Pub Date : 2021-07-27DOI: 10.1080/01966324.2021.1957730
M. Rafique, Sajid Ali, Ismail Shah, B. Ashraf
Abstract Different probability models are used to model survival data. However, it is important to know which model describe best the data because if the assumptions for parametric methods hold, the resulting estimates have smaller standard errors and are easier to interpret and helps in predictions. This article presents the Bayesian censored data modeling assuming Gumbel, double exponential, exponentially modified Gaussian, Weibull, and lognormal distributions as sampling models. In particular, a historical Leukemia data set is used to show the comparison among different models. Markov Chain Monte Carlo (MCMC) methods are used to compute the posterior summaries. Different model selection criteria, like, Akaike Information Criterion (AIC), Deviance Information Criterion (DIC), Leave-one-out Cross-Validation (LOOCV), and Watanabe-Akaike Information Criterion (WAIC) are used for model selection. It is observed from the comparative study that the lognormal model has the minimum values of different model selection criteria and considered to be the best for this Leukemia data.
{"title":"A Comparison of Different Bayesian Models for Leukemia Data","authors":"M. Rafique, Sajid Ali, Ismail Shah, B. Ashraf","doi":"10.1080/01966324.2021.1957730","DOIUrl":"https://doi.org/10.1080/01966324.2021.1957730","url":null,"abstract":"Abstract Different probability models are used to model survival data. However, it is important to know which model describe best the data because if the assumptions for parametric methods hold, the resulting estimates have smaller standard errors and are easier to interpret and helps in predictions. This article presents the Bayesian censored data modeling assuming Gumbel, double exponential, exponentially modified Gaussian, Weibull, and lognormal distributions as sampling models. In particular, a historical Leukemia data set is used to show the comparison among different models. Markov Chain Monte Carlo (MCMC) methods are used to compute the posterior summaries. Different model selection criteria, like, Akaike Information Criterion (AIC), Deviance Information Criterion (DIC), Leave-one-out Cross-Validation (LOOCV), and Watanabe-Akaike Information Criterion (WAIC) are used for model selection. It is observed from the comparative study that the lognormal model has the minimum values of different model selection criteria and considered to be the best for this Leukemia data.","PeriodicalId":35850,"journal":{"name":"American Journal of Mathematical and Management Sciences","volume":"41 1","pages":"244 - 258"},"PeriodicalIF":0.0,"publicationDate":"2021-07-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1080/01966324.2021.1957730","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43677972","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}
Pub Date : 2021-07-27DOI: 10.1080/01966324.2021.1946667
Ayaka Yagi, T. Seo, Y. Fujikoshi
Abstract In this article, we consider an AIC for a one-sample version of the growth curve model when the dataset has a monotone pattern of missing observations. It is well known that the AIC can be regarded as an approximately unbiased estimator of the AIC-type risk defined by the expected -predictive likelihood. Here, the likelihood is based on the observed data. First, when the covariance matrix is known, we derive an AIC, which is an exact unbiased estimator of the AIC-type risk function. Next, when the covariance matrix is unknown, we derive a conventional AIC using the estimators based on the complete data set only. Finally, a numerical example is presented to illustrate our model selection procedure.
{"title":"AIC for Growth Curve Model with Monotone Missing Data","authors":"Ayaka Yagi, T. Seo, Y. Fujikoshi","doi":"10.1080/01966324.2021.1946667","DOIUrl":"https://doi.org/10.1080/01966324.2021.1946667","url":null,"abstract":"Abstract In this article, we consider an AIC for a one-sample version of the growth curve model when the dataset has a monotone pattern of missing observations. It is well known that the AIC can be regarded as an approximately unbiased estimator of the AIC-type risk defined by the expected -predictive likelihood. Here, the likelihood is based on the observed data. First, when the covariance matrix is known, we derive an AIC, which is an exact unbiased estimator of the AIC-type risk function. Next, when the covariance matrix is unknown, we derive a conventional AIC using the estimators based on the complete data set only. Finally, a numerical example is presented to illustrate our model selection procedure.","PeriodicalId":35850,"journal":{"name":"American Journal of Mathematical and Management Sciences","volume":"41 1","pages":"185 - 199"},"PeriodicalIF":0.0,"publicationDate":"2021-07-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1080/01966324.2021.1946667","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42858900","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}
Pub Date : 2021-07-13DOI: 10.1080/01966324.2021.1941452
R. Rajesh, R. G., S. Sunoj
Abstract Length-biased data appear when sampling lifetimes by cross-section. This article presents a nonparametric kernel estimators of entropy function for the length-biased sample under type I censoring. We have shown that the proposed estimator is consistent and asymptotically normal under suitable regularity conditions. We have conducted simulation studies to assess the performance of the proposed estimators.
