This paper investigates stochastic comparisons of largest claim amounts of two sets of independent or interdependent portfolios in the sense of some stochastic orders. Let random variable Xi$$ {X}_i $$ ( i=1,…,n$$ i=1,dots, n $$ ) with distribution function F(x;αi)$$ Fleft(x;{alpha}_iright) $$ , represents the claim amount for ith risk of a portfolio. Here two largest claim amounts are compared considering that the claim variables follow a general semiparametric family of distributions having the property that the survival function F‾(x;α)$$ overline{F}left(x;alpha right) $$ is increasing in α$$ alpha $$ or is increasing and convex/concave in α$$ alpha $$ . The results obtained in this paper apply to a large class of well‐known distributions including the family of exponentiated/generalized distributions (e.g., exponentiated exponential, Weibull, gamma and Pareto family), Rayleigh distribution and Marshall–Olkin family of distributions. As a direct consequence of some main theorems, we also obtained the results for scale family of distributions. Several numerical examples are provided to illustrate the results.
{"title":"Stochastic comparisons of largest claim amounts from heterogeneous portfolios","authors":"Pradip Kundu, Amarjit Kundu, Biplab Hawlader","doi":"10.1111/stan.12296","DOIUrl":"https://doi.org/10.1111/stan.12296","url":null,"abstract":"This paper investigates stochastic comparisons of largest claim amounts of two sets of independent or interdependent portfolios in the sense of some stochastic orders. Let random variable Xi$$ {X}_i $$ ( i=1,…,n$$ i=1,dots, n $$ ) with distribution function F(x;αi)$$ Fleft(x;{alpha}_iright) $$ , represents the claim amount for ith risk of a portfolio. Here two largest claim amounts are compared considering that the claim variables follow a general semiparametric family of distributions having the property that the survival function F‾(x;α)$$ overline{F}left(x;alpha right) $$ is increasing in α$$ alpha $$ or is increasing and convex/concave in α$$ alpha $$ . The results obtained in this paper apply to a large class of well‐known distributions including the family of exponentiated/generalized distributions (e.g., exponentiated exponential, Weibull, gamma and Pareto family), Rayleigh distribution and Marshall–Olkin family of distributions. As a direct consequence of some main theorems, we also obtained the results for scale family of distributions. Several numerical examples are provided to illustrate the results.","PeriodicalId":51178,"journal":{"name":"Statistica Neerlandica","volume":"75 1","pages":"497 - 515"},"PeriodicalIF":1.5,"publicationDate":"2023-04-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"74143095","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Nelson Alirio Cruz, Luis Alberto López Pérez, Oscar Orlando Melo
This paper presents an experimental cross‐over design whose response variable is a count that belongs to the Poisson distribution. The methodology is extended to data with overdispersion or subdispersion. We present the theoretical development for analysis of cases with few treatments and a few periods. In this case, we consider the log‐linear link for estimation effects and the Delta method for the asymptotic inference of the estimators. When the number of periods and sequences increases, we propose an extension of the previous methodology, using the generalized linear models. In this extension, cross‐over designs for count data include treatments, sequences, time effects, covariables, and any correlation structure. The most important result of the methodology is that it allows the detection of significant factors within the cross‐over design when the response variable belongs to the exponential family, especially the treatment effects. Finally, we present the analysis of data obtained in a student hydration study and a simulation study. We show a comparison between the usual methods of analysis and those obtained in the present work, demonstrating the advantage over the usual methods in situations with carry‐over presence.
