized extreme value distribution parameters to analyze spatial extreme values of ultraviolet B (UVB) radiation across the Mexico City metropolitan area in the period 2000–2018. The model was fitted using a flexible semi-parametric approach and the parameters were estimated by the penalized maximum likelihood (PML) method. In order to investigate the performance of the model as well as the estimation method in the analysis of complex nonlinear trends for UVB radiation maxima, a simulation study was conducted. The results of the simulation study showed that penalized maximum likelihood yields better regularization to the model than the maximum likelihood estimates. We estimated return levels of extreme UVB radiation events through a nonstationary extreme value model using measurements of ozone (O3), nitrogen oxides (NOx), particles of 10 μm or less in diameter (PM10), carbon monoxide (CO), relative humidity (RH) and sulfur dioxide (SO2). The deviance statistics indicated that the nonstationary generalized extreme value (GEV) model adjusted was statistically better compared to the stationary model. The estimated smoothing functions of the location parameter of the GEV distribution on the spatial plane for different periods of time reveal the existence of well-defined trends in the maxima. In the temporal plane, a presence of temporal cyclic components oscillating over a weak linear component with a negative slope is noticed, while in the spatial plane, a weak nonlinear local trend is present on a plane with a positive slope towards the west, covering the entire study area. An explicit spatial estimate of the 25-year return period revealed that the more extreme risk levels are located in the western region of the study area. Full article
(This article belongs to the Special Issue Statistical Simulation and Computation)
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Open AccessArticle
Accelerated Life Test Method for the Doubly Truncated Burr Type XII Distribution
Mathematics 2020, 8(2), 162; https://doi.org/10.3390/math8020162 - 23 Jan 2020
Abstract
The Burr type XII (BurrXII) distribution is very flexible for modeling and has earned much attention in the past few decades. In this study, the maximum likelihood estimation method and two Bayesian estimation procedures are investigated based on constant-stress accelerated life test (ALT) [...] Read more.
The Burr type XII (BurrXII) distribution is very flexible for modeling and has earned much attention in the past few decades. In this study, the maximum likelihood estimation method and two Bayesian estimation procedures are investigated based on constant-stress accelerated life test (ALT) samples, which are obtained from the doubly truncated three-parameter BurrXII distribution. Because computational difficulty occurs for maximum likelihood estimation method, two Bayesian procedures are suggested to estimate model parameters and lifetime quantiles under the normal use condition. A Markov Chain Monte Carlo approach using the Metropolis–Hastings algorithm via Gibbs sampling is built to obtain Bayes estimators of the model parameters and to construct credible intervals. The proposed Bayesian estimation procedures are simple for practical use, and the obtained Bayes estimates are reliable for evaluating the reliability of lifetime products based on ALT samples. Monte Carlo simulations were conducted to evaluate the performance of these two Bayesian estimation procedures. Simulation results show that the second Bayesian estimation procedure outperforms the first Bayesian estimation procedure in terms of bias and mean squared error when users do not have sufficient knowledge to set up hyperparameters in the prior distributions. Finally, a numerical example about oil-well pumps is used for illustration. Full article
(This article belongs to the Special Issue Statistical Simulation and Computation)
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