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Keywords = method of variance estimates recovery

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30 pages, 8543 KB  
Article
Multi-Channel Coupled Variational Bayesian Framework with Structured Sparse Priors for High-Resolution Imaging of Complex Maneuvering Targets
by Xin Wang, Jing Yang and Yong Luo
Remote Sens. 2025, 17(14), 2430; https://doi.org/10.3390/rs17142430 - 13 Jul 2025
Viewed by 437
Abstract
High-resolution ISAR (Inverse Synthetic Aperture Radar) imaging plays a crucial role in dynamic target monitoring for aerospace, maritime, and ground surveillance. Among various remote sensing techniques, ISAR is distinguished by its ability to produce high-resolution images of non-cooperative maneuvering targets. To meet the [...] Read more.
High-resolution ISAR (Inverse Synthetic Aperture Radar) imaging plays a crucial role in dynamic target monitoring for aerospace, maritime, and ground surveillance. Among various remote sensing techniques, ISAR is distinguished by its ability to produce high-resolution images of non-cooperative maneuvering targets. To meet the increasing demands for resolution and robustness, modern ISAR systems are evolving toward wideband and multi-channel architectures. In particular, multi-channel configurations based on large-scale receiving arrays have gained significant attention. In such systems, each receiving element functions as an independent spatial channel, acquiring observations from distinct perspectives. These multi-angle measurements enrich the available echo information and enhance the robustness of target imaging. However, this setup also brings significant challenges, including inter-channel coupling, high-dimensional joint signal modeling, and non-Gaussian, mixed-mode interference, which often degrade image quality and hinder reconstruction performance. To address these issues, this paper proposes a Hybrid Variational Bayesian Multi-Interference (HVB-MI) imaging algorithm based on a hierarchical Bayesian framework. The method jointly models temporal correlations and inter-channel structure, introducing a coupled processing strategy to reduce dimensionality and computational complexity. To handle complex noise environments, a Gaussian mixture model (GMM) is used to represent nonstationary mixed noise. A variational Bayesian inference (VBI) approach is developed for efficient parameter estimation and robust image recovery. Experimental results on both simulated and real-measured data demonstrate that the proposed method achieves significantly improved image resolution and noise robustness compared with existing approaches, particularly under conditions of sparse sampling or strong interference. Quantitative evaluation further shows that under the continuous sparse mode with a 75% sampling rate, the proposed method achieves a significantly higher Laplacian Variance (LV), outperforming PCSBL and CPESBL by 61.7% and 28.9%, respectively and thereby demonstrating its superior ability to preserve fine image details. Full article
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22 pages, 4944 KB  
Article
Developing Diameter Distribution Models of Major Coniferous Species in South Korea
by Sanghyun Jung, Daesung Lee and Jungkee Choi
Forests 2025, 16(6), 961; https://doi.org/10.3390/f16060961 - 6 Jun 2025
Viewed by 589
Abstract
This study developed diameter distribution models using the Weibull function for Korean red pine (Pinus densiflora), Korean white pine (P. koraiensis), and Japanese larch (Larix kaempferi). The study data were collected from 49 Korean red pine stands, [...] Read more.
