In this paper, a Periodic review deterministic inventory model for deteriorating items with Exponential rate of demand is considered. The model is developed on the basis of constant rate of deteriorating item with shortages and the demand is partially backlogged. The aim of this paper is to find the optimal time to order by minimizing the total inventory cost. The model is illustrated numerically and the sensitivity analysis is also carried out with percentage changes in the parameters.
{"title":"A Periodic Review Deterministic Inventory Model with Exponential Rate of Demand for Deteriorating Items and Partial Backlogging","authors":"N. S. Indhumathy, P. Jayashree","doi":"10.12785/IJCTS/060206","DOIUrl":"https://doi.org/10.12785/IJCTS/060206","url":null,"abstract":"In this paper, a Periodic review deterministic inventory model for deteriorating items with Exponential rate of demand is considered. The model is developed on the basis of constant rate of deteriorating item with shortages and the demand is partially backlogged. The aim of this paper is to find the optimal time to order by minimizing the total inventory cost. The model is illustrated numerically and the sensitivity analysis is also carried out with percentage changes in the parameters.","PeriodicalId":130559,"journal":{"name":"International Journal of Computational & Theoretical Statistics","volume":"78 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2019-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"127086704","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}
Hospital management is generally focused on studying the length of stay of patients since the measure has an impact on hospital resources. It is a challenging task for the hospital management to model the length of stay as they are asymmetric and heterogeneous in nature. Diabetes is a major health problem prevalent worldwide which leads to hospitalization over a time period. The present study deals with stay of diabetes patients classified as very short, short, medium and long duration of stay based on quantile classification rather than arbitrary approach. In this study, we have attempted to include an important covariate known as medical record since it assist in reducing the stay of a patient and can thereby accommodate more patients deserving treatment as inpatients. Based on the multiple levels of the response variable, we have considered fitting multinomial regression model for length of stay on diabetes. Further, this study has considered the validation of variable selection procedure for model fitting using subsampling approach. In conclusion, it has been identified that medical records is one of the important factor affecting the stay of patients and subsampling approach has been helpful in building the final model.
{"title":"Modelling Length of Stay in Hospitals using Multinomial Regression","authors":"S. Harini, M. Subbiah, M. R. Srinivasan","doi":"10.12785/IJCTS/060202","DOIUrl":"https://doi.org/10.12785/IJCTS/060202","url":null,"abstract":"Hospital management is generally focused on studying the length of stay of patients since the measure has an impact on hospital resources. It is a challenging task for the hospital management to model the length of stay as they are asymmetric and heterogeneous in nature. Diabetes is a major health problem prevalent worldwide which leads to hospitalization over a time period. The present study deals with stay of diabetes patients classified as very short, short, medium and long duration of stay based on quantile classification rather than arbitrary approach. In this study, we have attempted to include an important covariate known as medical record since it assist in reducing the stay of a patient and can thereby accommodate more patients deserving treatment as inpatients. Based on the multiple levels of the response variable, we have considered fitting multinomial regression model for length of stay on diabetes. Further, this study has considered the validation of variable selection procedure for model fitting using subsampling approach. In conclusion, it has been identified that medical records is one of the important factor affecting the stay of patients and subsampling approach has been helpful in building the final model.","PeriodicalId":130559,"journal":{"name":"International Journal of Computational & Theoretical Statistics","volume":"230 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2019-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"130984583","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}
Subramanian Chandrasekharan, J. Sreedharan, A. Gopakumar
As fewer samples are meaningless and lead to fallacious conclusions, researchers are used to calculate minimum sample size before the conduct of any study. Although the larger samples can yield more accurate results, an extent for maximum sample size is not fixed. Though large samples are able to give précised and accurate estimates, the studies that collect more samples than the minimum required, may lead to fallacious conclusions. Generally, the test statistics are increasing functions of sample size and limit of the p value (as ‘n’ tents to infinity) results the statistical significance. The current paper investigated the pattern of changes in the estimates and testing results for varying sample sizes. The assessment of this type of patterns in the data and an extended study on this topic will help to find an interval for the sample size. Study concluded with a finding that larger sample does not make differences on the values of descriptive statistics, but has significant impact on the values of inferential statistics and therefore an upper bound for the sample size needs to be fixed. Hence this article gives relevant information about the need of finding adequate sample size interval (n1, n2) within which valid statistical conclusions can be derived, that assures significance of real difference.
