Prostate cancer occurs when cells in the prostate gland grow out of control. Almost all prostate cancers are adenocarcinomas. The survival rate for prostate cancer patients depends on the screening outcome, which can be either no prostate cancer, early detection, and late detection or advanced stage detection. The main objective of this study was to estimate the risk factors affecting the screening outcome of prostate cancer. With ordinal outcomes, a generalized Bayesian ordinal logistic model was considered in the analysis. The generalized Bayesian ordinal logistic model helped in estimation of coefficient parameters of the risk factors affecting each level of prostate cancer-screening outcomes. In the study, positive coefficients, that is, β k > 0 , indicated that the higher values on the explanatory variable increased the chances of the respondent being in a higher category of the dependent variable than the current one, while the negative coefficients, that is, β k < 0 , signified that the higher values on the explanatory variable increased the likelihood of being in the current or lower category of prostate cancer. For instance, from the analysis, positive or negative outcomes of prostate cancer showed that an increase in weight lowered the chances of an individual having the disease.
{"title":"Estimation of Risk Factors Affecting Screening Outcomes of Prostate Cancer Using the Bayesian Ordinal Logistic Model","authors":"J. Sirengo, D. Alilah, D. Mbete, R. Keli","doi":"10.1155/2023/4987764","DOIUrl":"https://doi.org/10.1155/2023/4987764","url":null,"abstract":"Prostate cancer occurs when cells in the prostate gland grow out of control. Almost all prostate cancers are adenocarcinomas. The survival rate for prostate cancer patients depends on the screening outcome, which can be either no prostate cancer, early detection, and late detection or advanced stage detection. The main objective of this study was to estimate the risk factors affecting the screening outcome of prostate cancer. With ordinal outcomes, a generalized Bayesian ordinal logistic model was considered in the analysis. The generalized Bayesian ordinal logistic model helped in estimation of coefficient parameters of the risk factors affecting each level of prostate cancer-screening outcomes. In the study, positive coefficients, that is, \u0000 \u0000 \u0000 \u0000 β\u0000 \u0000 \u0000 k\u0000 \u0000 \u0000 >\u0000 0\u0000 \u0000 , indicated that the higher values on the explanatory variable increased the chances of the respondent being in a higher category of the dependent variable than the current one, while the negative coefficients, that is, \u0000 \u0000 \u0000 \u0000 β\u0000 \u0000 \u0000 k\u0000 \u0000 \u0000 <\u0000 0\u0000 \u0000 , signified that the higher values on the explanatory variable increased the likelihood of being in the current or lower category of prostate cancer. For instance, from the analysis, positive or negative outcomes of prostate cancer showed that an increase in weight lowered the chances of an individual having the disease.","PeriodicalId":44760,"journal":{"name":"Journal of Probability and Statistics","volume":null,"pages":null},"PeriodicalIF":1.1,"publicationDate":"2023-03-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46516343","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Background. Survival analysis attracted the attention of different scientists from various domains such as engineering, health, and social sciences. It has been widely exploited in clinical trials when comparing different treatments looking at their survival probabilities. Kaplan–Meier curves plotted from the Kaplan–Meier estimates of survival probabilities are used to depict the general image for such situations. Methods. The weighted log-rank test has been dealt with by suggesting different weight functions which give specific strength in specific situations. In this work, we proposed a new weight function comprising all numbers at risk, i.e., the overall number at risk and the separate numbers at risk in the groups under study, to detect late differences between survival curves. Results. The new test has been found to be a good alternative after the FH (0, 1) test in detecting late differences, and it outperformed all tests in case of small samples and heavy censoring rates according to the simulation studies. The new test kept the same strength when applied to real data where it showed itself to be among the powerful ones or even outperforms all other tests under consideration. Conclusion. As the new test stays stronger in the case of small samples and heavy censoring rates, it may be a better choice whenever targeting the detection of late differences between the survival curves.