This study developed diameter distribution models using the Weibull function for Korean red pine (Pinus densiflora), Korean white pine (P. koraiensis), and Japanese larch (Larix kaempferi). The study data were collected from 49 Korean red pine stands, 54 Korean white pine stands, and 49 Japanese larch stands located in national forests in Gangwon and North Gyeongsang Provinces, South Korea. To identify the optimal method for modeling the diameter distribution of these three species, parameter recovery methods and parameter prediction methods were analyzed. To identify the optimal parameter recovery method for presenting the diameter distribution of these three species, ten parameter recovery methods were compared using moment-based, percentile-based, and hybrid approaches. For parameter prediction methods, major stand characteristics were used as independent variables to develop the models for the parameters a, b, and c of the Weibull function. For estimating the Weibull parameters, two methods—the estimated parameter recovery method and the parameter prediction method—were compared and analyzed. The optimal parameter recovery method was the one using the minimum DBH, the mean DBH, and the DBH variance. The coefficient of determination (R2) for the models predicting the minimum DBH, the mean DBH, and the DBH variance ranged from 0.7186 to 0.9747, and the R2 for the models directly predicting parameters ranged from 0.7032 to 0.9374, indicating high explanatory power and unbiased results. When comparing the two methods, the parameter prediction method showed higher accuracy and lower bias. In addition, paired t-tests were conducted to assess differences from the observed Weibull parameters. The results showed a significant difference for the estimated parameter recovery method, whereas no significant difference was found for the parameter prediction method, further supporting its reliability. Full article
(This article belongs to the Special Issue Silviculture and Management Strategy in Coniferous Forests)
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24 pages, 2889 KB  
Systematic Review
Hypertensive Disorders of Pregnancy and Peripartum Cardiomyopathy: A Meta-Analysis of Prevalence and Impact on Left Ventricular Function and Mortality
by Aleksandar Biljic-Erski, Nina Rajovic, Vedrana Pavlovic, Zoran Bukumiric, Aleksandar Rakic, Marija Rovcanin, Jelena Stulic, Radomir Anicic, Jovana Kocic, Jelena Cumic, Ksenija Markovic, Dimitrije Zdravkovic, Dejana Stanisavljevic, Srdjan Masic, Natasa Milic and Dejan Dimitrijevic
J. Clin. Med. 2025, 14(5), 1721; https://doi.org/10.3390/jcm14051721 - 4 Mar 2025
Cited by 1 | Viewed by 1509
Abstract
Background: The purpose of this meta-analysis was to examine the prevalence of hypertensive disorders of pregnancy (HDPs), particularly preeclampsia (PE), in peripartum cardiomyopathy (PPCM)-affected pregnancies, and to evaluate whether a HDP significantly alters the prognosis of PPCM, with specific reference to the recovery [...] Read more.
Background: The purpose of this meta-analysis was to examine the prevalence of hypertensive disorders of pregnancy (HDPs), particularly preeclampsia (PE), in peripartum cardiomyopathy (PPCM)-affected pregnancies, and to evaluate whether a HDP significantly alters the prognosis of PPCM, with specific reference to the recovery of left ventricular function (LVEF) and mortality. Methods: A total of 5468 potentially eligible studies were identified, and 104 were included in the meta-analysis. For pooling proportions, the inverse variance methods with logit transformation were used. Complete recovery of LVEF (>50%) and mortality were expressed by odds ratios (ORs), with 95% confidence intervals (CIs). The Peto OR (POR) was used in cases of rare events. Baseline LV function and baseline LV end-diastolic diameter (LVEDD) were summarized by the mean difference (MD) and 95% confidence interval (CI). Results: The summary estimate of the prevalence of HDPs and PE in women with PPCM was 36% and 25%, respectively. Patients with HDPs and, more specifically, PE with PPCM had a higher chance of complete recovery (OR = 1.87; 95%CI = 1.64 to 2.13; p < 0.001 and OR = 1.98; 95%CI 1.69 to 2.32; p < 0.001, respectively), a higher baseline LVEF (MD, 1.42; 95% CI 0.16 to 2.67; p = 0.03 and MD, 1.69; 95% CI 0.21 to 3.18; p = 0.03, respectively), and a smaller baseline LVEDD (MD, −1.31; 95% CI −2.50 to −0.13; p = 0.03 and MD, −2.63; 95% CI −3.75 to −1.51; p < 0.001, respectively). These results, however, did not translate into a significant difference in 12-month mortality (POR = 0.80; 95% CI = 0.57 to 1.13; p = 0.21 and POR = 1.56; 95% CI 0.90 to 2.73; p = 0.12, respectively). Conclusions: The findings of this study may contribute to evidence that can be utilized to aid in the risk stratification of patients with PPCM regarding their long-term prognoses. Full article
(This article belongs to the Special Issue Innovations in Preeclampsia)
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25 pages, 942 KB  
Article
Confidence Intervals for Function of Percentiles of Birnbaum-Saunders Distributions Containing Zero Values with Application to Wind Speed Modelling
by Warisa Thangjai, Sa-Aat Niwitpong, Suparat Niwitpong and Rada Somkhuean
Modelling 2025, 6(1), 16; https://doi.org/10.3390/modelling6010016 - 11 Feb 2025
Viewed by 787
Abstract
The Birnbaum–Saunders (BS) distribution, defined only for non-negative values, is asymmetrical. However, it can be transformed into a normal distribution, which is symmetric. The BS distribution is particularly useful for analyzing data consisting of values greater than zero. This study aims to introduce [...] Read more.