{"title":"Statistical Issues in Small and Large Sample: Need of Optimum Upper Bound for the Sample Size","authors":"Subramanian Chandrasekharan, J. Sreedharan, A. Gopakumar","doi":"10.12785/ijcts/060201","DOIUrl":"https://doi.org/10.12785/ijcts/060201","url":null,"abstract":"As fewer samples are meaningless and lead to fallacious conclusions, researchers are used to calculate minimum sample size before the conduct of any study. Although the larger samples can yield more accurate results, an extent for maximum sample size is not fixed. Though large samples are able to give précised and accurate estimates, the studies that collect more samples than the minimum required, may lead to fallacious conclusions. Generally, the test statistics are increasing functions of sample size and limit of the p value (as ‘n’ tents to infinity) results the statistical significance. The current paper investigated the pattern of changes in the estimates and testing results for varying sample sizes. The assessment of this type of patterns in the data and an extended study on this topic will help to find an interval for the sample size. Study concluded with a finding that larger sample does not make differences on the values of descriptive statistics, but has significant impact on the values of inferential statistics and therefore an upper bound for the sample size needs to be fixed. Hence this article gives relevant information about the need of finding adequate sample size interval (n1, n2) within which valid statistical conclusions can be derived, that assures significance of real difference.","PeriodicalId":130559,"journal":{"name":"International Journal of Computational & Theoretical Statistics","volume":"62 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2019-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"122959755","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}
Nadaraya-Watson (NW) estimator with fixed bandwidth and its adaptive forms with varying bandwidths are widely used kernel regression estimators in nonparametric regression. In this paper, we propose a generalized class of varying kernel regression estimators with its members based on various statistical measures of pilot density estimates. We study the performance of the members of this class in terms of mean integrated squared error (MISE).
{"title":"A Generalized Class of Varying Kernel Regression Estimators","authors":"Sharada V. Bhat, Bhargavi Deshpande","doi":"10.12785/IJCTS/060205","DOIUrl":"https://doi.org/10.12785/IJCTS/060205","url":null,"abstract":"Nadaraya-Watson (NW) estimator with fixed bandwidth and its adaptive forms with varying bandwidths are widely used kernel regression estimators in nonparametric regression. In this paper, we propose a generalized class of varying kernel regression estimators with its members based on various statistical measures of pilot density estimates. We study the performance of the members of this class in terms of mean integrated squared error (MISE).","PeriodicalId":130559,"journal":{"name":"International Journal of Computational & Theoretical Statistics","volume":"132 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2019-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"134182041","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}
We propose a generalized class of estimators for finite population variance using the auxiliary variable as well as rank of the auxiliary variable in stratified sampling. We identify many estimators as special cases of the proposed generalized class of estimators. We discuss the properties of all considered estimators up to first order of approximation. A real data set is used to observe the performances of estimators. It is observed that the proposed generalized class of estimators is more efficient than usual sample variance estimator, traditional ratio estimator, Bahl and Tuteja (1991) exponential ratio type estimator, usual difference estimator and Rao (1991) difference-type estimator.
{"title":"Using Rank of the Auxiliary Variable in Estimating Variance of the Stratified Sample Mean","authors":"J. Shabbir, Sat Gupta","doi":"10.12785/IJCTS/060207","DOIUrl":"https://doi.org/10.12785/IJCTS/060207","url":null,"abstract":"We propose a generalized class of estimators for finite population variance using the auxiliary variable as well as rank of the auxiliary variable in stratified sampling. We identify many estimators as special cases of the proposed generalized class of estimators. We discuss the properties of all considered estimators up to first order of approximation. A real data set is used to observe the performances of estimators. It is observed that the proposed generalized class of estimators is more efficient than usual sample variance estimator, traditional ratio estimator, Bahl and Tuteja (1991) exponential ratio type estimator, usual difference estimator and Rao (1991) difference-type estimator.","PeriodicalId":130559,"journal":{"name":"International Journal of Computational & Theoretical Statistics","volume":"57 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2019-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"129651421","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, several Educational Statistical Tools for summarizing a test marks are discussed. The mean, variance, 5number summary, Difficulty index and Discrimination index are discussed in details. The tools are simple, so that they can be understood by almost all instructors regardless of their backgrounds in statistics. The contents of the paper can be very useful for users of statistics at different areas and in particular, teachers.