{"title":"New Test for the Comparison of Survival Curves to Detect Late Differences","authors":"Ildephonse Nizeyimana, S. Mwalili, G. Orwa","doi":"10.1155/2023/9945446","DOIUrl":"https://doi.org/10.1155/2023/9945446","url":null,"abstract":"Background. Survival analysis attracted the attention of different scientists from various domains such as engineering, health, and social sciences. It has been widely exploited in clinical trials when comparing different treatments looking at their survival probabilities. Kaplan–Meier curves plotted from the Kaplan–Meier estimates of survival probabilities are used to depict the general image for such situations. Methods. The weighted log-rank test has been dealt with by suggesting different weight functions which give specific strength in specific situations. In this work, we proposed a new weight function comprising all numbers at risk, i.e., the overall number at risk and the separate numbers at risk in the groups under study, to detect late differences between survival curves. Results. The new test has been found to be a good alternative after the FH (0, 1) test in detecting late differences, and it outperformed all tests in case of small samples and heavy censoring rates according to the simulation studies. The new test kept the same strength when applied to real data where it showed itself to be among the powerful ones or even outperforms all other tests under consideration. Conclusion. As the new test stays stronger in the case of small samples and heavy censoring rates, it may be a better choice whenever targeting the detection of late differences between the survival curves.","PeriodicalId":44760,"journal":{"name":"Journal of Probability and Statistics","volume":null,"pages":null},"PeriodicalIF":1.1,"publicationDate":"2023-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48477253","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
M. Choudhary, S. P. Kour, Sunil Kumar, C. Bouza, Agustín Santiago
In the context of a sample survey, the collection of information on a sensitive variable is difficult, which may cause nonresponse and measurement errors. Due to this, the estimates can be biased and the variation may increase. To overcome this difficulty, we propose an estimator for the estimation of a sensitive variable by using auxiliary information in the presence of nonresponse and measurement errors simultaneously. The properties of the proposed estimators have been studied, and the results have been compared with those of the usual complete response estimator. Theoretical results have been verified through a simulation study using an artificial population and two real-life applications. With the outcomes of the proposed estimator, a suitable recommendation has been made to the survey statisticians for their real-life application.
{"title":"Using ORRT Models for Mean Estimation under Nonresponse and Measurement Errors in Stratified Successive Sampling","authors":"M. Choudhary, S. P. Kour, Sunil Kumar, C. Bouza, Agustín Santiago","doi":"10.1155/2023/1340068","DOIUrl":"https://doi.org/10.1155/2023/1340068","url":null,"abstract":"In the context of a sample survey, the collection of information on a sensitive variable is difficult, which may cause nonresponse and measurement errors. Due to this, the estimates can be biased and the variation may increase. To overcome this difficulty, we propose an estimator for the estimation of a sensitive variable by using auxiliary information in the presence of nonresponse and measurement errors simultaneously. The properties of the proposed estimators have been studied, and the results have been compared with those of the usual complete response estimator. Theoretical results have been verified through a simulation study using an artificial population and two real-life applications. With the outcomes of the proposed estimator, a suitable recommendation has been made to the survey statisticians for their real-life application.","PeriodicalId":44760,"journal":{"name":"Journal of Probability and Statistics","volume":null,"pages":null},"PeriodicalIF":1.1,"publicationDate":"2023-02-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42738081","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
O. L. Alcaraz López, E. M. García Fernández, M. Latva-aho
The linear combination of Student’s t random variables (RVs) appears in many statistical applications. Unfortunately, the Student’s t distribution is not closed under convolution, thus, deriving an exact and general distribution for the linear combination of K Student’s t RVs is infeasible, which motivates a fitting/approximation approach. Here, we focus on the scenario where the only constraint is that the number of degrees of freedom of each t − RV is greater than two. Notice that since the odd moments/cumulants of the Student’s t distribution are zero and the even moments/cumulants do not exist when their order is greater than the number of degrees of freedom, it becomes impossible to use conventional approaches based on moments/cumulants of order one or higher than two. To circumvent this issue, herein we propose fitting such a distribution to that of a scaled Student’s t RV by exploiting the second moment together with either the first absolute moment or the characteristic function (CF). For the fitting based on the absolute moment, we depart from the case of the linear combination of K = 2 Student’s t RVs and then generalize to K ≥ 2 through a simple iterative procedure. Meanwhile, the CF-based fitting is direct, but its accuracy (measured in terms of the Bhattacharyya distance metric) depends on the CF parameter configuration, for which we propose a simple but accurate approach. We numerically show that the CF-based fitting usually outperforms the absolute moment-based fitting and that both the scale and number of degrees of freedom of the fitting distribution increase almost linearly with K .