{"title":"Estimation of Shannon Entropy in the Presence of Length-Bias and Type I Censoring","authors":"R. Rajesh, R. G., S. Sunoj","doi":"10.1080/01966324.2021.1941452","DOIUrl":"https://doi.org/10.1080/01966324.2021.1941452","url":null,"abstract":"Abstract Length-biased data appear when sampling lifetimes by cross-section. This article presents a nonparametric kernel estimators of entropy function for the length-biased sample under type I censoring. We have shown that the proposed estimator is consistent and asymptotically normal under suitable regularity conditions. We have conducted simulation studies to assess the performance of the proposed estimators.","PeriodicalId":35850,"journal":{"name":"American Journal of Mathematical and Management Sciences","volume":"41 1","pages":"160 - 169"},"PeriodicalIF":0.0,"publicationDate":"2021-07-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1080/01966324.2021.1941452","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46026820","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}
Pub Date : 2021-07-08DOI: 10.1080/01966324.2021.1946666
O. Abo-Kasem, A. Elshahhat
Abstract Generalized hybrid censoring schemes, proposed by Chandrasekar et al. (Naval Research Logistics, 51(7), 994–1004, 2004), have several advantages over the conventional hybrid censoring schemes. In this paper, we introduce a new generalized Type-II hybrid censoring scheme for two samples. The maximum likelihood and Bayesian inferential approaches for estimating the unknown mean lifetimes of the experimental units for the two samples follow exponential population with different scale parameters are considered. The corresponding asymptotic confidence intervals of the maximum likelihood estimators are also obtained. Using gamma conjugate priors, the Bayes estimators are developed relative to both symmetric and asymmetric loss functions. Also, some popular censoring plans are generalized and can be obtained as a special cases from our results. One real-life data set is analyzed to discuss how the applicability of the proposed methods in real phenomenon. Finally, to examine the performance of proposed methods, a Monte Carlo simulation study is carried out.
摘要Chandrasekar等人提出的广义混合审查方案（Naval Research Logistics，51（7），994–10042004）与传统的混合审查方案相比具有几个优点。在本文中，我们介绍了一种新的两个样本的广义II型混合截尾方案。考虑了估计两个样本的实验单元未知平均寿命的最大似然和贝叶斯推理方法，这些方法遵循不同尺度参数的指数总体。给出了最大似然估计量的渐近置信区间。使用伽马共轭先验，相对于对称和非对称损失函数开发了贝叶斯估计量。此外，我们还推广了一些流行的审查方案，并将其作为特例从我们的结果中得到。分析了一个真实的数据集，讨论了所提出的方法在真实现象中的适用性。最后，为了检验所提出的方法的性能，进行了蒙特卡罗模拟研究。
{"title":"A New Two Sample Generalized Type-II Hybrid Censoring Scheme","authors":"O. Abo-Kasem, A. Elshahhat","doi":"10.1080/01966324.2021.1946666","DOIUrl":"https://doi.org/10.1080/01966324.2021.1946666","url":null,"abstract":"Abstract Generalized hybrid censoring schemes, proposed by Chandrasekar et al. (Naval Research Logistics, 51(7), 994–1004, 2004), have several advantages over the conventional hybrid censoring schemes. In this paper, we introduce a new generalized Type-II hybrid censoring scheme for two samples. The maximum likelihood and Bayesian inferential approaches for estimating the unknown mean lifetimes of the experimental units for the two samples follow exponential population with different scale parameters are considered. The corresponding asymptotic confidence intervals of the maximum likelihood estimators are also obtained. Using gamma conjugate priors, the Bayes estimators are developed relative to both symmetric and asymmetric loss functions. Also, some popular censoring plans are generalized and can be obtained as a special cases from our results. One real-life data set is analyzed to discuss how the applicability of the proposed methods in real phenomenon. Finally, to examine the performance of proposed methods, a Monte Carlo simulation study is carried out.","PeriodicalId":35850,"journal":{"name":"American Journal of Mathematical and Management Sciences","volume":"41 1","pages":"170 - 184"},"PeriodicalIF":0.0,"publicationDate":"2021-07-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1080/01966324.2021.1946666","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49153061","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}
