Asymptotic and Bootstrap Implementation of the D'Agostino-Berlanger-D'Agostino K2 Normality Test in R | Chapter 3 | Mathematics and Computer Science: Research Updates Vol. 9

 

The K² test could be one of the best tests for assessing normality, yet its use is limited, likely because it is not commonly included in standard statistical software, despite being implementable in R through the moments package. Moreover, its asymptotic approximation has been questioned for small samples, and no bootstrap version currently exists, even though it is feasible in R. This simulation study aimed to: (1) verify the linear independence and nonlinear relationship between √b₁ and b₂; (2) develop an R script for the K² test in both asymptotic and bootstrap versions; (3) assess the fit of the bootstrap distribution of the K² statistic to a chi-square distribution with two degrees of freedom; (4) compare the power of both implementations against non-normal distributions; and (5) contrast the bootstrap version of K² with the Shapiro–Wilk test in small samples. A Monte Carlo simulation with 10,000 replications was conducted, using 16 non-normal distributions as alternative hypotheses and sample sizes (n) ranging from 20 to 2,000 in increments of 20. Linear independence and a parabolic relationship between √b₁ and b₂ were confirmed, and the R script was verified to be functional. The script is available for download as a Word document from a GitHub repository. The bootstrap distribution of K² converged to a chi-square distribution for n ≥ 120. The asymptotic version of K² and the Shapiro–Wilk test showed greater power than the bootstrap version, except for mesokurtic asymmetric distributions. Bootstrap implementation is recommended in these cases for n < 120, while the asymptotic version is generally more powerful and appropriate for n ≥ 20. The developed R script is highly useful for assessing the normality assumption required by many parametric tests, such as t-tests and F-tests for comparing means and variances, as well as for characterising the distribution of a sample of quantitative data; therefore, its use is recommended for these purposes.

 

Author(s) Details

José Moral de la Rubia
School of Psychology, UANL, Mexico.

 

Please see the book here :- https://doi.org/10.9734/bpi/mcsru/v9/6969

 

Reliability Evaluation of Structures Excited by Earthquakes in Time Domain Using a Novel Concept | Chapter 3 | Science and Technology: Developments and Applications Vol. 3

A novel reliability evaluation method for structures excited by the seismic loading applied in the time domain is presented. Major sources of nonlinearity and uncertainty are incorporated into the algorithm. Structures are represented by finite elements. To demonstrate that the algorithm will work in different computational platforms, the stress-based finite element is used. Connections are more realistically considered partially restrained (PR) with different rigidities. Multiple site-specific design earthquake acceleration time histories are numerically generated using information on the seismic activities of the region using the broadband platform (BBP) available at the Southern California Earthquake Center (SCEC). The reliability of structures is estimated by exciting them with real and artificially generated earthquake time histories. The accuracy of the method is verified using Monte Carlo Simulation. With the help of examples, it is demonstrated that the proposed reliability concept is efficient and accurate. The procedure can extract the reliability information with the help of a few hundred deterministic analyses instead of millions needed for simulation and users can use any computer available to them. Post-Northridge PR beam-to-column connections are superior to the pre-Northridge FR connections. Structural reliabilities are estimated for the overall lateral deflection and inter-story drift limit states. Inter-story drifts are more critical than the overall lateral deflections. The Performance-Based Seismic Design (PBSD) guidelines are briefly discussed. The reliability method fills a knowledge gap and helps to implement the PBSD concept. Currently, the authors call the method REDSET (Reliability Evaluation of Dynamic Systems Excited in Time Domain). REDSET appears to be an exciting development replacing the classical random vibration concept and providing an alternative to the simulation approach.

 

Author (s) Details

 

J. Ramon Gaxiola-Camacho
Department of Civil Engineering, Autonomous University of Sinaloa, Culiacan, Sinaloa, México.

 

Achintya Haldar
Department of Civil Engineering and Engineering Mechanics, University of Arizona, Tucson, Arizona, USA and Indian Institute of Technology (IIT) – Delhi, India

 

Aaron Gutierrez-Lopez
Department of Civil Engineering, Autonomous University of Sinaloa, Culiacan, Sinaloa, México.

 

Please see the book here:- https://doi.org/10.9734/bpi/stda/v3/4011

A Novel Model of Radiosensitization and Microdosimetric Analysis in the Context of Metallic Nanoparticles | Chapter 13 | Advanced Concepts in Pharmaceutical Research Vol. 4

 Background: Auger cascades generated in high atomic number nanoparticles (NPs) following an ionization were considered as a potential mechanism for the NP radiosensitization. The Auger electrons have short ranges and can locally damage tumor cells, resulting in larger biological effect than radiation alone.

Aim: In this work, we investigated the microdosimetric consequences of the Auger cascade using the theory of dual radiation action (TDRA) and proposed a novel Bomb model as a general framework for describing NP-related radiosensitization. When triggered by an ionization event, the Bomb model considers the NPs that are close to a radiation sensitive cellular target generate dense secondary electrons and kill the cell according to a probability distribution, acting like a "bomb".

Methods: TDRA plus a distance model was used as the theoretical basis for calculating the change in α of the linear-quadratic survival model and the relative biological effectiveness (RBE). In TDRA, cellular lesions are assumed to be formed as a result of the combination of pairs of sublesions (e.g., chromosome break) in the sensitive sites of the cell. In addition, the yield of sublesions formed within spherical sites is assumed to be proportional to the energy deposited to the site. We calculated the quantities for SQ20B and Hela human cancer cells under 250kVp x-ray irradiation with the presence of gadolinium-based NPs (AGuIXTM), and 220kVp x-ray irradiation with the presence of 50 nm Gold NPs (AuNPs), respectively, and compared with existing experimental data. Geant4 based Monte Carlo (MC) simulations were used to (1) generate the electron spectrum and the phase space data of photons entering the NPs and to (2) calculate the proximity functions and other related parameters for the TDRA and the Bomb model.