学生随机变量(RVs)的线性组合出现在许多统计应用中。不幸的是，学生的t分布在卷积下不是封闭的，因此，为K个学生的t个rv的线性组合导出一个精确的和一般的分布是不可实现的，这激发了拟合/近似方法。这里，我们关注的场景是，唯一的约束条件是每个t - RV的自由度大于2。请注意，由于学生t分布的奇数矩/累积量为零，而当它们的阶数大于自由度数时，偶数矩/累积量不存在，因此不可能使用基于一阶或高于二阶的矩/累积量的传统方法。为了避免这个问题，本文提出通过利用第二矩和第一绝对矩或特征函数(CF)来拟合缩放后的Student 's t RV分布。对于基于绝对矩的拟合，我们从K = 2个学生的t rv线性组合的情况出发，通过简单的迭代过程推广到K≥2。同时，基于CF的拟合是直接的，但其精度(以Bhattacharyya距离度量衡量)取决于CF参数的配置，为此我们提出了一种简单而准确的方法。数值计算表明，基于cf的拟合通常优于基于绝对矩的拟合，并且拟合分布的规模和自由度数量几乎随K线性增加。
{"title":"Fitting the Distribution of Linear Combinations of \u0000 t\u0000 −\u0000 Variables with more than 2 Degrees of Freedom","authors":"O. L. Alcaraz López, E. M. García Fernández, M. Latva-aho","doi":"10.1155/2023/9967290","DOIUrl":"https://doi.org/10.1155/2023/9967290","url":null,"abstract":"The linear combination of Student’s \u0000 \u0000 t\u0000 \u0000 random variables (RVs) appears in many statistical applications. Unfortunately, the Student’s \u0000 \u0000 t\u0000 \u0000 distribution is not closed under convolution, thus, deriving an exact and general distribution for the linear combination of \u0000 \u0000 K\u0000 \u0000 Student’s \u0000 \u0000 t\u0000 \u0000 RVs is infeasible, which motivates a fitting/approximation approach. Here, we focus on the scenario where the only constraint is that the number of degrees of freedom of each \u0000 \u0000 t\u0000 −\u0000 \u0000 RV is greater than two. Notice that since the odd moments/cumulants of the Student’s \u0000 \u0000 t\u0000 \u0000 distribution are zero and the even moments/cumulants do not exist when their order is greater than the number of degrees of freedom, it becomes impossible to use conventional approaches based on moments/cumulants of order one or higher than two. To circumvent this issue, herein we propose fitting such a distribution to that of a scaled Student’s \u0000 \u0000 t\u0000 \u0000 RV by exploiting the second moment together with either the first absolute moment or the characteristic function (CF). For the fitting based on the absolute moment, we depart from the case of the linear combination of \u0000 \u0000 K\u0000 =\u0000 2\u0000 \u0000 Student’s \u0000 \u0000 t\u0000 \u0000 RVs and then generalize to \u0000 \u0000 K\u0000 ≥\u0000 2\u0000 \u0000 through a simple iterative procedure. Meanwhile, the CF-based fitting is direct, but its accuracy (measured in terms of the Bhattacharyya distance metric) depends on the CF parameter configuration, for which we propose a simple but accurate approach. We numerically show that the CF-based fitting usually outperforms the absolute moment-based fitting and that both the scale and number of degrees of freedom of the fitting distribution increase almost linearly with \u0000 \u0000 K\u0000 \u0000 .","PeriodicalId":44760,"journal":{"name":"Journal of Probability and Statistics","volume":null,"pages":null},"PeriodicalIF":1.1,"publicationDate":"2023-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46839023","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Method comparison studies mainly focus on determining if the two methods of measuring a continuous variable are agreeable enough to be used interchangeably. Typically, a standard mixed-effects model uses to model the method comparison data that assume normality for both random effects and errors. However, these assumptions are frequently violated in practice due to the skewness and heavy tails. In particular, the biases of the methods may vary with the extent of measurement. Thus, we propose a methodology for method comparison data to deal with these issues in the context of the measurement error model (MEM) that assumes a skew- t (ST) distribution for the true covariates and centered Student’s t (cT) distribution for the errors with known error variances, named STcT-MEM. An expectation conditional maximization (ECM) algorithm is used to compute the maximum likelihood (ML) estimates. The simulation study is performed to validate the proposed methodology. This methodology is illustrated by analyzing gold particle data and then compared with the standard measurement error model (SMEM). The likelihood ratio (LR) test is used to identify the most appropriate model among the above models. In addition, the total deviation index (TDI) and concordance correlation coefficient (CCC) were used to check the agreement between the methods. The findings suggest that our proposed framework for analyzing unreplicated method comparison data with asymmetry and heavy tails works effectively for modest and large samples.