Pub Date : 2021-06-21DOI: 10.1080/01966324.2021.1933661
M. Drisya, Joby K. Jose, K. Krishnendu
Abstract This paper deals with the estimation of the stress-strength reliability of time-dependent models. Suppose that a system is allowed to run continuously and is subjected to random stress at random time points. Then we can assume a decrease in the strength of the system during the completion of each run. Let the strength of the system decreases by a constant and the stress on the system increases by a constant over each run. Time taken for completion of a run is assumed to have continuous phase-type distribution, the initial strength of the system, as well as, initial stress on the system are assumed to have a finite mixture of either Weibull distributions or power transformed half logistic distributions. A detailed numerical illustration of the results is also carried out.
{"title":"Time-Dependent Stress-Strength Reliability Model with Phase-Type Cycle Time Based on Finite Mixture Models","authors":"M. Drisya, Joby K. Jose, K. Krishnendu","doi":"10.1080/01966324.2021.1933661","DOIUrl":"https://doi.org/10.1080/01966324.2021.1933661","url":null,"abstract":"Abstract This paper deals with the estimation of the stress-strength reliability of time-dependent models. Suppose that a system is allowed to run continuously and is subjected to random stress at random time points. Then we can assume a decrease in the strength of the system during the completion of each run. Let the strength of the system decreases by a constant and the stress on the system increases by a constant over each run. Time taken for completion of a run is assumed to have continuous phase-type distribution, the initial strength of the system, as well as, initial stress on the system are assumed to have a finite mixture of either Weibull distributions or power transformed half logistic distributions. A detailed numerical illustration of the results is also carried out.","PeriodicalId":35850,"journal":{"name":"American Journal of Mathematical and Management Sciences","volume":"41 1","pages":"128 - 147"},"PeriodicalIF":0.0,"publicationDate":"2021-06-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1080/01966324.2021.1933661","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49002510","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}
Pub Date : 2021-06-07DOI: 10.1080/01966324.2021.1935366
R. Maya, M. Irshad
Abstract Mathai and Haubold introduced a new generalized entropy namely Mathai-Haubold entropy and Dar and Al-Zahrani proposed the Mathai-Haubold entropy for the residual life time and called it as residual Mathai-Haubold entropy. In the present paper, we propose nonparametric estimators for the Mathai-Haubold entropy and the residual Mathai-Haubold entropy where the observations under consideration are exhibiting α-mixing (strong mixing) dependence condition. Asymptotic properties of the estimators are established under suitable regular conditions. A Monte Carlo simulation study is carried out to compare the performance of the estimators using the mean squared error. The methods are illustrated using a real data set.