The Birnbaum–Saunders (BS) distribution, defined only for non-negative values, is asymmetrical. However, it can be transformed into a normal distribution, which is symmetric. The BS distribution is particularly useful for analyzing data consisting of values greater than zero. This study aims to introduce six approaches for constructing confidence intervals for the difference and ratio of percentiles in Birnbaum–Saunders distributions containing zero values. The proposed approaches include the generalized confidence interval (GCI) approach, the bootstrap approach, the highest posterior density (HPD) approach based on the bootstrap method, the Bayesian approach, the HPD approach based on the Bayesian method, and the method of variance estimates recovery (MOVER) approach. To assess their performance, a Monte Carlo simulation study is conducted, focusing on coverage probability and average length. The results indicate that the MOVER approach and the HPD approach based on the Bayesian method perform better than other approaches for constructing confidence intervals for the difference between percentiles. Moreover, the GCI and Bayesian approaches outperform others when constructing confidence intervals for the ratio of percentiles. Finally, daily wind speed data from the Rayong and Prachin Buri provinces are used to demonstrate the efficacy of the proposed approaches. Full article
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23 pages, 4152 KB  
Article
Extraction of Carotenoids from Pumpkin (Cucurbita moschata) and Spinach (Spinacia oleracea) Using Environmentally Friendly Deep Eutectic Solvents (DESs)
by Koray Tanrıver, Mehmet Bilgin, Selin Şahin Sevgili, İrem Toprakçı Yüksel and Ebru Kurtulbaş Şahin
AppliedChem 2025, 5(1), 2; https://doi.org/10.3390/appliedchem5010002 - 9 Jan 2025
Cited by 2 | Viewed by 2114
Abstract
The annually wasted amount of food has surpassed 1 billion metric tons. Food waste is considered as an important source for the recovery of bioactive compounds, such as carotenoids. There is a demand for antioxidants, nutraceuticals and natural colorants in various industries and [...] Read more.
