Pub Date : 2023-12-06DOI: 10.18187/pjsor.v19i4.4185
Adam Abdelrahman Hussein Adam, Hakan SavaÅŸ Sazak
In this study, we propose two estimators called the 3-step MML and the combined estimators of the parameters of the modified Weibull distribution which is used in reliability models with bathtub-shaped failure rate function. The simulations show the superiority of both estimators over the graphical estimators. Particularly, the combined estimators are the better of the two. Two real-life data applications also show the superiority of the proposed estimators compared to the graphical estimators.
{"title":"Estimation of the Parameters of the Modified Weibull Distribution with Bathtub-shaped Failure Rate Function","authors":"Adam Abdelrahman Hussein Adam, Hakan SavaÅŸ Sazak","doi":"10.18187/pjsor.v19i4.4185","DOIUrl":"https://doi.org/10.18187/pjsor.v19i4.4185","url":null,"abstract":"In this study, we propose two estimators called the 3-step MML and the combined estimators of the parameters of the modified Weibull distribution which is used in reliability models with bathtub-shaped failure rate function. The simulations show the superiority of both estimators over the graphical estimators. Particularly, the combined estimators are the better of the two. Two real-life data applications also show the superiority of the proposed estimators compared to the graphical estimators.","PeriodicalId":19973,"journal":{"name":"Pakistan Journal of Statistics and Operation Research","volume":null,"pages":null},"PeriodicalIF":1.5,"publicationDate":"2023-12-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138597213","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 : 2023-12-05DOI: 10.18187/pjsor.v19i4.4317
Maha A. Aldahlan, Abdelhamid M. Rabie, Mostafa Abdelhamid, Abdul Hadi N. Ahmed, A. Afify
In this paper, we introduce the Marshall–Olkin Pareto type-I (MOPTI) distribution. Structural properties of the MOPTI distribution including the quantile function, mean residual life, and a new theorem for strength-stress measure are introduced. Five methods of estimation for the MOPTI parameters based on complete samples are presented. Furthermore, we explore the estimation of the MOPTI parameters under type-I and type-II censoring. Two Monte Carlo simulation studies are conducted to evaluate the performance of the estimation methods under complete and censored samples. A real-life data set is used to validate the proposed methods.
{"title":"The Marshall–Olkin Pareto Type-I Distribution: Properties, Inference under Complete and Censored Samples with Application to Breast Cancer Data","authors":"Maha A. Aldahlan, Abdelhamid M. Rabie, Mostafa Abdelhamid, Abdul Hadi N. Ahmed, A. Afify","doi":"10.18187/pjsor.v19i4.4317","DOIUrl":"https://doi.org/10.18187/pjsor.v19i4.4317","url":null,"abstract":"In this paper, we introduce the Marshall–Olkin Pareto type-I (MOPTI) distribution. Structural properties of the MOPTI distribution including the quantile function, mean residual life, and a new theorem for strength-stress measure are introduced. Five methods of estimation for the MOPTI parameters based on complete samples are presented. Furthermore, we explore the estimation of the MOPTI parameters under type-I and type-II censoring. Two Monte Carlo simulation studies are conducted to evaluate the performance of the estimation methods under complete and censored samples. A real-life data set is used to validate the proposed methods.","PeriodicalId":19973,"journal":{"name":"Pakistan Journal of Statistics and Operation Research","volume":null,"pages":null},"PeriodicalIF":1.5,"publicationDate":"2023-12-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138599101","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 : 2023-09-03DOI: 10.18187/pjsor.v19i3.4247
Chantha Wongoutong
Herein, a modified weighting for combined forecasting methods is established. These weights are used to adjust the correlation coefficient between the actual and predicted values from five individual forecasting models based on their correlation coefficient values and ranking. Time-series datasets with three patterns (stationary, trend, or both trend and seasonal) were analyzed by using the five individual forecasting models and three combined forecasting methods: simple-average, Bates-Granger, and the proposed approach. The MAPE and RMSE results indicate that the proposed method outperformed the others, especially when the time-series pattern was stationary and improved the forecasting accuracy of the worst and best individual forecasting models by 35–37% and 7–10%, respectively. Moreover, the proposed method showed improvements in MAPE and RMSE of around 18–20% and 9–11% compared to the simple-average and Bates-Granger methods, respectively. In addition, the combined forecasting methods outperformed the individual forecasting models when analyzing non-stationary data. Remarkably, the performances of the proposed and Bates-Granger methods were almost the same, with improvements in MAPE and RMSE in the range of 1–2% on average. Therefore, the proposed method for creating weights based on the correlation coefficients of the individual forecasting models greatly improves combined forecasting methods.
