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MANGKU, I W.
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Mathematics

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Estimation of the local intensity of a cyclic Poisson process by means of nearest neighbor distances MANGKU, I W.
MILANG Journal of Mathematics and Its Applications Vol. 1 No. 1 (2002): Journal of Mathematics and Its Applications
Publisher : School of Data Science, Mathematics and Informatics, IPB University

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.29244/jmap.1.1.1-12

Abstract

We consider the problem of estimating the local intensity of a cyclic Poisson point process, when we know the period. We suppose that only a single realization of the cyclic Poisson point process is observed within a bounded 'window', and our aim is to estimate consistently the local intensity at a given point. A nearest neighbor estimator of the local intensity is proposed, and we show that our estimator is weakly and strongly consistent, as the window expands.
ESTIMASI FERTILITAS DENGAN MODEL COALE-TRUSSELL DAN APLIKASINYA TERHADAP DATA INDONE RAMADHANI, A.; SUMARNO, H.; MANGKU, I W.
MILANG Journal of Mathematics and Its Applications Vol. 16 No. 1 (2017): Journal of Mathematics and Its Applications
Publisher : School of Data Science, Mathematics and Informatics, IPB University

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.29244/jmap.16.1.1-12

Abstract

Model fertilitas Coale-Trussell merupakan salah satu metode pengukuran fertilitas secara tidak langsung. Selain dapat menduga tingkat fertilitas, model ini juga dapat digunakan untuk melihat keefektifan alat Keluarga Berencana (KB) dengan menduga nilai parameter model yaitu spacing behaviour (????) dan stopping behaviour (????). Dengan mengasumsikan bahwa jumlah bayi yang dilahirkan terakhir menyebar Poisson, maka pendugaan nilai parameter model dapat menggunakan metode maksimum likelihood. Pada regresi Poisson menyaratkan di mana nilai tengah dan ragam dari variabel terikat harus sama. Apabila ragam lebih besar dari nilai tengah, maka terjadi masalah overdispersi pada data yang akan menyebabkan nilai parameter yang dihasilkan lebih kecil dari nilai parameter seharusnya. Masalah overdispersi akan diatasi dengan regresi binomial negatif. Pada penelitian ini, data yang digunakan adalah data Survei Demografi dan Kesehatan Indonesia (SDKI) tahun 2012 pada enam provinsi, yaitu Sumatera Barat, Yogyakarta, Nusa Tenggara Timur (NTT), Maluku, Kalimantan Barat, dan Sulawesi Utara. Hasil yang diperoleh adalah terdapat masalah overdispersi pada tiga provinsi yaitu Sumatera Barat, Yogyakarta, dan NTT. Hasil analisis regresi binomial negatif menunjukkan bahwa wanita provinsi Yogyakarta lebih efektif dalam menerapkan perilaku hentian kelahiran dibandingkan dengan provinsi lain, sedangkan efektivitas dalam penggunaan KB di provinsi Maluku dan NTT masih rendah.
KAJIAN NUMERIK PENDUGA FUNGSI INTENSITAS BERBENTUK EKSPONENSIAL DARI FUNGSI PERIODIK DITAMBAH TREN LINEAR SUATU PROSES POISSON NONHOMOGEN NASIB, S. K.; MANGKU, I W.; SUMARNO, H.
MILANG Journal of Mathematics and Its Applications Vol. 13 No. 2 (2014): Journal of Mathematics and Its Applications
Publisher : School of Data Science, Mathematics and Informatics, IPB University

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.29244/jmap.13.2.1-10

Abstract

Pada karya ilmiah ini dilakukan kajian numerik untuk melihat perilaku penduga tipe kernel bagi komponen periodik dari fungsi intensitas yang berbentuk eksponensial dari fungsi periodik ditambah tren linear pada suatu proses Poisson nonhomogen. Penyusunan penduga tipe kernel tersebut hanya menggunakan realisasi tunggal dari proses Poisson yang diamati pada interval pengamatan [0,n]. Pada kajian ini dipilih fungsi kernel seragam untuk mengevaluasi sifat-sifat asimtotik penduga dengan tujuan menentukan bandwidth yang dapat meminimumkan MSE, menenukan nilai n yang menghasilkan MSE penduga kurang dari 0.05, serta memverifikasi kenormalan asimtotik penduga.
L2-CONVERGENCE OF A NEAREST NEIGHBOR ESTIMATOR OF THE INTENSITY FUNCTION OF A CYCLIC POISSON PROCES MANGKU, I W.
MILANG Journal of Mathematics and Its Applications Vol. 13 No. 2 (2014): Journal of Mathematics and Its Applications
Publisher : School of Data Science, Mathematics and Informatics, IPB University

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.29244/jmap.13.2.49-62

Abstract

Abstract. We consider the problem of estimating the intensity func- tion of a cyclic Poisson process. We suppose that only a single realization of the cyclic Poisson process is observed within a bounded 'window', and our aim is to estimate consistently the intensity function at a given point. A nearest neighbor estimator of the intensity function is proposed, and we show that our estimator is L2-consistent, as the window expands.AMS 2010 subject classifications: 62E20, 62G05, 62G20.Key words and phrases: cyclic Poisson process, cyclic intensity function, nonparametric estimation, nearest neighbor estimator, period, consis- tency, L2-convergence.
PENDUGAAN KOMPONEN PERIODIK FUNGSI INTENSITAS BERBENTUK FUNGSI PERIODIK KALI TREN LINEAR SUATU PROSES POISSON NON-HOMOGEN ISMAYULIA, W.; MANGKU, I W.; SISWANDI, S.
MILANG Journal of Mathematics and Its Applications Vol. 12 No. 1 (2013): Journal of Mathematics and Its Applications
Publisher : School of Data Science, Mathematics and Informatics, IPB University