The annually wasted amount of food has surpassed 1 billion metric tons. Food waste is considered as an important source for the recovery of bioactive compounds, such as carotenoids. There is a demand for antioxidants, nutraceuticals and natural colorants in various industries and carotenoids are one of the commonly used compounds that fit this description. Pumpkin and spinach waste, whose combined amount is over 2 million metric tons, contains bioactive compounds and these wasted foods could be utilized for the recovery of carotenoids. Carotenoids are hydrophobic molecules; therefore, commercial extraction processes often use highly non-polar solvents, and these are rarely environmentally friendly. The aim of this research was to develop effective extraction processes for carotenoids from pumpkin and spinach using environmentally friendly green chemicals. A series of deep eutectic solvents (DESs) composed with L-menthol and carboxylic aliphatic acids were made for the extraction of carotenoids from pumpkin (Cucurbita moschata) and spinach (Spinacia oleracea) via mechanical mixing–assisted extraction (MMAE) and homogenization-assisted extraction (HAE). Response surface methodology (RSM) and analysis of variance (ANOVA) were used to analyze the data and optimization. The DESs composed from L-menthol and propionic acid had the best effect on the extraction of total carotenoid content (TCC) (represented as β-carotene) from pumpkin and spinach via solutions with 1:2 and 1:4 molar ratios, respectively. The yield of carotenoid extraction is expressed in μg-β-carotene/g of pumpkin or spinach. Under the calculated optimum conditions, the yields are estimated to be 11.528 μg-β-carotene/g-pumpkin for the MMAE method, 8.966 μg-β-carotene/g-pumpkin for the HAE method, 16.924 μg-β-carotene/g-spinach for the MMAE method and 18.870 μg-β-carotene/g-spinach for the HAE method. Full article
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20 pages, 484 KB  
Article
Estimating the Confidence Interval for the Common Coefficient of Variation for Multiple Inverse Gaussian Distributions
by Wasana Chankham, Sa-Aat Niwitpong and Suparat Niwitpong
Symmetry 2024, 16(7), 886; https://doi.org/10.3390/sym16070886 - 11 Jul 2024
Cited by 1 | Viewed by 1676
Abstract
The inverse Gaussian distribution is a two-parameter continuous probability distribution with positive support, which is used to account for the asymmetry of the positively skewed data that are often seen when modeling environmental phenomena, such as PM2.5 levels. The coefficient of [...] Read more.
The inverse Gaussian distribution is a two-parameter continuous probability distribution with positive support, which is used to account for the asymmetry of the positively skewed data that are often seen when modeling environmental phenomena, such as PM2.5 levels. The coefficient of variation is often used to assess variability within datasets, and the common coefficient of variation of several independent samples can be used to draw inferences between them. Herein, we provide estimation methods for the confidence interval for the common coefficient of variation of multiple inverse Gaussian distributions by using the generalized confidence interval (GCI), the fiducial confidence interval (FCI), the adjusted method of variance estimates recovery (MOVER), and the Bayesian credible interval (BCI) and highest posterior density (HPD) methods using the Jeffreys prior rule. The estimation methods were evaluated based on their coverage probabilities and average lengths, using a Monte Carlo simulation study. The findings indicate the superiority of the GCI over the other methods for nearly all of the scenarios considered. This was confirmed for a real-world scenario involving PM2.5 data from three provinces in northeastern Thailand that followed inverse Gaussian distributions. Full article
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19 pages, 488 KB  
Article
The Simultaneous Confidence Interval for the Ratios of the Coefficients of Variation of Multiple Inverse Gaussian Distributions and Its Application to PM2.5 Data
by Wasana Chankham, Sa-Aat Niwitpong and Suparat Niwitpong
Symmetry 2024, 16(3), 331; https://doi.org/10.3390/sym16030331 - 8 Mar 2024
Cited by 3 | Viewed by 1517
Abstract
Due to slash/burn agricultural activity and frequent forest fires, PM2.5 has become a significant air pollution problem in Thailand, especially in the north and north east regions. Since its dispersion differs both spatially and temporally, estimating PM2.5 concentrations discretely [...] Read more.
Due to slash/burn agricultural activity and frequent forest fires, PM2.5 has become a significant air pollution problem in Thailand, especially in the north and north east regions. Since its dispersion differs both spatially and temporally, estimating PM2.5 concentrations discretely by area, for which the inverse Gaussian distribution is suitable, can provide valuable information. Herein, we provide derivations of the simultaneous confidence interval for the ratios of the coefficients of variation of multiple inverse Gaussian distributions using the generalized confidence interval, the Bayesian interval based on the Jeffreys’ rule prior, the fiducial interval, and the method of variance estimates recovery. The efficacies of these methods were compared by considering the coverage probability and average length obtained from simulation results of daily PM2.5 datasets. The findings indicate that in most instances, the fiducial method with the highest posterior density demonstrated a superior performance. However, in certain scenarios, the Bayesian approach using the Jeffreys’ rule prior for the highest posterior density yielded favorable results. Full article
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17 pages, 618 KB  
Article
Simultaneous Confidence Intervals for All Pairwise Differences between Means of Weibull Distributions
by Manussaya La-ongkaew, Sa-Aat Niwitpong and Suparat Niwitpong
Symmetry 2023, 15(12), 2142; https://doi.org/10.3390/sym15122142 - 1 Dec 2023
Cited by 2 | Viewed by 1995
Abstract
The Weibull distribution is a continuous probability distribution that finds wide application in various fields for analyzing real-world data. Specifically, wind speed data often adhere to the Weibull distribution. In our study, our aim is to compare the mean wind speed datasets from [...] Read more.