{"title":"Analysis of cross‐over experiments with count data in the presence of carry‐over effects","authors":"Nelson Alirio Cruz, Luis Alberto López Pérez, Oscar Orlando Melo","doi":"10.1111/stan.12295","DOIUrl":"https://doi.org/10.1111/stan.12295","url":null,"abstract":"This paper presents an experimental cross‐over design whose response variable is a count that belongs to the Poisson distribution. The methodology is extended to data with overdispersion or subdispersion. We present the theoretical development for analysis of cases with few treatments and a few periods. In this case, we consider the log‐linear link for estimation effects and the Delta method for the asymptotic inference of the estimators. When the number of periods and sequences increases, we propose an extension of the previous methodology, using the generalized linear models. In this extension, cross‐over designs for count data include treatments, sequences, time effects, covariables, and any correlation structure. The most important result of the methodology is that it allows the detection of significant factors within the cross‐over design when the response variable belongs to the exponential family, especially the treatment effects. Finally, we present the analysis of data obtained in a student hydration study and a simulation study. We show a comparison between the usual methods of analysis and those obtained in the present work, demonstrating the advantage over the usual methods in situations with carry‐over presence.","PeriodicalId":51178,"journal":{"name":"Statistica Neerlandica","volume":"1 1","pages":"516 - 542"},"PeriodicalIF":1.5,"publicationDate":"2023-04-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"89772271","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
A stationary sequence of nonnegative random variables generated by autoregressive (AR) models may be used to describe the inter‐arrival times between events in counting processes. Even though, several such models are available in the literature, there is no unified approach to estimate their parameters. In this paper, we propose a class of combined estimating function method to estimate the model parameters of AR models with gamma marginals. The proposed method is compared with other estimation procedures and are illustrated by simulation and data analysis.
{"title":"Estimating function method for nonnegative autoregressive models","authors":"E. Hari, Prasad N. Balakrishna, E. H. Prasad","doi":"10.1111/stan.12294","DOIUrl":"https://doi.org/10.1111/stan.12294","url":null,"abstract":"A stationary sequence of nonnegative random variables generated by autoregressive (AR) models may be used to describe the inter‐arrival times between events in counting processes. Even though, several such models are available in the literature, there is no unified approach to estimate their parameters. In this paper, we propose a class of combined estimating function method to estimate the model parameters of AR models with gamma marginals. The proposed method is compared with other estimation procedures and are illustrated by simulation and data analysis.","PeriodicalId":51178,"journal":{"name":"Statistica Neerlandica","volume":"3 1","pages":"471 - 496"},"PeriodicalIF":1.5,"publicationDate":"2023-03-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"86547801","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
D. Burger, Sean van der Merwe, E. Lesaffre, P. C. le Roux, Morgan J. Raath‐Krüger
There is no literature on outlier‐robust parametric mixed‐effects quantile regression models for continuous proportion data as an alternative to systematically identifying and eliminating outliers. To fill this gap, we formulate a robust method by extending the recently proposed fixed‐effects quantile regression model based on the heavy‐tailed Johnson‐ t$$ t $$ distribution for continuous proportion data to the mixed‐effects modeling context, using a Bayesian approach. Our proposed method is motivated by and used to model the extreme quantiles of the vitality of cushion plants to provide insights into the ecology of the system in which the plants are dominant. We conducted a simulation study to assess the new method's performance and robustness to outliers. We show that the new model has good accuracy and confidence interval coverage properties and is remarkably robust to outliers. In contrast, our study demonstrates that the current approach in the literature for modeling hierarchically structured bounded data's quantiles is susceptible to outliers, especially when modeling the extreme quantiles. We conclude that the proposed model is an appropriate robust alternative to the current approach for modeling the quantiles of correlated continuous proportions when outliers are present in the data.
