I. U. Siloko, E. A. Siloko, O. Ikpotokin, C. Ishiekwene, B. A. Afere
The techniques of asymptotic mean integrated squared error’s reduction in kernel density estimation is the focus of this paper. The asymptotic mean integrated squared error (AMISE) is an optimality criterion function that measures the performance of a kernel density estimator. This criterion function is made up of two components, and the contributions of both components to the AMISE are mainly regulated by the smoothing parameter. Kernel density estimation are of vitally importance in statistical data analysis especially for exploratory and visualization purposes. In performance evaluation, a method is better when it produces a smaller value of the AMISE; hence effort is being made to develop techniques that reduce the AMISE while ensuring that in practical implementation using real data, the statistical properties of the given observations are retained. We consider the kernel density derivative and kernel boosting as the AMISE reduction techniques. In kernel boosting, we introduce the optimal smoothing parameter selector for each boosting steps as the number of iteration increases. The presented results show that the AMISE decreases with higher kernel derivatives and also as the number of boosting steps increases.
{"title":"On Asymptotic Mean Integrated Squared Error’s Reduction Techniques in Kernel Density Estimation","authors":"I. U. Siloko, E. A. Siloko, O. Ikpotokin, C. Ishiekwene, B. A. Afere","doi":"10.12785/IJCTS/060110","DOIUrl":"https://doi.org/10.12785/IJCTS/060110","url":null,"abstract":"The techniques of asymptotic mean integrated squared error’s reduction in kernel density estimation is the focus of this paper. The asymptotic mean integrated squared error (AMISE) is an optimality criterion function that measures the performance of a kernel density estimator. This criterion function is made up of two components, and the contributions of both components to the AMISE are mainly regulated by the smoothing parameter. Kernel density estimation are of vitally importance in statistical data analysis especially for exploratory and visualization purposes. In performance evaluation, a method is better when it produces a smaller value of the AMISE; hence effort is being made to develop techniques that reduce the AMISE while ensuring that in practical implementation using real data, the statistical properties of the given observations are retained. We consider the kernel density derivative and kernel boosting as the AMISE reduction techniques. In kernel boosting, we introduce the optimal smoothing parameter selector for each boosting steps as the number of iteration increases. The presented results show that the AMISE decreases with higher kernel derivatives and also as the number of boosting steps increases.","PeriodicalId":373764,"journal":{"name":"International Journal of Computational and Theoretical Statistics","volume":"136 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2019-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"132274769","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}
The level of performance and participation in Science, Technology, Engineering and Mathematics (STEM) career subjects remains low in Kenya despite STEM’s critical role in economic development. Numerous factors contribute to students’ academic achievement in STEM education. This study focusses on modelling school factors that affect the performance in mathematics and science in Kenyan secondary schools using Canonical Correlation Analysis (CCA). The objectives of the study include determining: the magnitude of the relationship between school factors and performance in STEM education, the most influential subject in describing the level of STEM education, the most contributing school factor to STEM education and a model to predict performance in STEM education given school factors. This research utilised data from 9,834 candidates of year 2015 Kenya Certificate of Secondary Education (KCSE) from 77 public secondary schools in Nairobi County. CCA is a multivariate data analysis technique that seeks to establish whether two sets of variables, predictor and criterion, are independent of each other. Given that the two sets of variables are dependent, CCA is able to represent a relationship between the sets of variables rather than individual variables. From the 2015 KCSE data, CCA revealed that school factors significantly correlate with the level of performance in STEM education. Based on standardised canonical coefficients and canonical loadings, the subjects that mainly influence the level of performance in STEM education were found to be mathematics and physics. Further assessment of the canonical cross loadings from the two variate pairs revealed that the proportion of students with mean grades of C+ and above and the proportions of students taking biology and physics were found to contribute very highly to the level of performance in STEM education. The study recommends increased staffing in physics due to the fact that physics is an optional subject yet it has comparatively larger loadings than biology and chemistry which have higher levels of participation. Also, the study recommends that further studies should be done to establish the relationship between individual factors and participation and performance in STEM career subjects. iv
{"title":"Modelling School Factors and Performance in Mathematics and Science in Kenyan Secondary Schools Using Canonical Correlation Analysis","authors":"Jeremiah M Mucunu","doi":"10.12785/ijcts/050201","DOIUrl":"https://doi.org/10.12785/ijcts/050201","url":null,"abstract":"The level of performance and participation in Science, Technology, Engineering and Mathematics (STEM) career subjects remains low in Kenya despite STEM’s critical role in economic development. Numerous factors contribute to students’ academic achievement in STEM education. This study focusses on modelling school factors that affect the performance in mathematics and science in Kenyan secondary schools using Canonical Correlation Analysis (CCA). The objectives of the study include determining: the magnitude of the relationship between school factors and performance in STEM education, the most influential subject in describing the level of STEM education, the most contributing school factor to STEM education and a model to predict performance in STEM education given school factors. This research utilised data from 9,834 candidates of year 2015 Kenya Certificate of Secondary Education (KCSE) from 77 public secondary schools in Nairobi County. CCA is a multivariate data analysis technique that seeks to establish whether two sets of variables, predictor and criterion, are independent of each other. Given that the two sets of variables are dependent, CCA is able to represent a relationship between the sets of variables rather than individual variables. From the 2015 KCSE data, CCA revealed that school factors significantly correlate with the level of performance in STEM education. Based on standardised canonical coefficients and canonical loadings, the subjects that mainly influence the level of performance in STEM education were found to be mathematics and physics. Further assessment of the canonical cross loadings from the two variate pairs revealed that the proportion of students with mean grades of C+ and above and the proportions of students taking biology and physics were found to contribute very highly to the level of performance in STEM education. The study recommends increased staffing in physics due to the fact that physics is an optional subject yet it has comparatively larger loadings than biology and chemistry which have higher levels of participation. Also, the study recommends that further studies should be done to establish the relationship between individual factors and participation and performance in STEM career subjects. iv","PeriodicalId":373764,"journal":{"name":"International Journal of Computational and Theoretical Statistics","volume":"11 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2018-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"133833162","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
In this paper, we derive the explicit expression for the moments of generalized order statistics (gos) from Ailamujia distribution and some computational work is also carried out. Further, some recurrence relations for both single and product moments of gos for this distribution are derived and the results are deduced for order statistics and record values.