{"title":"An Improved Measurement Error Model for Analyzing Unreplicated Method Comparison Data under Asymmetric Heavy-Tailed Distributions","authors":"Jeevana Duwarahan, Lakshika S. Nawarathna","doi":"10.1155/2022/3453912","DOIUrl":"https://doi.org/10.1155/2022/3453912","url":null,"abstract":"Method comparison studies mainly focus on determining if the two methods of measuring a continuous variable are agreeable enough to be used interchangeably. Typically, a standard mixed-effects model uses to model the method comparison data that assume normality for both random effects and errors. However, these assumptions are frequently violated in practice due to the skewness and heavy tails. In particular, the biases of the methods may vary with the extent of measurement. Thus, we propose a methodology for method comparison data to deal with these issues in the context of the measurement error model (MEM) that assumes a skew-\u0000 \u0000 t\u0000 \u0000 (ST) distribution for the true covariates and centered Student’s \u0000 \u0000 t\u0000 \u0000 (cT) distribution for the errors with known error variances, named STcT-MEM. An expectation conditional maximization (ECM) algorithm is used to compute the maximum likelihood (ML) estimates. The simulation study is performed to validate the proposed methodology. This methodology is illustrated by analyzing gold particle data and then compared with the standard measurement error model (SMEM). The likelihood ratio (LR) test is used to identify the most appropriate model among the above models. In addition, the total deviation index (TDI) and concordance correlation coefficient (CCC) were used to check the agreement between the methods. The findings suggest that our proposed framework for analyzing unreplicated method comparison data with asymmetry and heavy tails works effectively for modest and large samples.","PeriodicalId":44760,"journal":{"name":"Journal of Probability and Statistics","volume":null,"pages":null},"PeriodicalIF":1.1,"publicationDate":"2022-12-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43032382","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
In this paper, we apply the random time change by the real white noise to deterministic dynamical systems. We prove that the obtained random dynamical systems are solutions of some stochastic differential equations whenever the deterministic dynamical systems are solutions of ordinary differential equations.
{"title":"On Random Dynamical Systems Generated by White Noise Time Change of Deterministic Dynamical Systems","authors":"M. Hmissi, F. Mokchaha","doi":"10.1155/2022/3881486","DOIUrl":"https://doi.org/10.1155/2022/3881486","url":null,"abstract":"In this paper, we apply the random time change by the real white noise to deterministic dynamical systems. We prove that the obtained random dynamical systems are solutions of some stochastic differential equations whenever the deterministic dynamical systems are solutions of ordinary differential equations.","PeriodicalId":44760,"journal":{"name":"Journal of Probability and Statistics","volume":null,"pages":null},"PeriodicalIF":1.1,"publicationDate":"2022-12-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"64777174","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
C. A. Mushagalusa, A. B. Fandohan, R. G. Glèlè Kakaï
Machine learning algorithms, especially random forests (RFs), have become an integrated part of the modern scientific methodology and represent an efficient alternative to conventional parametric algorithms. This study aimed to assess the influence of data features and overdispersion on RF regression performance. We assessed the effect of types of predictors (100, 75, 50, and 20% continuous, and 100% categorical), the number of predictors (p = 816 and 24), and the sample size (N = 50, 250, and 1250) on RF parameter settings. We also compared RF performance to that of classical generalized linear models (Poisson, negative binomial, and zero-inflated Poisson) and the linear model applied to log-transformed data. Two real datasets were analysed to demonstrate the usefulness of RF for overdispersed data modelling. Goodness-of-fit statistics such as root mean square error (RMSE) and biases were used to determine RF accuracy and validity. Results revealed that the number of variables to be randomly selected for each split, the proportion of samples to train the model, the minimal number of samples within each terminal node, and RF regression performance are not influenced by the sample size, number, and type of predictors. However, the ratio of observations to the number of predictors affects the stability of the best RF parameters. RF performs well for all types of covariates and different levels of dispersion. The magnitude of dispersion does not significantly influence RF predictive validity. In contrast, its predictive accuracy is significantly influenced by the magnitude of dispersion in the response variable, conditional on the explanatory variables. RF has performed almost as well as the models of the classical Poisson family in the presence of overdispersion. Given RF’s advantages, it is an appropriate statistical alternative for counting data.