目前还没有关于连续比例数据的异常值-鲁棒参数混合效应分位数回归模型作为系统识别和消除异常值的替代方法的文献。为了填补这一空白，我们通过使用贝叶斯方法，将最近提出的基于连续比例数据的重尾Johnson - t $$ t $$分布的固定效应分位数回归模型扩展到混合效应建模环境，从而制定了一种鲁棒方法。我们提出的方法是由缓冲植物活力的极端分位数模型驱动的，并用于对植物占主导地位的系统的生态学提供见解。我们进行了仿真研究，以评估新方法的性能和对异常值的鲁棒性。结果表明，新模型具有良好的精度和置信区间覆盖性能，对异常值具有显著的鲁棒性。相比之下，我们的研究表明，目前文献中用于分层结构有界数据分位数建模的方法容易受到异常值的影响，特别是在建模极端分位数时。我们得出的结论是，当数据中存在异常值时，所提出的模型是对相关连续比例的分位数建模的当前方法的适当鲁棒替代方法。
{"title":"A robust mixed‐effects parametric quantile regression model for continuous proportions: Quantifying the constraints to vitality in cushion plants","authors":"D. Burger, Sean van der Merwe, E. Lesaffre, P. C. le Roux, Morgan J. Raath‐Krüger","doi":"10.1111/stan.12293","DOIUrl":"https://doi.org/10.1111/stan.12293","url":null,"abstract":"There is no literature on outlier‐robust parametric mixed‐effects quantile regression models for continuous proportion data as an alternative to systematically identifying and eliminating outliers. To fill this gap, we formulate a robust method by extending the recently proposed fixed‐effects quantile regression model based on the heavy‐tailed Johnson‐ t$$ t $$ distribution for continuous proportion data to the mixed‐effects modeling context, using a Bayesian approach. Our proposed method is motivated by and used to model the extreme quantiles of the vitality of cushion plants to provide insights into the ecology of the system in which the plants are dominant. We conducted a simulation study to assess the new method's performance and robustness to outliers. We show that the new model has good accuracy and confidence interval coverage properties and is remarkably robust to outliers. In contrast, our study demonstrates that the current approach in the literature for modeling hierarchically structured bounded data's quantiles is susceptible to outliers, especially when modeling the extreme quantiles. We conclude that the proposed model is an appropriate robust alternative to the current approach for modeling the quantiles of correlated continuous proportions when outliers are present in the data.","PeriodicalId":51178,"journal":{"name":"Statistica Neerlandica","volume":"4 1","pages":"444 - 470"},"PeriodicalIF":1.5,"publicationDate":"2023-03-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"90397245","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
A variety of inferential tests are available for single and multilevel mediation but most come with notable limitations that balance tradeoffs between power and Type I error. We extend the partial posterior p value method (p3 method) to test multilevel mediation. This contemporary resampling‐based composite approach is specifically suited for complex null hypotheses. We develop the p3 method and investigate its performance within the context of two‐level cluster‐randomized multilevel mediation studies. Similar to its performance in single‐level studies, we found that the p3 method performed well relative to other mediation tests suggesting it provides a judicious balance between Type I error rate and power. While bias‐corrected bootstrapping achieved the best overall performance, the p3 method serves as an alternative tool for researchers investigating multilevel mediation that is especially useful when conducting a priori power analyses. To encourage utilization, we provide R code for implementing the p3 method.
{"title":"A partial posterior p value test for multilevel mediation","authors":"Kyle Cox, Ben Kelcey","doi":"10.1111/stan.12291","DOIUrl":"https://doi.org/10.1111/stan.12291","url":null,"abstract":"A variety of inferential tests are available for single and multilevel mediation but most come with notable limitations that balance tradeoffs between power and Type I error. We extend the partial posterior p value method (p3 method) to test multilevel mediation. This contemporary resampling‐based composite approach is specifically suited for complex null hypotheses. We develop the p3 method and investigate its performance within the context of two‐level cluster‐randomized multilevel mediation studies. Similar to its performance in single‐level studies, we found that the p3 method performed well relative to other mediation tests suggesting it provides a judicious balance between Type I error rate and power. While bias‐corrected bootstrapping achieved the best overall performance, the p3 method serves as an alternative tool for researchers investigating multilevel mediation that is especially useful when conducting a priori power analyses. To encourage utilization, we provide R code for implementing the p3 method.","PeriodicalId":51178,"journal":{"name":"Statistica Neerlandica","volume":"39 1","pages":"408 - 428"},"PeriodicalIF":1.5,"publicationDate":"2023-03-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"80357683","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
In this paper, we introduce a new portmanteau test for the iid hypothesis, where the elements of the sample are allowed to take values in a general space (e.g., a function space). We study the finite sample properties of our test, evaluating its performance in terms of empirical size and power. In particular, we compare the empirical power of our test with the power of other tests in the literature designed to work in a specific data setting, as the one‐way analysis of variance test used in experimental data analysis and three portmanteau tests used in time series analysis. In every case, we found conditions where our test outperformed in power to the competing test. Finally, to illustrate the usefulness of our test, we implement it on two real‐world applications based on function‐valued data.
