scholarly journals FAKTOR-FAKTOR YANG MEMPENGARUHI KASUS DBD DI SULAWESI SELATAN DENGAN MENGGUNAKAN REGRESI POISSON INVERSE GAUSSIAN

2021 ◽  
Author(s):  
SYAMSUL ALAM
Keyword(s):  
Poisson Distribution ◽  
Poisson Regression ◽  
Likelihood Function ◽  
Continuous Distribution ◽  
Inverse Gaussian ◽  
Average Value ◽  
South Sulawesi ◽  
Mixed Poisson Distribution ◽  
Gaussian Regression ◽  
Close Form

Poisson regression is used to model enumeration data such as data on the number of DHF cases. This model has the assumption that is fulfilled is the average and the variance must have the same value or it is called the equidispersion. But this assumption is not fulfilled because the data on the number of dengue cases experienced violations of this assumption. The violation is that the average value is smaller than the variance value or it is called overdispersion. This results in incorrect conclusions because the prediction standard error is underestimated. The way to prevent this is by combining the Poisson distribution and discrete or continuous distribution, this combination is called Mixed Poisson Distribution. Researchers use one of the Mixed Poisson methods, namely Inverse Gaussian Poisson Regression (PIG) because the method is used when the data is overdispersed and the parameters are known or close form on the likelihood function. Based on the results of the study, it is known that the height of the area is a factor that significantly influences DHF cases in South Sulawesi and the model form is as follows: π=exp(5,902-0,0004189 X_2)Keyword: DHF Cases; Poisson Regression; Overdispersion; Poisson Inverse Gaussian Regression;

scholarly journals FAKTOR-FAKTOR YANG MEMPENGARUHI KASUS DBD DI SULAWESI SELATAN DENGAN MENGGUNAKAN REGRESI POISSON INVERSE GAUSSIAN

2021 ◽  
Author(s):  
SYAMSUL ALAM
Keyword(s):  
Poisson Distribution ◽  
Inverse Gaussian ◽  
Mixed Poisson Distribution ◽  
Close Form

Regresi Poisson digunakan untuk memodelkan data yang bersifat cacahan seperti data jumlah kasus DBD. Model ini memiliki asumsi yang dipenuhi ialah rata-rata dan variansinya harus memiliki nilai yang sama besar atau disebut equidispersi. Tapi asumsi tersebut tidak terpenuhi karena data jumlah kasus DBD mengalami pelanggaran Asumsi ini. Pelanggarannya ialah nilai rata-rata lebih kecil dari nilai variansi atau disebut overdispersi. Hal ini mengakibabkan kesimpulan yang diperoleh tidak benar karena pendugaan standar error mengalami underestimate. Cara untuk mencegahnya yaitu dengan menggabungkan antara distribusi poisson dan distribusi diskrit atau kontinu, penggabungan ini dinamakan Mixed Poisson Distribution. Peneliti menggunakan metode salah satu dari Mixed Poisson yaitu Regresi Poisson Inverse Gaussian (PIG) karena metode digunakan apabila data tersebut mengalami overdispersi dan parameter diketahui atau close form pada fungsi likelihood. Berdasarkan hasil dari penelitian diketahui bahwa ketinggian wilayah ialah faktor yang mempengaruhi kasus DBD di Sulawesi Selatan secara signifikan dan diperoleh bentuk model yaitu sebagai berikut:π=exp(5,902-0,0004189 X_2)Kata0Kunci : Kasus DBD;0Regresi Poisson;0Overdispersi;0Regresi Poisson0Inverse Gaussian;

scholarly journals Parameter Estimation and Hypothesis Testing of Multivariate Poisson Inverse Gaussian Regression

Symmetry ◽  
2020 ◽  
Vol 12 (10) ◽  
pp. 1738
Author(s):  
Selvi Mardalena ◽  
Purhadi Purhadi ◽  
Jerry Dwi Trijoyo Purnomo ◽  
Dedy Dwi Prastyo
Keyword(s):  
Parameter Estimation ◽  
Maximum Likelihood ◽  
Hypothesis Testing ◽  
Poisson Regression ◽  
Ratio Test ◽  
Inverse Gaussian ◽  
Count Response ◽  
The Mean ◽  
Gaussian Regression ◽  
Response Variables

