Estimasi Hazard Rate Temporal Point Process

sifatnya acak baik dalam ruang maupun waktu. Point process dikarakterisasikan oleh intensitas bersyaratnya (conditional Intensity). Pada penelitian ini intensitas bersyarat proses titik temporal (temporal point process)  dipandang sebagai proses pembaruan (renewal process) dimana selisih waktu sejak kejadian terakhir tidak tergantung pada selang sebelumnya. Intensitas bersyarat yang bersesuaian pada model ini disebut hazard rate. Untuk mengestimasi parameter  hazard rate digunakan metode Hazard Rate Single Decrement (HRSD) yang diadaptasi  dari metode estimasi dalam studi aktuaria yang dipakai dalam pembentukan tabel mortalita. Pada metode ini, satu individu diasosiasikan dengan satu kejadian. Jika informasi yang digunakan pada pembentukan tabel mortalita adalah tanggal lahir dan tanggal meninggal, maka pada temporal point process digunakan informasi waktu mulai dan berakhirnya suatu kejadian. Selanjutnya pada bagian akhir,  ditinjau dua kasus yaitu estimasi hazard rate dengan waktu antar kejadian berdistribusi uniform dan eksponensial

HAZARD RATE ESTIMATION OF TEMPORAL POINT PROCESS CASE STUDY: EARTHQUAKE HAZARD RATE IN NUSATENGGARA REGION

Hazard rate estimation is one of the important topics in forecasting earthquake occurrence. Forecasting earthquake occurrence is a part of the statistical seismology where the main subject is the point process. Generally, earthquake hazard rate is estimated based on the point process likelihood equation called the Hazard Rate Likelihood of Point Process (HRLPP). In this research, we have developed estimation method, that is hazard rate single decrement HRSD. This method was adapted from estimation method in actuarial studies. Here, one individual associated with an earthquake. The information of epicenter and time of earthquake occurrence are used to estimate hazard rate. At the end, a case study of earthquake occurrence forecast will be given. Furthermore, we compare the hazard rate between HRLPP and HRSD metho

Pemodelan Regresi Nonparametrik Spline Poisson Pada Tingkat Kematian Bayi di Sulawesi Selatan

Poisson regression analysis is a method used to analyze the relationship between predictor variables and response variables with a Poisson distribution. However, not all data have an orderly pattern, so the Poisson regression is not appropriate to use. To solve this problem, a multivariable Poisson nonparametric regression with a spline truncated estimator was used. In this research, the estimation parameters of multivariable Poisson nonparametric regression was applied to data of infant mortality rates in South Sulawesi in 2017. The infant mortality rate can be measured from the number of infant deaths under one year. The method of selecting the optimal knot point uses the Generalized Cross Validation (GCV) method. The best model is formed on a linear spline model with one knot point. Based on the estimation of the parameters formed, it shows that the variable number of babies with low birth weight (x1) and the number of infants who are exclusively breastfed (x3) significantly affect the number of infant deaths.  Keywords: GCV, Multivariable Nonparametric Regression, Poisson, Spline Truncated, Total Infant Mortality

Exploratory Analysis of Rainfall Occurrence in South Sulawesi Region Using Spatial Point Process

This paper study the probability of rainfall occurrence in round\ud year in different segment in South Sulawesi region. In this research, rainfall\ud occurrence in round year described by one line which has divided into 12\ud months. Each one of those months is assumed that the probability of a\ud rainfall follow a homogeneous Poisson distribution. To modeling the\ud rainfall occurrence in round year, a spatial point process is used. The\ud parameter of the model is estimated by Seemingly Unrelated Regression\ud (SUR) method and Ordinary Least Square (OLS) method with assume that\ud two stations have a correlation in residual model. Results of case study on\ud monthly rainfall data indicate that when the residual correlation\ud (autocorrelation) on all models is weakly and not significant. Thus, it has\ud not good enough to use the SUR method for increase efficiency compared\ud with the OLS method. Moreover, results of the parameter estimation of the\ud model for two selected stations (Paotere and Mandai) showed that the SUR\ud method is more representative than the OLS metho

Analisis Peluang Steady State Pada Kasus Covid-19 di Indonesia Menggunakan Rantai Markov

Covid-19 in Indonesia began to be recorded on March 2, 2020 with the number of positive patient cases as many as 2 people with the passage of time Covid-19 cases in Indonesia are always increasing. To see the development of Covid-19 cases in the future period, the opportunity for the number of Covid-19 cases can be used using the Markov chain. The Markov chain method is carried out using a transition probability matrix which is seen from the number of additions to positive Covid-19 patients in a steady state or a situation for a long period of time. Based on the results of the range of additions to the number of positive cases of Covid-19, 6 states were used. Furthermore, the calculation of the Markov Chain in the stationary state of Covid-19 cases in Indonesia after 328 days or 11 months obtained the probability of each state, namely state 1 of 0.0005, state 2 of 0.0069, state 3 of 0.1707, state 4 of 0.1462, state 5 of 0.1884 , and state 6 is 0.4873. Prediction of the addition of positive Covid-19 patients obtained results as many as 2058 patients in state 5 for July 1, 2022 with actual data as many as 2049 patients

Estimasi Parameter Model Poisson Hidden Markov Pada Data Banyaknya Kedatangan Klaim Asuransi Jiwa