{"title":"A portmanteau test for the iid hypothesis","authors":"Ricardo Bórquez","doi":"10.1111/stan.12290","DOIUrl":"https://doi.org/10.1111/stan.12290","url":null,"abstract":"In this paper, we introduce a new portmanteau test for the iid hypothesis, where the elements of the sample are allowed to take values in a general space (e.g., a function space). We study the finite sample properties of our test, evaluating its performance in terms of empirical size and power. In particular, we compare the empirical power of our test with the power of other tests in the literature designed to work in a specific data setting, as the one‐way analysis of variance test used in experimental data analysis and three portmanteau tests used in time series analysis. In every case, we found conditions where our test outperformed in power to the competing test. Finally, to illustrate the usefulness of our test, we implement it on two real‐world applications based on function‐valued data.","PeriodicalId":51178,"journal":{"name":"Statistica Neerlandica","volume":"14 1","pages":"391 - 402"},"PeriodicalIF":1.5,"publicationDate":"2023-02-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"86661955","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
An advantage of the standard mixture cure model over an usual survival model is how it accounts for the population heterogeneity. It allows a joint estimation for the distribution related to the susceptible and non‐susceptible subjects. The estimation algorithm may provide ±∞$$ pm infty $$ coefficients when the likelihood cannot be maximized. This phenomenon is known as Monotone Likelihood (ML), common in survival and logistic regressions. The ML tends to appear in situations with small sample size, many censored times, many binary or unbalanced covariates. Particularly, it occurs when all uncensored cases correspond to one level of a binary covariate. The existing frequentist solution is an adaptation of the Firth correction, originally proposed to reduce bias of maximum likelihood estimates. It prevents ±∞$$ pm infty $$ estimates by penalizing the likelihood, with the penalty interpreted as the Bayesian Jeffreys prior. In this paper, the penalized likelihood of the standard mixture cure model is considered with different penalties (Bayesian priors). A Monte Carlo simulation study indicates good inference results, especially for balanced data sets. Finally, a real application involving a melanoma data illustrates the approach.
{"title":"Bayesian solution to the monotone likelihood in the standard mixture cure model","authors":"F. M. Almeida, V. D. Mayrink, E. Colosimo","doi":"10.1111/stan.12289","DOIUrl":"https://doi.org/10.1111/stan.12289","url":null,"abstract":"An advantage of the standard mixture cure model over an usual survival model is how it accounts for the population heterogeneity. It allows a joint estimation for the distribution related to the susceptible and non‐susceptible subjects. The estimation algorithm may provide ±∞$$ pm infty $$ coefficients when the likelihood cannot be maximized. This phenomenon is known as Monotone Likelihood (ML), common in survival and logistic regressions. The ML tends to appear in situations with small sample size, many censored times, many binary or unbalanced covariates. Particularly, it occurs when all uncensored cases correspond to one level of a binary covariate. The existing frequentist solution is an adaptation of the Firth correction, originally proposed to reduce bias of maximum likelihood estimates. It prevents ±∞$$ pm infty $$ estimates by penalizing the likelihood, with the penalty interpreted as the Bayesian Jeffreys prior. In this paper, the penalized likelihood of the standard mixture cure model is considered with different penalties (Bayesian priors). A Monte Carlo simulation study indicates good inference results, especially for balanced data sets. Finally, a real application involving a melanoma data illustrates the approach.","PeriodicalId":51178,"journal":{"name":"Statistica Neerlandica","volume":"1 1","pages":"365 - 390"},"PeriodicalIF":1.5,"publicationDate":"2023-02-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"73074811","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
In medical clinical studies, uni‐ and bilateral data naturally occurs if each patient contributes either one or both of paired organ measurements in a stratified design. This paper mainly proposes a common test of risk differences between proportions for stratified uni‐ and bilateral correlated data. Likelihood ratio, score, and Wald‐type test statistics are constructed using global, unconstrained, and constrained maximum likelihood estimations of parameters. Simulation studies are conducted to evaluate the performance of these test procedures in terms of type I error rates and powers. Empirical results show that the likelihood ratio test is more robust and powerful than other statistics. A real example is used to illustrate the proposed methods.