The Weibull distribution is a continuous probability distribution that finds wide application in various fields for analyzing real-world data. Specifically, wind speed data often adhere to the Weibull distribution. In our study, our aim is to compare the mean wind speed datasets from different areas in Thailand. To achieve this, we proposed simultaneous confidence intervals for all pairwise differences between the means of Weibull distributions. The generalized confidence interval (GCI), method of variance estimates recovery (MOVER), and a Bayesian approach, utilizing both gamma and uniform prior distributions, are proposed to construct simultaneous confidence intervals. Through simulations, we find that the Bayesian highest posterior density (HPD) interval using a gamma prior distribution demonstrates satisfactory performance, while the GCI proves to be a viable alternative. Finally, we applied these proposed approaches to real wind speed data in northeastern and southern Thailand to illustrate their effectiveness and practicality. Full article
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17 pages, 26690 KB  
Article
DRFM Repeater Jamming Suppression Method Based on Joint Range-Angle Sparse Recovery and Beamforming for Distributed Array Radar
by Bowen Han, Xiaodong Qu, Xiaopeng Yang, Zhengyan Zhang and Wolin Li
Remote Sens. 2023, 15(13), 3449; https://doi.org/10.3390/rs15133449 - 7 Jul 2023
Cited by 4 | Viewed by 2286
Abstract
Distributed array radar achieves high angular resolution and measurement accuracy, which could provide a solution to suppress digital radio frequency memory (DRFM) repeater jamming. However, owing to the large aperture of a distributed radar, the far-field plane wave assumption is no longer satisfied. [...] Read more.
Distributed array radar achieves high angular resolution and measurement accuracy, which could provide a solution to suppress digital radio frequency memory (DRFM) repeater jamming. However, owing to the large aperture of a distributed radar, the far-field plane wave assumption is no longer satisfied. Consequently, traditional adaptive beamforming methods cannot work effectively due to mismatched steering vectors. To address this issue, a DRFM repeater jamming suppression method based on joint range-angle sparse recovery and beamforming for distributed array radar is proposed in this paper. First, the steering vectors of the distributed array are reconstructed according to the spherical wave model under near-field conditions. Then, a joint range-angle sparse dictionary is generated using reconstructed steering vectors, and the range-angle position of jamming is estimated using the weighted L1-norm singular value decomposition (W-L1-SVD) algorithm. Finally, beamforming with joint range-angle nulling is implemented based on the linear constrained minimum variance (LCMV) algorithm for jamming suppression. The performance and effectiveness of proposed method is validated by simulations and experiments on an actual ground-based distributed array radar system. Full article
(This article belongs to the Special Issue Advanced Radar Signal Processing and Applications)
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24 pages, 358 KB  
Article
Confidence Intervals for Mean and Difference between Means of Delta-Lognormal Distributions Based on Left-Censored Data
by Warisa Thangjai and Sa-Aat Niwitpong
Symmetry 2023, 15(6), 1216; https://doi.org/10.3390/sym15061216 - 7 Jun 2023
Cited by 1 | Viewed by 2485
Abstract
A delta-lognormal distribution consists of zero and positive values. The positive values follow a lognormal distribution, which is an asymmetric distribution. It is well known that the logarithm of these values follows a normal distribution, which is a symmetric distribution. The delta-lognormal distribution [...] Read more.