Multivariate Poisson regression is used in order to model two or more count response variables. The Poisson regression has a strict assumption, that is the mean and the variance of response variables are equal (equidispersion). Practically, the variance can be larger than the mean (overdispersion). Thus, a suitable method for modelling these kind of data needs to be developed. One alternative model to overcome the overdispersion issue in the multi-count response variables is the Multivariate Poisson Inverse Gaussian Regression (MPIGR) model, which is extended with an exposure variable. Additionally, a modification of Bessel function that contain factorial functions is proposed in this work to make it computable. The objective of this study is to develop the parameter estimation and hypothesis testing of the MPIGR model. The parameter estimation uses the Maximum Likelihood Estimation (MLE) method, followed by the Newton–Raphson iteration. The hypothesis testing is constructed using the Maximum Likelihood Ratio Test (MLRT) method. The MPIGR model that has been developed is then applied to regress three response variables, i.e., the number of infant mortality, the number of under-five children mortality, and the number of maternal mortality on eight predictors. The unit observation is the cities and municipalities in Java Island, Indonesia. The empirical results show that three response variables that are previously mentioned are significantly affected by all predictors.

scholarly journals Parameter estimation and hypothesis testing of geographically and temporally weighted bivariate Poisson inverse Gaussian regression model

2021 ◽  
Vol 880 (1) ◽  
pp. 012045
Author(s):  
Meylita Sari ◽  
Sutikno ◽  
Purhadi
Keyword(s):  
Parameter Estimation ◽  
Maximum Likelihood ◽  
Hypothesis Testing ◽  
Count Data ◽  
Poisson Regression ◽  
Statistical Test ◽  
Ratio Test ◽  
Inverse Gaussian ◽  
Test Statistics ◽  
Gaussian Regression

Abstract One of the appropriate methods used to model count data response and its corresponding predictors is Poisson regression. Poisson regression strictly assumes that the mean and variance of response variables should be equal (equidispersion). Nonetheless, some cases of the count data unsatisfied this assumption because variance can be larger than mean (over-dispersion). If overdispersion is violated, causing the underestimate standard error. Furthermore, this will lead to incorrect conclusions in the statistical test. Thus, a suitable method for modelling this kind of data needs to develop. One alternative model to outcome the overdispersion issue in bivariate response variable is the Bivariate Poisson Inverse Gaussian Regression (BPIGR) model. The BPIGR model can produce a global model for all locations. On the other hand, each location and time have different geographic conditions, social, cultural, and economical so that Geographically and Temporally Bivariate Poisson Inverse Gaussian Regression (GTWBPIGR)) is needed. The weighting function spatial-temporal in GTWBPIGR generates a different local model for each period. GTWBPIGR model solves the overdispersion case and generates global models for each period and location. The parameter estimation of the GTWBPIGR model uses the Maximum Likelihood Estimation (MLE) method, followed by Newton Raphson iteration. Meanwhile, the test statistics on the hypothesis testing is simultaneously testing of the GTWBPIGR model is obtained with the Maximum Likelihood Ratio Test (MLRT) approach, using n large samples of the statistical test is chi-square distribution. Moreover, the test statistics for partially testing used the Z-test statistic.

Features of relativistic charged particles produced in catastrophic destruction of heavy emulsion nuclei at 4.5 A GeV

1998 ◽  
Vol 76 (7) ◽  
pp. 559-566 ◽  
Author(s):  
P Singh ◽  
M S Khan ◽  
H Khushnood
Keyword(s):  
Poisson Distribution ◽  
Linear Dependence ◽  
Charged Particles ◽  
Average Multiplicity ◽  
Average Value ◽  
Multiplicity Distributions ◽  
Good Agreement ◽  
Fireball Model

Total disintegration events produced in 4.5 A GeV/c 12C--AgBr reactions are analysed to investigate the characteristics of secondary charged particles produced in such collisions. The results reveal that multiplicity distributions of grey, black, and relativistic charged particles agree with the Poisson distribution. The average multiplicity of grey particles is found to increase with the increasing mass of projectile, while the average value of black particles is found to decrease with the increasing mass of projectile. This result is in good agreement with the prediction of fireball model. Finally, the linear dependence of grey and compound multiplicities on black, heavy, and relativistic charged particles is also observed. PACS No.: 25.70

scholarly journals ANALISIS SISTEM PELAYANAN KERETA API DI STASIUN SEMARANG TAWANG MENGGUNAKAN PROSES BAYESIAN

2020 ◽  
Vol 9 (4) ◽  
pp. 495-504
Author(s):  
Lifana Nugraeni ◽  
Sugito Sugito ◽  
Dwi Ispriyanti
Keyword(s):  
Poisson Distribution ◽  
Posterior Distribution ◽  
Public Transportation ◽  
Bayesian Method ◽  
Service System ◽  
Likelihood Function ◽  
Performance Standard ◽  
Sample Distribution ◽  
Service Patterns ◽  
Transportation Facilities