{"title":"Testing the common risk difference of proportions for stratified uni‐ and bilateral correlated data","authors":"Zhiming Li, Changxing Ma, Keyi Mou","doi":"10.1111/stan.12288","DOIUrl":"https://doi.org/10.1111/stan.12288","url":null,"abstract":"In medical clinical studies, uni‐ and bilateral data naturally occurs if each patient contributes either one or both of paired organ measurements in a stratified design. This paper mainly proposes a common test of risk differences between proportions for stratified uni‐ and bilateral correlated data. Likelihood ratio, score, and Wald‐type test statistics are constructed using global, unconstrained, and constrained maximum likelihood estimations of parameters. Simulation studies are conducted to evaluate the performance of these test procedures in terms of type I error rates and powers. Empirical results show that the likelihood ratio test is more robust and powerful than other statistics. A real example is used to illustrate the proposed methods.","PeriodicalId":51178,"journal":{"name":"Statistica Neerlandica","volume":"36 1","pages":"340 - 364"},"PeriodicalIF":1.5,"publicationDate":"2023-02-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"78938507","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Proportional hazards are often used to model event time data subject to censoring. Samples involving discrete covariates with strong effects can lead to infinite maximum partial likelihood estimates. A methodology is presented for eliminating nuisance parameters estimated at infinity using approximate conditional inference. Of primary interest is testing in cases in which the parameter of primary interest has a finite estimate, but in which other parameters are estimated at infinity.
{"title":"Inference in the presence of likelihood monotonicity for proportional hazards regression","authors":"J. Kolassa, Juan Zhang","doi":"10.1111/stan.12287","DOIUrl":"https://doi.org/10.1111/stan.12287","url":null,"abstract":"Proportional hazards are often used to model event time data subject to censoring. Samples involving discrete covariates with strong effects can lead to infinite maximum partial likelihood estimates. A methodology is presented for eliminating nuisance parameters estimated at infinity using approximate conditional inference. Of primary interest is testing in cases in which the parameter of primary interest has a finite estimate, but in which other parameters are estimated at infinity.","PeriodicalId":51178,"journal":{"name":"Statistica Neerlandica","volume":"43 1","pages":"322 - 339"},"PeriodicalIF":1.5,"publicationDate":"2023-01-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"77308751","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
In this paper, new statistical algorithms for accurate peak detection in the metabolomic data are proposed. Specifically, liquid chromatograph‐mass spectrometry data are analyzed. The discretized skew‐t mixture model for peak detection is proposed. It shows great flexibility and capability in fitting skewed or heavy‐tailed peaks. The methodology is further extended to cross‐sample peak alignment for identifying the true peaks. A measure of peak credibility is provided through the assessment of misclassification probabilities between two cross‐sample peaks. The proposed algorithms are applied to spike‐in data with promising results.
{"title":"Discretized skew‐t mixture model for deconvoluting liquid chromatograph mass spectrometry data","authors":"Xuwen Zhu, Xiang Zhang","doi":"10.1111/stan.12285","DOIUrl":"https://doi.org/10.1111/stan.12285","url":null,"abstract":"In this paper, new statistical algorithms for accurate peak detection in the metabolomic data are proposed. Specifically, liquid chromatograph‐mass spectrometry data are analyzed. The discretized skew‐t mixture model for peak detection is proposed. It shows great flexibility and capability in fitting skewed or heavy‐tailed peaks. The methodology is further extended to cross‐sample peak alignment for identifying the true peaks. A measure of peak credibility is provided through the assessment of misclassification probabilities between two cross‐sample peaks. The proposed algorithms are applied to spike‐in data with promising results.","PeriodicalId":51178,"journal":{"name":"Statistica Neerlandica","volume":"16 1","pages":"284 - 303"},"PeriodicalIF":1.5,"publicationDate":"2023-01-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"78459194","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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