{"title":"Random Forests in Count Data Modelling: An Analysis of the Influence of Data Features and Overdispersion on Regression Performance","authors":"C. A. Mushagalusa, A. B. Fandohan, R. G. Glèlè Kakaï","doi":"10.1155/2022/2833537","DOIUrl":"https://doi.org/10.1155/2022/2833537","url":null,"abstract":"Machine learning algorithms, especially random forests (RFs), have become an integrated part of the modern scientific methodology and represent an efficient alternative to conventional parametric algorithms. This study aimed to assess the influence of data features and overdispersion on RF regression performance. We assessed the effect of types of predictors (100, 75, 50, and 20% continuous, and 100% categorical), the number of predictors (p = 816 and 24), and the sample size (N = 50, 250, and 1250) on RF parameter settings. We also compared RF performance to that of classical generalized linear models (Poisson, negative binomial, and zero-inflated Poisson) and the linear model applied to log-transformed data. Two real datasets were analysed to demonstrate the usefulness of RF for overdispersed data modelling. Goodness-of-fit statistics such as root mean square error (RMSE) and biases were used to determine RF accuracy and validity. Results revealed that the number of variables to be randomly selected for each split, the proportion of samples to train the model, the minimal number of samples within each terminal node, and RF regression performance are not influenced by the sample size, number, and type of predictors. However, the ratio of observations to the number of predictors affects the stability of the best RF parameters. RF performs well for all types of covariates and different levels of dispersion. The magnitude of dispersion does not significantly influence RF predictive validity. In contrast, its predictive accuracy is significantly influenced by the magnitude of dispersion in the response variable, conditional on the explanatory variables. RF has performed almost as well as the models of the classical Poisson family in the presence of overdispersion. Given RF’s advantages, it is an appropriate statistical alternative for counting data.","PeriodicalId":44760,"journal":{"name":"Journal of Probability and Statistics","volume":null,"pages":null},"PeriodicalIF":1.1,"publicationDate":"2022-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44361782","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
In the Fundamental Review of the Trading Book (FRTB), the latest regulation for minimum capital market risk requirements, one of the major changes, is replacing the Incremental Risk Charge (IRC) with the Default Risk Charge (DRC). The DRC measures only the default and does not consider the migration rating risk. The second new change in this approach was that the DRC now includes equity assets, contrary to the IRC. This paper studies DRC modeling under the Internal Model Approach (IMA) and the regulator conditions that every DRC component must respect. The FRTB presents the DRC measurement as Value at Risk (VaR) over a one-year horizon, with the quantile equal to 99.9%. We use multifactor adjustment to measure the DRC and compare it with the Monte Carlo Model to understand how the approach fits. We then define concentration in the DRC and propose two methods to quantify the concentration risk: the Ad Hoc and Add-On methods. Finally, we study the behavior of the DRC with respect to the concentration risk.