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.29244/jmap.12.1.49-62

Abstract

In this manuscript, estimation of the periodic component of intensity having form periodic function multiplied by the linear trend of a non homogeneous Poisson process is discussed. The estimator is constructed using a single realization of the Poisson process observed in the interval  0,???? . It is assumed that the period of the periodic component is known. The convergence of the Mean Square Error (MSE) of the estimator has been proved. In addition, asymptotic approximations to the bias, variance, and Mean Square Error (MSE) of the estimator have been proved. An asymptotic optimal bandwidth is also given.
DISCRIMINANT FUNCTIONS AND THEIR MISCLASSIFICATION ERRORS MANGKU, I W.
MILANG Journal of Mathematics and Its Applications Vol. 1 No. 2 (2002): Journal of Mathematics and Its Applications
Publisher : School of Data Science, Mathematics and Informatics, IPB University

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.29244/jmap.1.2.37-48

Abstract

This paper is a survey study on discriminant functions and their misclassification errors. Here we consider three groups of discriminant functions, namely discriminant functions for respec- tively multivariate normal variables, multivariate binary variables, and a mixture of multivariate binary and normal variables. Finally we derive their misclassification errors.
ESTIMATING THE PROBABILITY OF MISCLASSIFICATIONS IN TWO-GROUPS DISCRIMINANT ANALYSIS MANGKU, I W.
MILANG Journal of Mathematics and Its Applications Vol. 3 No. 1 (2004): Journal of Mathematics and Its Applications
Publisher : School of Data Science, Mathematics and Informatics, IPB University

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.29244/jmap.3.1.1-10

Abstract

This paper is a survey study on estimation of the pro- bability of misclassifications in two-groups discriminant analysis using the linear discriminant function as the classification rule. Here we consider two groups of estimators, namely parametric esti- mators and empirical estimators. The results of some comparative studies on the performances of the considered estimators are also discussed.
APPLICATION OF BOOTSTRAP METHOD ON ESTIMATION OF THE ERROR RATES IN DISCRIMINANT ANALYSIS MANGKU, I W.
MILANG Journal of Mathematics and Its Applications Vol. 3 No. 2 (2004): Journal of Mathematics and Its Applications
Publisher : School of Data Science, Mathematics and Informatics, IPB University

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.29244/jmap.3.2.1-10

Abstract

This paper is a survey study on applications of boot- strap methods for estimating the probability of misclassifications in two-groups discriminant analysis. Here we use the linear discrimi- nant function as classification rule. Some comparative studies on the performances of the considered estimators are also discussed.
ESTIMATING THE INTENSITY IN THE FORM OF A POWER FUNCTION OF AN INHOMOGENEOUS POISSON PROCESS MANGKU, I W.; WIDIYASTUTI, I.; PURNABA, I G. P.
MILANG Journal of Mathematics and Its Applications Vol. 4 No. 1 (2005): Journal of Mathematics and Its Applications
Publisher : School of Data Science, Mathematics and Informatics, IPB University

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.29244/jmap.4.1.51-57

Abstract

An estimator of the intensity in the form of a power function of an inhomogeneous Poisson process is constructed and investigated. It is assumed that only a single realization of the Poisson process is observed in a bounded window. We prove that the proposed estimator is consistent when the size of the window indefinitely expands. The asymptotic bias, variance and the mean- squared error of the proposed estimator are computed. Asymptotic normality of the estimator is also established.
A NOTE ON ESTIMATION OF THE GLOBAL INTENSITY OF A CYCLIC POISSON PROCESS IN THE PRESENCE OF LINEAR TREND MANGKU, I W.
MILANG Journal of Mathematics and Its Applications Vol. 4 No. 2 (2005): Journal of Mathematics and Its Applications
Publisher : School of Data Science, Mathematics and Informatics, IPB University

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.29244/jmap.4.2.1-12

Abstract

We construct and investigate a consistent kernel-type nonparametric estimator of the global intensity of a cyclic Poisson process in the presence of linear trend. It is assumed that only a single realization of the Poisson process is observed in a bounded window. We prove that the proposed estimator is consistent when the size of the window indefinitely expands. The asymptotic bias and variance of the proposed estimator are computed. Bias reduction of the estimator is also proposed.1991 Mathematics Subject Classification: 60
Co-Authors AWATIF, A. BUDIARTI, R. Dhifa Maulia, Syammira Fauzan, M. Daryl HERNIWAT, H. ISMAYULIA, W. Khoerunnisa, N. M. F. Aziz NASIB, S. K. PURNABA, I G. P. RAMADHANI, A. RAMDANI, P. S. Utami, S. SISWANDI, S. SUMARNO, H. SYAMSURI, S. Triwulandari, R.R. Carissa WIDIYASTUTI, I.