Results: The Auger cascade electrons have greater proximity function than photoelectric and Compton electrons in water by up to 30%, but the resulting increases in α are smaller than those derived from experimental data. The calculated RBEs cannot explain the experimental findings. The relative increase in α predicted by TDRA is lower than the experimental result by a factor of at least 45 for SQ20B cells with AGuIX under 250kVp x-ray irradiation; and at least 4 for Hela cells with AuNPs under 220kVp x-ray irradiation. The application of the Bomb model to Hela cells with AuNPs under 220kVp x-ray irradiation indicated that a single ionization event in NPs caused by higher energy photons has a greater probability of killing a cell. NPs that are closer to the cell nucleus are more effective for radiosensitization. The comparison of Hela cell with AuNPs irradiated with photons of different energy implies that NP ionization by photon of higher energies have higher killing power, and the Compton scattering in NP may have a stronger effect than photoelectric effect, even though the latter can result in Auger cascade.

Conclusion: Microdosimetric calculations of the RBE for cell death of the Auger electron cascade cannot explain the experimentally observed radiosensitization by AGuIX or AuNP, while the proposed Bomb model can be a potential candidate for describing NP-related radiosensitization at low NP concentrations.

Author(s) Details:

Huagang Yan,
School of Biomedical Engineering, Capital Medical University, Beijing 100069, China.

David J. Carlson,
Department of Radiation Oncology, University of Pennsylvania, Philadelphia, PA 19104, USA.

Wu Liu,
Department of Radiation Oncology, Stanford University School of Medicine, Stanford, CA, 94305, USA.

Please see the link here: https://stm.bookpi.org/ACPR-V4/article/view/13015

Study on Linear Programming in Risk Management | Chapter 13 | Novel Research Aspects in Mathematical and Computer Science Vol. 1

 The deterministic nature of the linear programming model is well-known. One method for dealing with uncertainty is to calculate the range of optimality. The effect of changing each objective function coefficient one at a time is studied after achieving the optimal solution (typically using the simplex approach). The optimality range is defined as the region in which the choice variables remain constant. This sensitivity analysis aids the analyst in gaining a better understanding of the problem. It is, however, impractical since the coefficients of objective functions do not tend to stay constant. They are frequently profit contributions from sold items, and their selling prices fluctuate at random. A realistic linear programme is built for simultaneously randomising the coefficients from any probability distribution. A novel method for creating a copula of random objective function coefficients based on a given rank correlation is also presented. The value distribution of the applicable objective function is generated. This distribution is analysed directly for central tendency, spread, skewness, and extreme values for the purposes of risk analysis. Risk analysis and business analytics are important areas in education and training for the information economy.

Author(S) Details

Dennis Ridley
School of Business and Industry, Florida A&M University, USA and Department of Scientific Computing, Florida State University, USA.

Felipe Llaugel
Universidad Autonoma de Santo Domingo, USA.

Inger Daniels
School of Business and Industry, Florida A&M University, USA.

Abdullah Khan
School of Business, Claflin University, USA.

View Book:- https://stm.bookpi.org/NRAMCS-V1/article/view/6559

Pure Premium Calculation of Rice Farm Insurance Scheme in Indonesia Based on The 4-Parameter Beta Mixture Distribution: A Recent Study | Chapter 13 | New Approaches in Engineering Research Vol. 10

 Rice farm insurance (Asuransi Usaha Tani Padi – AUTP programme) was developed by the Indonesian government to safeguard rice farms against losses caused by floods, droughts, and pest and disease infestations. The method for calculating pure premiums for the rice farm insurance plan in Indonesia has been explored, assuming that the distribution of rice yield data is normal, gamma, or normal mixture distribution. For the situation of rice yield data distribution in the form of symmetry, the normal distribution can be applied. When the distribution of rice yield data is skewed to the right or positively skewed, the gamma distribution can be employed. In addition, unimodal distributions include the normal and gamma distributions. The method of calculating pure premiums for the rice farm insurance plan in Indonesia has also been studied, under the assumption that rice yield data follows a normal mixture distribution. The multimodal distribution can be classified as the normal mixing distribution. The normal mixture distribution's characteristic is appropriate for rice yield data in Indonesia that includes data from multiple provinces. The 4-parameter beta mixed distribution, on the other hand, can be used to analyse rice yield data in Indonesia. In terms of the tail shape of the distribution, this distribution is more flexible than the conventional mixing distribution. In this research, the AUTP program's pure premium calculation approach is defined using the assumption that rice yield data distribution is a 4-parameter beta mixed distribution. The method's performance is assessed using Monte Carlo simulation. When the sample size is increased, the Monte Carlo simulation results reveal that the suggested method has higher accuracy and precision. The approach is applied to data on rice productivity in numerous Indonesian provinces from 1970 to 2016.

Author (S) Details

Aceng Komarudin Mutaqin
Department of Statistics, Universitas Islam Bandung, Indonesia.

Yayat Karyana
Department of Statistics, Universitas Islam Bandung, Indonesia.

Siti Sunendiari
Department of Statistics, Universitas Islam Bandung, Indonesia.

View Book :- https://stm.bookpi.org/NAER-V10/article/view/2989