{"title":"A modified weighting system for combined forecasting methods based on the correlation coefficients of the individual forecasting models","authors":"Chantha Wongoutong","doi":"10.18187/pjsor.v19i3.4247","DOIUrl":"https://doi.org/10.18187/pjsor.v19i3.4247","url":null,"abstract":"Herein, a modified weighting for combined forecasting methods is established. These weights are used to adjust the correlation coefficient between the actual and predicted values from five individual forecasting models based on their correlation coefficient values and ranking. Time-series datasets with three patterns (stationary, trend, or both trend and seasonal) were analyzed by using the five individual forecasting models and three combined forecasting methods: simple-average, Bates-Granger, and the proposed approach. The MAPE and RMSE results indicate that the proposed method outperformed the others, especially when the time-series pattern was stationary and improved the forecasting accuracy of the worst and best individual forecasting models by 35–37% and 7–10%, respectively. Moreover, the proposed method showed improvements in MAPE and RMSE of around 18–20% and 9–11% compared to the simple-average and Bates-Granger methods, respectively. In addition, the combined forecasting methods outperformed the individual forecasting models when analyzing non-stationary data. Remarkably, the performances of the proposed and Bates-Granger methods were almost the same, with improvements in MAPE and RMSE in the range of 1–2% on average. Therefore, the proposed method for creating weights based on the correlation coefficients of the individual forecasting models greatly improves combined forecasting methods.","PeriodicalId":19973,"journal":{"name":"Pakistan Journal of Statistics and Operation Research","volume":null,"pages":null},"PeriodicalIF":1.5,"publicationDate":"2023-09-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47256562","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 : 2023-09-03DOI: 10.18187/pjsor.v19i3.4241
F. Yanuar, Tasya Abrari, I. Hg
The Open Unemployment Level (OUL) is the percentage of the unemployed to the total labor force. One of the provinces with the highest OUL score in Indonesia is West Java Province. If an object of observation is affected by spatial effects, namely spatial dependence and spatial diversity, then the regression model used is the Spatial Autoregressive (SAR) model. Quantile regression minimizes absolute weighted residuals that are not symmetrical. It is perfect for use on data distribution that is not normally distributed, dense at the ends of the data distribution, or there are outliers. The Spatial Autoregressive Quantile Regression (SARQR) is a model that combines spatial autoregressive models with quantile regression. This research used the data regarding OUR in West Java in 2020 from the Central Bureau of Statistics. This study compares the estimation results based on SAR and SARQR models to obtain an acceptable model. In this study, it was found that the SARQR model is better than SAR at dealing with the problems of dependency and diversity in spatial data modeling and is not easily affected by the presence of outlier data.