The Poisson hidden Markov model is a model that consists of two parts. The first part is the cause of events that are hidden or cannot be observed directly and form a Markov chain, while the second part is the process of observation or observable parts that depend on the cause of the event and following the Poisson distribution. The Poisson hidden Markov model parameters are estimated using the Maximum Likelihood Estimator (MLE). But it is difficult to find analytical solutions from the ln-likelihood function. Therefore, the Expectation Maximization (EM) algorithm is used to obtain its numerical solutions which are then applied to life insurance data. The best model is obtained with 2 states or m = 2 based on the smallest Bayesian Information Criterion (BIC) value of 338,778 and the average predicted number of claims arrivals is 0.385 per day

Penerapan Sparse Principal Component Analysis dalam Menghasilkan Matriks Loading yang Sparse

Abstract Sparse Principal Component Analysis (Sparse PCA) is one of the development of  PCA. Sparse PCA modifies new variables as a linier combination of  p old variables (original variable) which  is yielded by PCA method. Modifying new variables is conducted by producing a loading yang sparse matrix, such that old variable which is not effective (value of loading is zero) able be exit from PCA.  In this study, Sparse PCA method was applied on data of Indonesia Poverty population in 2015, that contains 13 variables and 34 observation with variable reduction such that yields 4 (four) new variables, which can explain 80.1% of total variance data. This study show, the loading matrix that has been yielded by using Sparse PCA method to become sparse with there exist 11 elements (loading value) zero entry of matrix, such that the model that has been produced to be simpler and easy to be interpreted. Keywords:  Principal Component Analysis, Sparse Principal Component Analysis, reduksi dimensi, matriks loading yang sparse Abstrak Sparse Principal Component Analysis (Sparse PCA) merupakan salah satu pengembangan dari metode PCA. Sparse PCA memodifikasi variabel-variabel baru yang merupakan kombinasi linear dari  variabel lama (variabel asli) yang dihasilkan oleh metode PCA. Pemodifikasian variabel baru ini dilakukan dengan dengan menghasilkan matriks loading yang sparse sehingga variabel lama yang tidak efektif (memiliki nilai loading sama dengan nol) dapat dikeluarkan dari model PCA. Pada penelitian ini, metode Sparse PCA diterapkan pada data Indikator Kemiskinan Penduduk Indonesia Tahun 2015 yang memuat 13 variabel dan 34 observasi dengan reduksi variabel menghasilkan 4 (empat) variabel baru yang telah mampu menjelaskan 80,1% dari total variansi data. Hasil penelitian menunjukkan, matriks loading yang dihasilkan menggunakan metode Sparse PCA menjadi sparse dengan terdapat 11 elemen (nilai loading) matriks bernilai nol sehingga model yang dihasilkan menjadi lebih sederhana dan mudah untuk diinterpretasikan. Kata Kunci: Principal Component Analysis, Sparse Principal Component Analysis, reduksi dimensi, matriks loading yang spars

ANALISIS KOVARIANSI RANCANGAN PETAK TERBAGI PADA RANCANGAN ACAK KELOMPOK (RAK) DENGAN DATA HILANG

Pada skripsi ini akan di kaji analisis kovariansi rancangan petak terbagi (split plot design) pada Rancangan Acak Kelompok (RAK) dengan satu data hilang. Analisis kovariansi pada rancangan petak terbagi dilakukan melalui dua analisis yaitu analisis petak utama dan analisis anak petak. Sebagai aplikasi selanjutnya diberikan studi kasus pada percobaan dengan satu data hilang. Dari  hasil analisis rancangan petak terbagi pada Rancangan Acak Kelompok (RAK) dengan satu data hilang diperoleh nilai koefisien keragaman dari analisis variansi lebih kecil dibandingkan analisis kovariansi. Hal ini menunjukkan analisis variansi lebih baik dibandingkan analisis kovariansi pada rancangan petak terbagi (split plot design) pada Rancangan Acak Kelompok (RAK) dengan satu data hilang.

On the Study of Probabilistic Prediction of the Next Large Earthquake in Nusa Tenggara Region

A probabilistic approach can be used to predict the time of the next earthquake on a specific fault. Estimation of the time interval until the next large earthquake in a seismic region is a challenging problem. The most elementary model in probabilistic seismic hazard modeling is the exponential model. Our previous study showed that the exponential sojourn time model for Nusa Tenggara earthquake sequences (Engdahl catalogue) lead us to develop models with greater flexibility than the exponential model. A number candidate statistical distributions have been proposed for computation of conditional probabilistic of future earthquakes, including the Pareto and rayleigh models. In this study, the Weibull model is adopted. Parameters of the model were estimated using maximum likelihood method. The contribution of this paper is to show that the actuarial concepts can be adopted to the study of stochastic prediction of the next large earthquake. The result shows that the Weibull model predicts a damaging earthquake approximately before February 201

Exploratory Analysis of Point Process Applied to Nusa Tenggara Earthquake Sequences

Indonesia is an area with the geographical position which lay in intercourse of three tectonic plates that is Indo-Australia, Eurasia, and Pacific. The accumulation of energy round about the plates intercourse causes earth layer can't hold on it. Hence, there is a big of possibility happened earthquake with high intensity in this area. Nusa tenggara which lay in the plate intercourse become one of the area in Indonesia which has the high risk of earthquake. Generally, earthquake occurrence happened at random, so that it was modeled with Poisson. The results of the exploratory data analysis indicate that the earthquake of Nusa Tenggara do not happened at random but are clustered at certain area (dependent location). Moreover, the occurrence of earthquake in Nusa Tenggara zone less representative modelled with Poisson. This paper discusses the modeling of earthquake at Nusa tenggara zone using stochastic point processes with inter occurrence time is modeled through renewal process. as illustration, we will study pattern by using exploratory approach for Nusa tenggara earthquake sequences