Yesi Santika, Widiarti Widiarti, Fitriani Fitriani, M. Usman
Small area estimation is defined as a statistical technique for estimating the parameters of a subpopulation with a small sample size. One method of estimating small area parameters is the Empirical Bayes (EB) method. The accuracy of the Empirical Bayes (EB) estimator can be measured by evaluating the Mean Squared Error (MSE). In this study, 3 methods to determine MSE in the EB estimator of the Beta-Bernoulli model will be compared, namely the Bootstrap, Jackknife Jiang and Area-specific Jackknife methods. The study is carried out theoretically and empirically through simulation with R-studio software version 1.2.5033. The simulation results in a number of areas and pairs of prior distribution parameter values, namely Beta, show the effect of sample size and parameter value pairs on the Mean Square Error (MSE) value. The larger the number of areas and the smaller the initial 𝛽, the smaller the MSE value. The area-specific Jackknife method produces the smallest MSE in the number of areas 100 and the Beta parameter value 0.1.
{"title":"Perbandingan Metode Bootstrap, Jacknife Jiang Dan Area Specific Jacknife Pada Pendugaan Mean Square Error Model Beta-Bernoulli","authors":"Yesi Santika, Widiarti Widiarti, Fitriani Fitriani, M. Usman","doi":"10.23960/JSM.V2I1.2756","DOIUrl":"https://doi.org/10.23960/JSM.V2I1.2756","url":null,"abstract":"Small area estimation is defined as a statistical technique for estimating the parameters of a subpopulation with a small sample size. One method of estimating small area parameters is the Empirical Bayes (EB) method. The accuracy of the Empirical Bayes (EB) estimator can be measured by evaluating the Mean Squared Error (MSE). In this study, 3 methods to determine MSE in the EB estimator of the Beta-Bernoulli model will be compared, namely the Bootstrap, Jackknife Jiang and Area-specific Jackknife methods. The study is carried out theoretically and empirically through simulation with R-studio software version 1.2.5033. The simulation results in a number of areas and pairs of prior distribution parameter values, namely Beta, show the effect of sample size and parameter value pairs on the Mean Square Error (MSE) value. The larger the number of areas and the smaller the initial 𝛽, the smaller the MSE value. The area-specific Jackknife method produces the smallest MSE in the number of areas 100 and the Beta parameter value 0.1.","PeriodicalId":286978,"journal":{"name":"Jurnal Siger Matematika","volume":"11 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-03-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"123779597","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}
Forecasting is a method used to estimate or predict a value in the future using data from the past. With the development of methods in time series data analysis, a hybrid method was developed in which a combination of several models was carried out in order to produce a more accurate forecast. The purpose of this study was to determine whether the TSR-ARIMA hybrid method has a better level of accuracy than the individual TSR method so that more accurate forecasting results are obtained. The data in this study are monthly data on the number of passengers on American airlines for the period January 1949 to December 1960. Based on the analysis, the TSR-ARIMA hybrid method produces a MAPE of 3,061% and the TSR method produces an MAPE of 7,902%.
{"title":"Peramalan Data Runtun Waktu menggunakan Model Hybrid Time Series Regression – Autoregressive Integrated Moving Average","authors":"Melisa Arumsari, A. Dani","doi":"10.23960/JSM.V2I1.2736","DOIUrl":"https://doi.org/10.23960/JSM.V2I1.2736","url":null,"abstract":"Forecasting is a method used to estimate or predict a value in the future using data from the past. With the development of methods in time series data analysis, a hybrid method was developed in which a combination of several models was carried out in order to produce a more accurate forecast. The purpose of this study was to determine whether the TSR-ARIMA hybrid method has a better level of accuracy than the individual TSR method so that more accurate forecasting results are obtained. The data in this study are monthly data on the number of passengers on American airlines for the period January 1949 to December 1960. Based on the analysis, the TSR-ARIMA hybrid method produces a MAPE of 3,061% and the TSR method produces an MAPE of 7,902%.","PeriodicalId":286978,"journal":{"name":"Jurnal Siger Matematika","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-03-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"129709727","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}
Nowdays, the use of a group of autonomous robots are grown increasingly, especially for an application dealing with hazardous material and or dangerous situation. In this case, autonomous robot movement where there is no interference from a human on the execution process is very important. The concern is how this group of autonomous robots could arrive as fast as possible to the target location to perform the tasks given. If it includes the movement of groups of autonomous robots then particle swarm optimization (PSO) is one of a simple yet powerful method available. Fuzzy logic as a logic system has been proven can be combined with various numbers of applications or methods to get a more optimal result. One of them is the combination of fuzzy logic with PSO method. This paper implemented the fuzzy-PSO optimization method to simulate a group of robots movement to the target location using scratch programming. The fuzzy-PSO optimization results, then compared to the results of classic PSO optimization. It is found that the robots with fuzzy-PSO optimization movement arrived at the location target in average more than 40% faster compared to the robots with classic PSO optimization movement.