Along with the times, transportation has progressed. Regarding the means of transportation, one of the phenomenon that is easily encountered in everyday life is the queue at public transportation facilities. One of the queues that occurred at public transportation facilities is  the train queue at Semarang Tawang Station. The number of trains that passes the station can cause the train service at the station busy. This study aims to see whether the train service system of Semarang Tawang Station is good or not. This can be consider by the queues method, determining the distribution of arrival patterns and service patterns to obtain a queues system model and a system performance standard. In this study, the distribution of arrival patterns and service patterns are determined by calculating the posterior distribution using the Bayesian method. The bayesian method was chosen because it is able to combine the sample distribution in the current study with the previous information for the same cases. The prior distribution and the likelihood function are the elements needed to obtain the posterior distribution. The distribution of arrival patterns and service patterns obtained from previous information follows the Poisson distribution. Based on the calculation of the posterior distribution, the result shows that the distribution of the arrival pattern is a discrete uniform distribution and the distribution of the service pattern is a Poisson distribution. The result shows that the train service system at Semarang Tawang Station has a model (Uniform Discrete / Gamma / 7: GD / ~ / ~) and has good service based on the performance values obtained.

scholarly journals Model Generalized Poisson Regression (GPR) dan Penerapannya pada Angka Pengangguran bagi Penduduk Usia Kerja di Provinsi Sulawesi Selatan

2021 ◽  
Vol 3 (2) ◽  
pp. 109
Author(s):  
Hisyam Ihsan ◽  
Wahidah Sanusi ◽  
Risna Ulfadwiyanti
Keyword(s):  
Maximum Likelihood ◽  
Maximum Likelihood Estimation ◽  
Unemployment Rate ◽  
Poisson Regression ◽  
Likelihood Estimation ◽  
Generalized Poisson ◽  
South Sulawesi ◽  
Working Age ◽  
Working Age Population ◽  
Generalized Poisson Regression

Abstrak. Penelitian ini membahas tentang pembentukan model Generalized Poisson Regression (GPR) dan penerapannya pada angka pengangguran bagi penduduk usia kerja di Provinsi Sulawesi Selatan. Jenis penelitian ini adalah penelitian terapan yang menggunakan model regresi nonlinear, yaitu model regresi Poisson dan model GPR. Variabel respon yang digunakan adalah jumlah angka pengangguran pada usia kerja yang termasuk angkatan kerja di Provinsi Sulawesi Selatan pada tahun 2017. Adapun variabel-variabel prediktor yang digunakan yaitu persentase angkatan kerja terhadap penduduk usia kerja, Indeks Pembangunan Manusia, persentase bekerja terhadap angkatan kerja, kepadatan penduduk, dan pertumbuhan ekonomi. Penelitian menggunakan metode Maximum Likelihood Estimation (MLE) untuk mengestimasikan parameter dan menghasilkan sebuah model GPR. Variabel prediktor yang memberikan pengaruh secara signifikan adalah Indeks Pembangunan Manusia dan  persentase bekerja terhadap angkatan kerja.Kata kunci: Angka Pengangguran, Regresi Poisson, Overdispersi, Generalized Poisson Regression, Maximum Likelihood Estimation  Abstract. This study discusses the formation of the Generalized Poisson Regression (GPR) model and its application to the unemployment rate for the working age population in South Sulawesi Province. This type of research is applied research that uses the Poisson regression model, namely Poisson regression and GPR models. The response variabel used is the total unemployment rate at working age which includes the workforce in South Sulawesi Province in 2017. The predictor variables used are the percentage of the workforce on the working age population, the Human Development Index, the percentage of work on the labor force, population density, and economic growth. This research uses the Maximum Likelihood Estimation (MLE) method to estimate parameters and produce a GPR model. The predictor variables which have a significant influence are the Human Development Index and the percentage of work on the labor force.Keywords: Unemployment Rate, Poisson Regression, Overdispersion, Generalized Poisson Regression, Maximum Likelihood Estimation

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