{"title":"Kernel Estimation of Mathai-Haubold Entropy and Residual Mathai-Haubold Entropy Functions under α-Mixing Dependence Condition","authors":"R. Maya, M. Irshad","doi":"10.1080/01966324.2021.1935366","DOIUrl":"https://doi.org/10.1080/01966324.2021.1935366","url":null,"abstract":"Abstract Mathai and Haubold introduced a new generalized entropy namely Mathai-Haubold entropy and Dar and Al-Zahrani proposed the Mathai-Haubold entropy for the residual life time and called it as residual Mathai-Haubold entropy. In the present paper, we propose nonparametric estimators for the Mathai-Haubold entropy and the residual Mathai-Haubold entropy where the observations under consideration are exhibiting α-mixing (strong mixing) dependence condition. Asymptotic properties of the estimators are established under suitable regular conditions. A Monte Carlo simulation study is carried out to compare the performance of the estimators using the mean squared error. The methods are illustrated using a real data set.","PeriodicalId":35850,"journal":{"name":"American Journal of Mathematical and Management Sciences","volume":"41 1","pages":"148 - 159"},"PeriodicalIF":0.0,"publicationDate":"2021-06-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1080/01966324.2021.1935366","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47297258","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}
Pub Date : 2021-06-07DOI: 10.1080/01966324.2021.1931587
Heba S. Mohammed
Abstract In this paper, Bayesian prediction bounds for order statistics of future observations from a family of exponentiated distributions are obtained in the presence of a single outlier arising from different members of the same family of distributions. During an experimentation, we come across circumstances where one or more observations may not be homogeneous to rest of the observations and hence can be treated as outliers. Nowadays, the classification for outlier prediction are applied in various fields like bioinformatics, natural language processing, military application, geographical domains etc. We consider single outliers of two types in future observations when the sample size of the future sample is a random variable. The exponentiated exponential distribution has been used as a special case from the suggested family. We introduce numerical examples and compute Bayesian prediction bounds based on the real data, by using Markov chain Monte Carlo (MCMC) algorithm.
{"title":"Bayesian Prediction Bounds from a Family of Exponentiated Distributions in the Presence of Outliers","authors":"Heba S. Mohammed","doi":"10.1080/01966324.2021.1931587","DOIUrl":"https://doi.org/10.1080/01966324.2021.1931587","url":null,"abstract":"Abstract In this paper, Bayesian prediction bounds for order statistics of future observations from a family of exponentiated distributions are obtained in the presence of a single outlier arising from different members of the same family of distributions. During an experimentation, we come across circumstances where one or more observations may not be homogeneous to rest of the observations and hence can be treated as outliers. Nowadays, the classification for outlier prediction are applied in various fields like bioinformatics, natural language processing, military application, geographical domains etc. We consider single outliers of two types in future observations when the sample size of the future sample is a random variable. The exponentiated exponential distribution has been used as a special case from the suggested family. We introduce numerical examples and compute Bayesian prediction bounds based on the real data, by using Markov chain Monte Carlo (MCMC) algorithm.","PeriodicalId":35850,"journal":{"name":"American Journal of Mathematical and Management Sciences","volume":"41 1","pages":"88 - 99"},"PeriodicalIF":0.0,"publicationDate":"2021-06-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1080/01966324.2021.1931587","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41960926","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}
Pub Date : 2021-04-30DOI: 10.1080/01966324.2021.1914250
R. B. Athirakrishnan, E. I. Abdul-Sathar
Abstract This article proposes E-Bayesian and Hierarchical Bayesian estimation method to estimate the scale parameter and reversed hazard rate of inverse Rayleigh distribution. These estimators are derived under squared error, entropy and precautionary loss functions. The definition and properties of proposed estimators are given. The proposed estimators are suitable for all sample sizes and perform better than the existing classical estimator, such as MLE, with high efficiency. Simulated and real data sets are also discussed for studying the performance of the estimators, which shows that the proposed estimators are efficient and easy to use.