{"title":"The Construction of Unemployment Rate Model Using SAR, Quantile Regression, and SARQR Model","authors":"F. Yanuar, Tasya Abrari, I. Hg","doi":"10.18187/pjsor.v19i3.4241","DOIUrl":"https://doi.org/10.18187/pjsor.v19i3.4241","url":null,"abstract":"The Open Unemployment Level (OUL) is the percentage of the unemployed to the total labor force. One of the provinces with the highest OUL score in Indonesia is West Java Province. If an object of observation is affected by spatial effects, namely spatial dependence and spatial diversity, then the regression model used is the Spatial Autoregressive (SAR) model. Quantile regression minimizes absolute weighted residuals that are not symmetrical. It is perfect for use on data distribution that is not normally distributed, dense at the ends of the data distribution, or there are outliers. The Spatial Autoregressive Quantile Regression (SARQR) is a model that combines spatial autoregressive models with quantile regression. This research used the data regarding OUR in West Java in 2020 from the Central Bureau of Statistics. This study compares the estimation results based on SAR and SARQR models to obtain an acceptable model. In this study, it was found that the SARQR model is better than SAR at dealing with the problems of dependency and diversity in spatial data modeling and is not easily affected by the presence of outlier data.","PeriodicalId":19973,"journal":{"name":"Pakistan Journal of Statistics and Operation Research","volume":null,"pages":null},"PeriodicalIF":1.5,"publicationDate":"2023-09-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47007622","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 : 2023-09-03DOI: 10.18187/pjsor.v19i3.3983
Ramesh Ganesan, Mathavan N
The objective of this article is studying on cost and time minimization of interval transportation problem (ITP) by using Best Candidate Method (BCM), Improved ASM method (IASM), ASM method, Zero Suffix Method (ZSM) and Zero Point Method (ZPM) with new interval arithmetic operations. We have obtained a better optimum result campared with existing methods available in the literature. The problems considered in this article are solved by the above listed methods without converting them into classical transportation problems. A comparative results are also given.
{"title":"A Class of Methods Using Interval Arithmetic Operations for Solving Multi–Objective Interval Transportation Problems","authors":"Ramesh Ganesan, Mathavan N","doi":"10.18187/pjsor.v19i3.3983","DOIUrl":"https://doi.org/10.18187/pjsor.v19i3.3983","url":null,"abstract":"The objective of this article is studying on cost and time minimization of interval transportation problem (ITP) by using Best Candidate Method (BCM), Improved ASM method (IASM), ASM method, Zero Suffix Method (ZSM) and Zero Point Method (ZPM) with new interval arithmetic operations. We have obtained a better optimum result campared with existing methods available in the literature. The problems considered in this article are solved by the above listed methods without converting them into classical transportation problems. A comparative results are also given.","PeriodicalId":19973,"journal":{"name":"Pakistan Journal of Statistics and Operation Research","volume":null,"pages":null},"PeriodicalIF":1.5,"publicationDate":"2023-09-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"67519602","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 : 2023-09-03DOI: 10.18187/pjsor.v19i3.4230
A. Afify, R. R. Pescim, G. Cordeiro, H. A. Mahran
A new weighted exponentiated-exponential distribution is proposed to model financial data. It has heavy-tailed behavior which is suitable for data with right tails. Some actuarial measures for the new model are determined, and simulations are reported. Its parameters are estimated using nine approaches including a Bayesian method. A new Log-WEx-Exponential regression model is defined for right censored data. The importance of the new models is proved by applications to financial data.
{"title":"A New Heavy-Tailed Exponential Distribution: Inference, Regression Model and Applications","authors":"A. Afify, R. R. Pescim, G. Cordeiro, H. A. Mahran","doi":"10.18187/pjsor.v19i3.4230","DOIUrl":"https://doi.org/10.18187/pjsor.v19i3.4230","url":null,"abstract":"A new weighted exponentiated-exponential distribution is proposed to model financial data. It has heavy-tailed behavior which is suitable for data with right tails. Some actuarial measures for the new model are determined, and simulations are reported. Its parameters are estimated using nine approaches including a Bayesian method. A new Log-WEx-Exponential regression model is defined for right censored data. The importance of the new models is proved by applications to financial data.","PeriodicalId":19973,"journal":{"name":"Pakistan Journal of Statistics and Operation Research","volume":null,"pages":null},"PeriodicalIF":1.5,"publicationDate":"2023-09-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46460036","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 : 2023-09-03DOI: 10.18187/pjsor.v19i3.4113
A. Adetunji, Shamsul Rijal Muhammad Sabri
In this study, a new three-parameter mixed Poisson Cubic Rank Transmuted New Weighted Exponential Distribution is proposed. The new discrete distribution is obtained by mixing the Poisson distribution with a newly obtained Cubic Rank Transmuted New Weighted Exponential Distribution. Various shapes and mathematical properties of both mixing distribution and the new count distribution are examined. Special cases of the new proposition are also identified. The distribution along with its special cases and other count distributions are assumed for skewed and dispersed count observations. The maximum likelihood estimation is used to provide estimates for the parameters of all examined distributions. Results show that the new proposition along with some of its special cases provide good fit for all the examined data.