{"title":"Mathematical Modeling of Concentration Risk under the Default Risk Charge Using Probability and Statistics Theory","authors":"Badreddine Slime","doi":"10.1155/2022/3063505","DOIUrl":"https://doi.org/10.1155/2022/3063505","url":null,"abstract":"In the Fundamental Review of the Trading Book (FRTB), the latest regulation for minimum capital market risk requirements, one of the major changes, is replacing the Incremental Risk Charge (IRC) with the Default Risk Charge (DRC). The DRC measures only the default and does not consider the migration rating risk. The second new change in this approach was that the DRC now includes equity assets, contrary to the IRC. This paper studies DRC modeling under the Internal Model Approach (IMA) and the regulator conditions that every DRC component must respect. The FRTB presents the DRC measurement as Value at Risk (VaR) over a one-year horizon, with the quantile equal to 99.9%. We use multifactor adjustment to measure the DRC and compare it with the Monte Carlo Model to understand how the approach fits. We then define concentration in the DRC and propose two methods to quantify the concentration risk: the Ad Hoc and Add-On methods. Finally, we study the behavior of the DRC with respect to the concentration risk.","PeriodicalId":44760,"journal":{"name":"Journal of Probability and Statistics","volume":null,"pages":null},"PeriodicalIF":1.1,"publicationDate":"2022-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47063455","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Bashir Ahmed Albashir Abdulali, Mohd Aftar Abu Bakar, K. Ibrahim, N. M. Ariff
The generalized extreme value distribution (GEVD) and various extreme value distributions are commonly applied in air pollution, telecommunications, operational risk management, finance, insurance, material sciences, economics, and hydrology, among many other industries that deal with extreme events. Extreme value distributions (EVDs) typically limit the distribution of maximum and minimum values for many random observations drawn from the same arbitrary distribution. Besides that, it is a crucial method for forecasting future events and emerged as critical method for predicting future events. As a result, prior research is required to select the best estimation method to obtain a reliable value for the parameters of extreme value distributions. This study provides an overview of three-parameter estimation methods based on goodness-of-fit statistics and root mean square error (RMSE). This paper reviewed and compared three estimation methods used to approximate values of parameters for simulated observations taken from the EVD and GEVD. The method of moments (MOMs), maximum likelihood estimator (MLE), and maximum product of spacing (MPS) were the methods investigated in this study. Our findings indicated that the MPS performed better based on the mean square errors (MSEs); meanwhile, the MPS had similar goodness-of-fit statistic values compared to the MLE.
{"title":"Extreme Value Distributions: An Overview of Estimation and Simulation","authors":"Bashir Ahmed Albashir Abdulali, Mohd Aftar Abu Bakar, K. Ibrahim, N. M. Ariff","doi":"10.1155/2022/5449751","DOIUrl":"https://doi.org/10.1155/2022/5449751","url":null,"abstract":"The generalized extreme value distribution (GEVD) and various extreme value distributions are commonly applied in air pollution, telecommunications, operational risk management, finance, insurance, material sciences, economics, and hydrology, among many other industries that deal with extreme events. Extreme value distributions (EVDs) typically limit the distribution of maximum and minimum values for many random observations drawn from the same arbitrary distribution. Besides that, it is a crucial method for forecasting future events and emerged as critical method for predicting future events. As a result, prior research is required to select the best estimation method to obtain a reliable value for the parameters of extreme value distributions. This study provides an overview of three-parameter estimation methods based on goodness-of-fit statistics and root mean square error (RMSE). This paper reviewed and compared three estimation methods used to approximate values of parameters for simulated observations taken from the EVD and GEVD. The method of moments (MOMs), maximum likelihood estimator (MLE), and maximum product of spacing (MPS) were the methods investigated in this study. Our findings indicated that the MPS performed better based on the mean square errors (MSEs); meanwhile, the MPS had similar goodness-of-fit statistic values compared to the MLE.","PeriodicalId":44760,"journal":{"name":"Journal of Probability and Statistics","volume":null,"pages":null},"PeriodicalIF":1.1,"publicationDate":"2022-10-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45984192","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
In this paper, we introduce the R package NetDA, which aims to deal with multiclassification with network structures in predictors accommodated. To address the natural feature of network structures, we apply Gaussian graphical models to characterize dependence structures of the predictors and directly estimate the precision matrix. After that, the estimated precision matrix is employed to linear discriminant functions and quadratic discriminant functions. The R package NetDA is now available on CRAN, and the demonstration of functions is summarized as a vignette in the online documentation.
{"title":"NetDA: An R Package for Network-Based Discriminant Analysis Subject to Multilabel Classes","authors":"Li‐Pang Chen","doi":"10.1155/2022/1041752","DOIUrl":"https://doi.org/10.1155/2022/1041752","url":null,"abstract":"In this paper, we introduce the R package NetDA, which aims to deal with multiclassification with network structures in predictors accommodated. To address the natural feature of network structures, we apply Gaussian graphical models to characterize dependence structures of the predictors and directly estimate the precision matrix. After that, the estimated precision matrix is employed to linear discriminant functions and quadratic discriminant functions. The R package NetDA is now available on CRAN, and the demonstration of functions is summarized as a vignette in the online documentation.","PeriodicalId":44760,"journal":{"name":"Journal of Probability and Statistics","volume":null,"pages":null},"PeriodicalIF":1.1,"publicationDate":"2022-09-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45687083","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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