A delta-lognormal distribution consists of zero and positive values. The positive values follow a lognormal distribution, which is an asymmetric distribution. It is well known that the logarithm of these values follows a normal distribution, which is a symmetric distribution. The delta-lognormal distribution is used in medical and environmental sciences. This study considers the challenges of constructing confidence intervals for the mean and difference between means of delta-lognormal distributions containing left-censored data and applies them to compare two daily rainfall average areas in Thailand. Three different approaches for constructing confidence intervals for the mean of the delta-lognormal distribution containing left-censored data, based on the generalized confidence interval approach, the Bayesian approach, and the parametric bootstrap approach, are developed. Moreover, four different approaches for constructing confidence intervals for the difference between means of delta-lognormal distributions containing left-censored data, based on the generalized confidence interval approach, the Bayesian approach, the parametric bootstrap approach, and the method of variance estimates recovery approach, are considered. The performance of the proposed confidence intervals is evaluated by Monte Carlo simulation. The simulation studies indicate that the Bayesian approach can be considered as an alternative to construct a credible interval for the mean of the delta-lognormal distribution containing left-censored data. Additionally, the generalized confidence interval and Bayesian approaches can be recommended as alternatives to estimate the confidence interval for the difference between means of delta-lognormal distributions containing left-censored data. All approaches are illustrated using the daily rainfall data from Chiang Mai and Lampang provinces in Thailand. Full article
19 pages, 23018 KB  
Article
Comparison of GRACE/GRACE-FO Spherical Harmonic and Mascon Products in Interpreting GNSS Vertical Loading Deformations over the Amazon Basin
by Pengfei Wang, Song-Yun Wang, Jin Li, Jianli Chen and Zhaoxiang Qi
Remote Sens. 2023, 15(1), 252; https://doi.org/10.3390/rs15010252 - 1 Jan 2023
Cited by 7 | Viewed by 4483
Abstract
We compute the vertical displacements in the Amazon Basin using the Gravity Recovery and Climate Experiment (GRACE) and GRACE Follow-On (GRACE-FO) observations, including both the gravity spherical harmonic (SH) solutions from the Center for Space Research (CSR), GeoForschungsZentrum (GFZ) and Jet Propulsion Laboratory [...] Read more.
We compute the vertical displacements in the Amazon Basin using the Gravity Recovery and Climate Experiment (GRACE) and GRACE Follow-On (GRACE-FO) observations, including both the gravity spherical harmonic (SH) solutions from the Center for Space Research (CSR), GeoForschungsZentrum (GFZ) and Jet Propulsion Laboratory (JPL) and mascons from CSR, JPL and Goddard Space Flight Center (GSFC). The correlation coefficients, annual amplitude and root mean squares (RMS) reductions are calculated to assess the agreements between the GRACE/GRACE-FO and Global Navigation Satellite System (GNSS) vertical displacements at 22 selected GNSS stations. For the six GRACE/GRACE-FO products (i.e., CSR SH, GFZ SH, JPL SH, CSR mascon, GSFC mascon and JPL mascon), the mean annual amplitude reductions are 77.6%, 76.4%, 76.3%, 78.6%, 78.5% and 76.6%, respectively, the corresponding mean RMS reductions are 63.2%, 61.7%, 62.3%, 64.9%, 65.3% and 63.8%, respectively, and the mean correlation coefficients are all over 0.93. On the whole, mascon solutions agree slightly better with GNSS solutions than SH solutions do. The CSR SH and the GSFC mascon solutions show the best agreements with the GNSS solution among the 3 SH and 3 mascon products, respectively. We estimate GRACE/GRACE-FO noises using the three-cornered hat (TCH) method and find that the CSR SH and GSFC mascons also have the smallest noise variances among the SH and mascon products, respectively. By analyzing the GNSS stations from the central and southern Amazon Basin, we find that: (1) the RMS reductions when the mascon solutions are removed from GNSS height series are slightly larger than those using the SH solutions in the center, while in south all the RMS reductions are fairly close; (2) for both SH solutions and mascon solutions, the correlation coefficients in the center are slightly larger than those in the south, but conversely, the mean annual amplitude reductions in the center are much smaller than those in the south. Full article
(This article belongs to the Special Issue GRACE for Earth System Mass Change: Monitoring and Measurement)
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15 pages, 495 KB  
Article
Estimation of the Confidence Interval for the Ratio of the Coefficients of Variation of Two Weibull Distributions and Its Application to Wind Speed Data
by Manussaya La-ongkaew, Sa-Aat Niwitpong and Suparat Niwitpong
Symmetry 2023, 15(1), 46; https://doi.org/10.3390/sym15010046 - 24 Dec 2022
Cited by 9 | Viewed by 2077
Abstract
The Weibull distribution, one of the most significant distributions with applications in numerous fields, is associated with numerous distributions such as generalized gamma distribution, exponential distribution, and Rayleigh distribution, which are asymmetric. Nevertheless, it shares a close relationship with a normal distribution where [...] Read more.