{"title":"Mixed Poisson Transmuted New Weighted Exponential Distribution with Applications on Skewed and Dispersed Count Data","authors":"A. Adetunji, Shamsul Rijal Muhammad Sabri","doi":"10.18187/pjsor.v19i3.4113","DOIUrl":"https://doi.org/10.18187/pjsor.v19i3.4113","url":null,"abstract":"In this study, a new three-parameter mixed Poisson Cubic Rank Transmuted New Weighted Exponential Distribution is proposed. The new discrete distribution is obtained by mixing the Poisson distribution with a newly obtained Cubic Rank Transmuted New Weighted Exponential Distribution. Various shapes and mathematical properties of both mixing distribution and the new count distribution are examined. Special cases of the new proposition are also identified. The distribution along with its special cases and other count distributions are assumed for skewed and dispersed count observations. The maximum likelihood estimation is used to provide estimates for the parameters of all examined distributions. Results show that the new proposition along with some of its special cases provide good fit for all the examined data.","PeriodicalId":19973,"journal":{"name":"Pakistan Journal of Statistics and Operation Research","volume":null,"pages":null},"PeriodicalIF":1.5,"publicationDate":"2023-09-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47473926","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 : 2023-09-03DOI: 10.18187/pjsor.v19i3.4089
Mohamed K. A. Refaie, Asmaa Ayoob Yaqoob, Mahmoud Ali Selim, Emadeldin I. A. Ali
In this study, the authors of the current work describe a novel exponentiated Weibull distribution that they have invented. The study was written by the writers of the current work. It is required to analyze those properties once the pertinent mathematical properties have been derived. In addition to the dispersion index, the anticipated value, variance, skewness, and kurtosis are also statistically examined. The dispersion index is likewise examined. Other beneficial shapes that the new density can assume include "bathtub," "right skewed," "bimodal and left skewed," "unimodal and left skewed," and "bimodal and right skewed." Additionally, these forms can be merged to create a "bathtub." The term "bathtub (U-HRF)," "constant," "monotonically increasing," "upside down-increasing (reversed U-increasing)," "J-HRF," "upside down-constant," "increasing-constant," or "upside down (reversed U)" may be used to describe the new rate of failure. The greatest likelihood method's efficiency is assessed via graphical analysis. The main measures for this procedure’s evaluation are biases and mean squared errors. The reader is given a scenario that graphically displays the adaptability and value of the innovative distribution through the use of three separate sets of actual data.
{"title":"A Novel Version of the Exponentiated Weibull Distribution: Copulas, Mathematical Properties and Statistical Modeling","authors":"Mohamed K. A. Refaie, Asmaa Ayoob Yaqoob, Mahmoud Ali Selim, Emadeldin I. A. Ali","doi":"10.18187/pjsor.v19i3.4089","DOIUrl":"https://doi.org/10.18187/pjsor.v19i3.4089","url":null,"abstract":"In this study, the authors of the current work describe a novel exponentiated Weibull distribution that they have invented. The study was written by the writers of the current work. It is required to analyze those properties once the pertinent mathematical properties have been derived. In addition to the dispersion index, the anticipated value, variance, skewness, and kurtosis are also statistically examined. The dispersion index is likewise examined. Other beneficial shapes that the new density can assume include \"bathtub,\" \"right skewed,\" \"bimodal and left skewed,\" \"unimodal and left skewed,\" and \"bimodal and right skewed.\" Additionally, these forms can be merged to create a \"bathtub.\" The term \"bathtub (U-HRF),\" \"constant,\" \"monotonically increasing,\" \"upside down-increasing (reversed U-increasing),\" \"J-HRF,\" \"upside down-constant,\" \"increasing-constant,\" or \"upside down (reversed U)\" may be used to describe the new rate of failure. The greatest likelihood method's efficiency is assessed via graphical analysis. The main measures for this procedure’s evaluation are biases and mean squared errors. The reader is given a scenario that graphically displays the adaptability and value of the innovative distribution through the use of three separate sets of actual data.","PeriodicalId":19973,"journal":{"name":"Pakistan Journal of Statistics and Operation Research","volume":null,"pages":null},"PeriodicalIF":1.5,"publicationDate":"2023-09-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45231633","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 : 2023-09-03DOI: 10.18187/pjsor.v19i3.4143
S. Bharali, Jiten Hazarika, Kuldeep Goswami
A mathematical model is a mathematical connection that describes some real-life scenario. To handle real-world problems securely and effectively, simulation modelling is required. In this article, the author investigates the stochastic regression model scenario in which the dependent and independent variables in a linear regression model follow a distribution. We assume that the dependent and independent variables both exhibit Type I Extreme Value Distribution. The estimators are then derived using the Modified Maximum Likelihood (MML) estimation method. In accordance with this, a hypothesis testing technique is developed.