{"title":"Moment Properties of Generalized Order Statistics from Ailamujia Distribution","authors":"Neetu Gupta, Z. Anwar, A. Dar","doi":"10.12785/IJCTS/050207","DOIUrl":"https://doi.org/10.12785/IJCTS/050207","url":null,"abstract":"In this paper, we derive the explicit expression for the moments of generalized order statistics (gos) from Ailamujia distribution and some computational work is also carried out. Further, some recurrence relations for both single and product moments of gos for this distribution are derived and the results are deduced for order statistics and record values.","PeriodicalId":373764,"journal":{"name":"International Journal of Computational and Theoretical Statistics","volume":"97 2","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2018-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"113954378","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}
This paper introduces a new method, called GPQ method, for the computation of overlapping coefficient of two Pareto distributions. Expected lengths and coverage probabilities of the confidence intervals are also calculated using the generalized pivotal quantity. The comparison of the method is done with the best available method, that is, bootstrap percentile method. The general performance of the proposed method is better than the existing methods. An illustrative example is also presented.
{"title":"Generalized Inference for the Overlapping Coefficientof two Pareto Distributions","authors":"Sibil Jose, Seemon Thomas","doi":"10.12785/ijcts/050205","DOIUrl":"https://doi.org/10.12785/ijcts/050205","url":null,"abstract":"This paper introduces a new method, called GPQ method, for the computation of overlapping coefficient of two Pareto distributions. Expected lengths and coverage probabilities of the confidence intervals are also calculated using the generalized pivotal quantity. The comparison of the method is done with the best available method, that is, bootstrap percentile method. The general performance of the proposed method is better than the existing methods. An illustrative example is also presented.","PeriodicalId":373764,"journal":{"name":"International Journal of Computational and Theoretical Statistics","volume":"125 5 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2018-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"129726331","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}
A stochastic model in this paper possesses the survival of the human system to withstand the threshold level. This model will apply for any environmental population to accesses when the virus damages the human system in the time period. Through shock model approach in stochastic process we find out the mean along with numerical simulations are concluded.
{"title":"Cessation Point of HIV Transmission through Stochastic Approach","authors":"Thirumurugan Ammasi, V. Raman","doi":"10.12785/IJCTS/050203","DOIUrl":"https://doi.org/10.12785/IJCTS/050203","url":null,"abstract":"A stochastic model in this paper possesses the survival of the human system to withstand the threshold level. This model will apply for any environmental population to accesses when the virus damages the human system in the time period. Through shock model approach in stochastic process we find out the mean along with numerical simulations are concluded.","PeriodicalId":373764,"journal":{"name":"International Journal of Computational and Theoretical Statistics","volume":"15 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2018-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"133706138","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}
Abstract: This paper derives a new four-parameter generalized exponential power lifetime probability model for life time data, which generalizes some well-known exponential power lifetime distributions. It is observed that our proposed new distribution bears most of the properties of skewed distributions in reliability and life testing context. It is skewed to the right as well as its failure rate function has the increasing and bathtub shape behaviors. The estimation of the parameters, and simulation and applications of the proposed model have also been discussed.
{"title":"A New Extension of the Exponential Power Distribution with Application to Lifetime Data","authors":"M. Shakil, B. M. Kibria, M. Elgarhy","doi":"10.12785/ijcts/050202","DOIUrl":"https://doi.org/10.12785/ijcts/050202","url":null,"abstract":"Abstract: This paper derives a new four-parameter generalized exponential power lifetime probability model for life time data, which generalizes some well-known exponential power lifetime distributions. It is observed that our proposed new distribution bears most of the properties of skewed distributions in reliability and life testing context. It is skewed to the right as well as its failure rate function has the increasing and bathtub shape behaviors. The estimation of the parameters, and simulation and applications of the proposed model have also been discussed.","PeriodicalId":373764,"journal":{"name":"International Journal of Computational and Theoretical Statistics","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2018-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"129443365","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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