The Weibull distribution, one of the most significant distributions with applications in numerous fields, is associated with numerous distributions such as generalized gamma distribution, exponential distribution, and Rayleigh distribution, which are asymmetric. Nevertheless, it shares a close relationship with a normal distribution where a process of transformation allows them to become symmetric. The Weibull distribution is commonly used to study the failure of components and phenomena. It has been applied to a variety of scenarios, including failure time, claims amount, unemployment duration, survival time, and especially wind speed data. A suitable area for installing a wind turbine requires a wind speed that is both sufficiently high and consistent, and so comparing the variation in wind speed in two areas is eminently desirable. In this paper, methods to estimate the confidence interval for the ratio of the coefficients of variation of two Weibull distributions are proposed and applied to compare the variation in wind speed in two areas. The methods are the generalized confidence interval (GCI), the method of variance estimates recovery (MOVER), and Bayesian methods based on the gamma and uniform priors. The Bayesian methods comprise the equal-tailed confidence interval and the highest posterior density (HPD) interval. The effectiveness of the methods was evaluated in terms of their coverage probabilities and expected lengths and also empirically applied to wind speed datasets from two different areas in Thailand. The results indicate that the HPD interval based on the uniform prior outperformed the others in most of the scenarios tested and so it is suggested for estimating the confidence interval for the ratio of the coefficients of variation of two Weibull distributions. Full article
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17 pages, 1732 KB  
Article
Simultaneous Confidence Intervals for All Pairwise Differences between the Coefficients of Variation of Multiple Birnbaum–Saunders Distributions
by Wisunee Puggard, Sa-Aat Niwitpong and Suparat Niwitpong
Symmetry 2022, 14(12), 2666; https://doi.org/10.3390/sym14122666 - 16 Dec 2022
Cited by 3 | Viewed by 1639
Abstract
In situations where several positive random variables cannot be described using symmetrical distributions, a positively asymmetric distribution which has garnered much attention for studying them is the Birnbaum-Saunders (BS) distribution. This distribution was originally proposed to study fatigue over time in materials and [...] Read more.