{"title":"Summarizing Test Grades Using Descriptive Statistical Tools","authors":"M. Al-Saleh","doi":"10.12785/IJCTS/060204","DOIUrl":"https://doi.org/10.12785/IJCTS/060204","url":null,"abstract":"In this paper, several Educational Statistical Tools for summarizing a test marks are discussed. The mean, variance, 5number summary, Difficulty index and Discrimination index are discussed in details. The tools are simple, so that they can be understood by almost all instructors regardless of their backgrounds in statistics. The contents of the paper can be very useful for users of statistics at different areas and in particular, teachers.","PeriodicalId":130559,"journal":{"name":"International Journal of Computational & Theoretical Statistics","volume":"23 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2019-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"127214272","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}
GMM estimators properties for panel data have been very well known in the econometric literature and it has been observed that for small sample cases, they perform well. The OLS (Ordinary Least Squares) is not applicable when lagged endogenous and exogenous variables are correlated with the error term. Hence, here an attempt is made to estimate AR(1) time series model with one additional regressor by considering First-difference GMM and Level GMM estimation methods proposed by Arellano and Bond (1991) and Arellano and Bover (1995) respectively. In order study the performances of the above mentioned estimators in comparison with the OLS estimator Monte Carlo simulation study is carried out. Further, a comparison among these estimators has been done in terms of bias and RMSE. Study disclose that for an autoregressive parameter, Level GMM estimator performs better than First-difference GMM and OLS estimators when T, the sample size is small and ρ, the autoregressive parameter is close to unity. Whereas for the parameter of additional regressor β, Level GMM estimator performs better than the other two mentioned estimators for all the values of ρ and T.
面板数据的GMM估计器属性在计量经济学文献中已经非常有名，并且已经观察到，对于小样本情况，它们表现良好。当滞后的内生变量和外生变量与误差项相关时，普通最小二乘法(OLS)不适用。因此，本文尝试通过考虑Arellano and Bond(1991)和Arellano and Bover(1995)分别提出的First-difference GMM和Level GMM估计方法，对带有一个额外回归量的AR(1)时间序列模型进行估计。为了研究上述估计器的性能，并与OLS估计器进行了蒙特卡罗仿真研究。此外，这些估计器之间的比较已经在偏差和RMSE方面完成。研究表明，对于自回归参数，当样本量T较小且自回归参数ρ接近于单位时，水平GMM估计量比一差GMM估计量和OLS估计量表现更好。而对于附加回归量β的参数，对于所有的ρ和T值，Level GMM估计器的性能都优于其他两种估计器。
{"title":"GMM Estimation of AR(1) Time Series Model with One Additional Regressor","authors":"B. Chakalabbi, Sanmati Neregal, Sagar Matur","doi":"10.12785/IJCTS/060203","DOIUrl":"https://doi.org/10.12785/IJCTS/060203","url":null,"abstract":"GMM estimators properties for panel data have been very well known in the econometric literature and it has been observed that for small sample cases, they perform well. The OLS (Ordinary Least Squares) is not applicable when lagged endogenous and exogenous variables are correlated with the error term. Hence, here an attempt is made to estimate AR(1) time series model with one additional regressor by considering First-difference GMM and Level GMM estimation methods proposed by Arellano and Bond (1991) and Arellano and Bover (1995) respectively. In order study the performances of the above mentioned estimators in comparison with the OLS estimator Monte Carlo simulation study is carried out. Further, a comparison among these estimators has been done in terms of bias and RMSE. Study disclose that for an autoregressive parameter, Level GMM estimator performs better than First-difference GMM and OLS estimators when T, the sample size is small and ρ, the autoregressive parameter is close to unity. Whereas for the parameter of additional regressor β, Level GMM estimator performs better than the other two mentioned estimators for all the values of ρ and T.","PeriodicalId":130559,"journal":{"name":"International Journal of Computational & Theoretical Statistics","volume":"61 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2019-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"124925348","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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