{"title":"E-Bayesian and Hierarchical Bayesian Estimation of Inverse Rayleigh Distribution","authors":"R. B. Athirakrishnan, E. I. Abdul-Sathar","doi":"10.1080/01966324.2021.1914250","DOIUrl":"https://doi.org/10.1080/01966324.2021.1914250","url":null,"abstract":"Abstract This article proposes E-Bayesian and Hierarchical Bayesian estimation method to estimate the scale parameter and reversed hazard rate of inverse Rayleigh distribution. These estimators are derived under squared error, entropy and precautionary loss functions. The definition and properties of proposed estimators are given. The proposed estimators are suitable for all sample sizes and perform better than the existing classical estimator, such as MLE, with high efficiency. Simulated and real data sets are also discussed for studying the performance of the estimators, which shows that the proposed estimators are efficient and easy to use.","PeriodicalId":35850,"journal":{"name":"American Journal of Mathematical and Management Sciences","volume":"41 1","pages":"70 - 87"},"PeriodicalIF":0.0,"publicationDate":"2021-04-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1080/01966324.2021.1914250","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48224390","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}
Pub Date : 2021-04-26DOI: 10.1080/01966324.2021.1910885
G. C. McDonald
Abstract This article addresses the issue of computing an implementation constant required to apply a nonparametric subset selection procedure. Specifically, several approximations to the cumulative distribution function (cdf) of a statistic, based on ranks assigned randomly to continuous data arising from a randomized block designed experiment, are given and compared to the exact cdf. One of these approximations is simulation based using an R code. The second is based on a normal approximation to the rank sums. In the special case of comparing two populations, algebraic properties of the cdfs are derived and validated with the exact tabulations previously given in the literature. An application of these approximation methods is given for a published study of state traffic fatality rates for the years 1994 through 2012.
{"title":"Computing Probabilties for Rank Statistics Used with Block Design Nonparametric Subset Selection Rules","authors":"G. C. McDonald","doi":"10.1080/01966324.2021.1910885","DOIUrl":"https://doi.org/10.1080/01966324.2021.1910885","url":null,"abstract":"Abstract This article addresses the issue of computing an implementation constant required to apply a nonparametric subset selection procedure. Specifically, several approximations to the cumulative distribution function (cdf) of a statistic, based on ranks assigned randomly to continuous data arising from a randomized block designed experiment, are given and compared to the exact cdf. One of these approximations is simulation based using an R code. The second is based on a normal approximation to the rank sums. In the special case of comparing two populations, algebraic properties of the cdfs are derived and validated with the exact tabulations previously given in the literature. An application of these approximation methods is given for a published study of state traffic fatality rates for the years 1994 through 2012.","PeriodicalId":35850,"journal":{"name":"American Journal of Mathematical and Management Sciences","volume":"41 1","pages":"38 - 50"},"PeriodicalIF":0.0,"publicationDate":"2021-04-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1080/01966324.2021.1910885","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44815492","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}
Pub Date : 2021-04-23DOI: 10.1080/01966324.2021.1914251
Marcel Jansen, E. Cramer, J. Górny
Abstract This paper introduces multi-sample Type-II progressive hybrid censoring which allows to incorporate data from independently conducted Type-II (progressive) hybrid censored experiments for the first time. Assuming exponentially distributed lifetimes with mean the maximum likelihood estimator of is obtained and its exact distribution is established. Moreover, we propose an exact confidence interval as well as two asymptotic confidence intervals for the unknown mean. The results are illustrated by simulations and a data set.
{"title":"Exact Likelihood Inference for an Exponential Parameter under a Multi-Sample Type-II Progressive Hybrid Censoring Model","authors":"Marcel Jansen, E. Cramer, J. Górny","doi":"10.1080/01966324.2021.1914251","DOIUrl":"https://doi.org/10.1080/01966324.2021.1914251","url":null,"abstract":"Abstract This paper introduces multi-sample Type-II progressive hybrid censoring which allows to incorporate data from independently conducted Type-II (progressive) hybrid censored experiments for the first time. Assuming exponentially distributed lifetimes with mean the maximum likelihood estimator of is obtained and its exact distribution is established. Moreover, we propose an exact confidence interval as well as two asymptotic confidence intervals for the unknown mean. The results are illustrated by simulations and a data set.","PeriodicalId":35850,"journal":{"name":"American Journal of Mathematical and Management Sciences","volume":"41 1","pages":"101 - 127"},"PeriodicalIF":0.0,"publicationDate":"2021-04-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1080/01966324.2021.1914251","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42927573","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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