In situations where several positive random variables cannot be described using symmetrical distributions, a positively asymmetric distribution which has garnered much attention for studying them is the Birnbaum-Saunders (BS) distribution. This distribution was originally proposed to study fatigue over time in materials and has become widely employed for reliability and fatigue studies. In statistics, the coefficient of variation (CV) is employed to measure relative variation. Furthermore, comparing the CVs of several samples from BS distributions is an important approach to assess the variation among them. Herein, we propose estimation methods for the simultaneous confidence intervals (SCIs) for all pairwise differences between the CVs of multiple BS distributions based on the percentile bootstrap, the generalized confidence interval (GCI), the method of variance estimates recovery (MOVER) based on the asymptotic confidence interval (ACI) and GCI, Bayesian credible interval, and the highest posterior density (HPD) interval. The coverage probabilities and average lengths of the proposed methods were examined via a simulation study to determine their performance. The results demonstrate that GCI and the MOVER based on the GCI method provided satisfactory performances in almost every case studied. Particulate matter ≤ 2.5 μm (PM2.5) concentration datasets from three areas in northern Thailand were used to illustrate the effectiveness of the proposed methods. Full article
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22 pages, 1453 KB  
Article
Simultaneous Confidence Intervals for the Ratios of the Means of Zero-Inflated Gamma Distributions and Its Application
by Theerapong Kaewprasert, Sa-Aat Niwitpong and Suparat Niwitpong
Mathematics 2022, 10(24), 4724; https://doi.org/10.3390/math10244724 - 12 Dec 2022
Cited by 4 | Viewed by 1637
Abstract
Heavy rain in September (the middle of the rainy season in Thailand) can cause unexpected events and natural disasters such as flooding in many areas of the country. Rainfall series that contain both zero and positive values belong to the zero-inflated gamma distribution, [...] Read more.
Heavy rain in September (the middle of the rainy season in Thailand) can cause unexpected events and natural disasters such as flooding in many areas of the country. Rainfall series that contain both zero and positive values belong to the zero-inflated gamma distribution, which combines the binomial and gamma distributions. Precipitation in various areas of a country can be estimated by using simultaneous confidence intervals (CIs) for the ratios of the means of multiple zero-inflated gamma populations. Herein, we propose six simultaneous CIs constructed using the fiducial generalized CI method, Bayesian and highest posterior density (HPD) interval methods based on the Jeffreys’rule or uniform prior, and method of variance estimates recovery (MOVER). The performances of the proposed simultaneous CI methods were evaluated using a Monte Carlo simulation in terms of the coverage probabilities and expected lengths. The results from a comparative simulation study show that the HPD interval based on the Jeffreys’rule prior performed the best in most cases, while in some situations, the fiducial generalized CI performed well. All of the methods were applied to estimate the simultaneous CIs for the ratios of the means of natural rainfall data from six regions in Thailand. Full article
(This article belongs to the Special Issue Current Developments in Theoretical and Applied Statistics)
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14 pages, 327 KB  
Article
Confidence Intervals for Common Coefficient of Variation of Several Birnbaum–Saunders Distributions
by Wisunee Puggard, Sa-Aat Niwitpong and Suparat Niwitpong
Symmetry 2022, 14(10), 2101; https://doi.org/10.3390/sym14102101 - 9 Oct 2022
Cited by 9 | Viewed by 1931
Abstract
The Birnbaum–Saunders (BS) distribution, also known as the fatigue life distribution, is right-skewed and used to model the failure times of industrial components. It has received much attention due to its attractive properties and its relationship to the normal distribution (which is symmetric). [...] Read more.
The Birnbaum–Saunders (BS) distribution, also known as the fatigue life distribution, is right-skewed and used to model the failure times of industrial components. It has received much attention due to its attractive properties and its relationship to the normal distribution (which is symmetric). Furthermore, the coefficient of variation (CV) is commonly used to analyze variation within a dataset. In some situations, the independent samples are collected from different instruments or laboratories. Consequently, it is of importance to make inference for the common CV. To this end, confidence intervals based on the generalized confidence interval (GCI), method of variance estimates recovery (MOVER), large-sample (LS), Bayesian credible interval (BayCrI), and highest posterior density interval (HPDI) methods are proposed herein to estimate the common CV of several BS distributions. Their performances in terms of their coverage probabilities and average lengths were investigated by using Monte Carlo simulation. The simulation results indicate that the HPDI-based confidence interval outperformed the others in all of the investigated scenarios. Finally, the efficacies of the proposed confidence intervals are illustrated by applying them to real datasets of PM10 (particulate matter ≤ 10 μm) concentrations from three pollution monitoring stations in Chiang Mai, Thailand. Full article
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