{"title":"Marginal and Conditional both Extreme Value Distributions: A Case of Stochastic Regression Model","authors":"S. Bharali, Jiten Hazarika, Kuldeep Goswami","doi":"10.18187/pjsor.v19i3.4143","DOIUrl":"https://doi.org/10.18187/pjsor.v19i3.4143","url":null,"abstract":"A mathematical model is a mathematical connection that describes some real-life scenario. To handle real-world problems securely and effectively, simulation modelling is required. In this article, the author investigates the stochastic regression model scenario in which the dependent and independent variables in a linear regression model follow a distribution. We assume that the dependent and independent variables both exhibit Type I Extreme Value Distribution. The estimators are then derived using the Modified Maximum Likelihood (MML) estimation method. In accordance with this, a hypothesis testing technique is developed.","PeriodicalId":19973,"journal":{"name":"Pakistan Journal of Statistics and Operation Research","volume":null,"pages":null},"PeriodicalIF":1.5,"publicationDate":"2023-09-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44511744","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 : 2023-09-03DOI: 10.18187/pjsor.v19i3.4157
Dari Sani
In this paper, an EPQ model for items that exhibit delay in deterioration is developed. It is assumed that there is no demand and no deterioration during production buildup period. Demand starts immediately after production but no deterioration. Then a period of deterioration sets in until the stock finishes. It is also supposed that the cost of a unit product is inversely related to the rate of demand and directly related to the process reliability (as assumed by Tripathy et al. (2015) and modified by Dari and Sani (2015)). The demand before deterioration sets in is quadratic time dependent while demand after deterioration sets in is a constant. Shortages are allowed and partially backordered. A numerical model is given to compare the simulation model and the statistical analysis conducted on the model to see the effect of measurement changes in other system parameters.
{"title":"An EPQ Model for Delayed Deteriorating Items with Reliability Consideration, Quadratic Demand and Shortages","authors":"Dari Sani","doi":"10.18187/pjsor.v19i3.4157","DOIUrl":"https://doi.org/10.18187/pjsor.v19i3.4157","url":null,"abstract":"In this paper, an EPQ model for items that exhibit delay in deterioration is developed. It is assumed that there is no demand and no deterioration during production buildup period. Demand starts immediately after production but no deterioration. Then a period of deterioration sets in until the stock finishes. It is also supposed that the cost of a unit product is inversely related to the rate of demand and directly related to the process reliability (as assumed by Tripathy et al. (2015) and modified by Dari and Sani (2015)). The demand before deterioration sets in is quadratic time dependent while demand after deterioration sets in is a constant. Shortages are allowed and partially backordered. A numerical model is given to compare the simulation model and the statistical analysis conducted on the model to see the effect of measurement changes in other system parameters.","PeriodicalId":19973,"journal":{"name":"Pakistan Journal of Statistics and Operation Research","volume":null,"pages":null},"PeriodicalIF":1.5,"publicationDate":"2023-09-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48311375","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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