{"title":"SIMULATION OF ROBOT MOVEMENT IN 2-DIMENSIONAL SPACE USING FUZZY-PARTICLE SWARM OPTIMIZATION","authors":"I. Irianto, Tan Hauw-Sen","doi":"10.23960/jsm.v1i1.2487","DOIUrl":"https://doi.org/10.23960/jsm.v1i1.2487","url":null,"abstract":"Nowdays, the use of a group of autonomous robots are grown increasingly, especially for an application dealing with hazardous material and or dangerous situation. In this case, autonomous robot movement where there is no interference from a human on the execution process is very important. The concern is how this group of autonomous robots could arrive as fast as possible to the target location to perform the tasks given. If it includes the movement of groups of autonomous robots then particle swarm optimization (PSO) is one of a simple yet powerful method available. Fuzzy logic as a logic system has been proven can be combined with various numbers of applications or methods to get a more optimal result. One of them is the combination of fuzzy logic with PSO method. This paper implemented the fuzzy-PSO optimization method to simulate a group of robots movement to the target location using scratch programming. The fuzzy-PSO optimization results, then compared to the results of classic PSO optimization. It is found that the robots with fuzzy-PSO optimization movement arrived at the location target in average more than 40% faster compared to the robots with classic PSO optimization movement.","PeriodicalId":286978,"journal":{"name":"Jurnal Siger Matematika","volume":"13 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2020-03-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"129139204","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}
Anis Mahfud Al’afi, Widiarti Widiarti, D. Kurniasari, M. Usman
Air transportation is now a mode of transportation that is often the first choice. Although the transportation costs are relatively expensive, it can save a lot of time to get to the destination. Therefore, predicting the number of aircraft passengers is an interesting thing to study. In this study forecasting the number of aircraft passengers at Raden Intan II Airport using spectral analysis methods. Spectral analysis is used to obtain more complete information about the time series data characteristics to examine the periodicity. After getting the periodicity the data is modeled using the ARIMA Seasonal Method . Based on the analysis results it is known that the best model for forecasting aircraft passengers at Raden Intan II Airport is Seasonal ARIMA (0,1,1) (0,1,1) 3
{"title":"Peramalan Data Time Series Seasonal Menggunakan Metode Analisis Spektral","authors":"Anis Mahfud Al’afi, Widiarti Widiarti, D. Kurniasari, M. Usman","doi":"10.23960/jsm.v1i1.2484","DOIUrl":"https://doi.org/10.23960/jsm.v1i1.2484","url":null,"abstract":"Air transportation is now a mode of transportation that is often the first choice. Although the transportation costs are relatively expensive, it can save a lot of time to get to the destination. Therefore, predicting the number of aircraft passengers is an interesting thing to study. In this study forecasting the number of aircraft passengers at Raden Intan II Airport using spectral analysis methods. Spectral analysis is used to obtain more complete information about the time series data characteristics to examine the periodicity. After getting the periodicity the data is modeled using the ARIMA Seasonal Method . Based on the analysis results it is known that the best model for forecasting aircraft passengers at Raden Intan II Airport is Seasonal ARIMA (0,1,1) (0,1,1) 3","PeriodicalId":286978,"journal":{"name":"Jurnal Siger Matematika","volume":"46 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2020-03-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"125684390","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}
Penentuan skewness pada graf lengkap Kn dilakukan dengan cara menggambar kembali graf tersebut sedemikian sehingga menjadi planar dan kemudian menghitung jumlah edge yang pengambarannnya mengakibatkan graf tersebut menjadi tidak planar . Penentuan skewness pada graf lengkap Kn secara manual sangat tidak efisien untuk n yang besar. Oleh karena itu, penetuan skewness pada graf lengkap Kn perlu dilakukan secara komputasi. Dalam penelitian ini dilakukan penentuan skewness pada graf lengkap Kn secara komputasi dengan menggunakan perangkat lunak Mathematica . Selain hasilnya lebih efektif dan efisien juga dapat ditemukan berapa banyak cara pembuangan edge pada graf lengkap Kn agar graf tersebut menjadi planar .
{"title":"Penentuan Skewness Pada Graf Lengkap Kn Dengan Menggunakan Mathematica","authors":"Subian Saidi, A. Faisol","doi":"10.23960/jsm.v1i1.2453","DOIUrl":"https://doi.org/10.23960/jsm.v1i1.2453","url":null,"abstract":"Penentuan skewness pada graf lengkap Kn dilakukan dengan cara menggambar kembali graf tersebut sedemikian sehingga menjadi planar dan kemudian menghitung jumlah edge yang pengambarannnya mengakibatkan graf tersebut menjadi tidak planar . Penentuan skewness pada graf lengkap Kn secara manual sangat tidak efisien untuk n yang besar. Oleh karena itu, penetuan skewness pada graf lengkap Kn perlu dilakukan secara komputasi. Dalam penelitian ini dilakukan penentuan skewness pada graf lengkap Kn secara komputasi dengan menggunakan perangkat lunak Mathematica . Selain hasilnya lebih efektif dan efisien juga dapat ditemukan berapa banyak cara pembuangan edge pada graf lengkap Kn agar graf tersebut menjadi planar .","PeriodicalId":286978,"journal":{"name":"Jurnal Siger Matematika","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2020-03-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"128814953","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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