Estimating the Variance Function of a Compound Cyclic Poisson Process

Makhmudah, Fitriani Ida; Mangku, I Wayan; Sumarno, Hadi

doi:10.17654/ms100060911

Cited by 9 publications

(15 citation statements)

References 0 publications

Supporting

Mentioning

Contrasting

Unclassified

Order By: Relevance

“…Proses Poisson periodik majemuk tidak mengikuti pola sebaran pada umumnya, sehingga yang dapat dihitung hanya berupa nilai harapan dan ragam, dimana keduanya merupakan peubah acak yang nilainya bermacam-macam bergantung pada waktu pengamatan, sehingga disebut fungsi nilai harapan dan fungsi ragam. Penelitian mengenai fungsi nilai harapan dan fungsi ragam proses Poisson periodik majemuk telah dilaporkan oleh Mangku, et.al [11], pendugaan fungsi nilai harapan dan fungsi ragam pada proses Poisson periodik majemuk telah dilaporkan oleh Ruhiyat, et.al [12] dan Makhmudah, et.al [13]. Pada waktu pengamatan relatif lama, kedua fungsi tersebut memiliki sebaran asimtotik yaitu mengikuti sebaran tertentu.…”

Section: Pendahuluanunclassified

See 1 more Smart Citation

Interval Kepercayaan Untuk Fungsi Nilai Harapan dan Fungsi Ragam Proses Poisson Periodik Majemuk

2022

Self Cite

View full text Add to dashboard Cite

Compound cyclic Poisson process have the mean and variance functions. The objective of this paper is to construct confidence intervals for respectively the mean and variance functions of a compound cyclic Poisson process with significance level 0alpha1 and to do a simulation study to observe the probabilities that parameters are contained in the confidence intervals. We do not assume any parametric form for the intensity function except that it is periodic. We consider in the observed there is only one realization of the cyclic Poisson process in a bounded interval. The main results are two theory about confidence intervals for parameters. The simulation shows that the probability values of the observed parameters contained in the confidence intervals are in accordance with the theory.

show abstract

Section: Pendahuluanunclassified

“…Persamaan ( 12) dan (13) berturut-turut adalah fungsi nilai harapan dan fungsi ragam dari Y (t) [11,13]. Terlihat θ dan Λ (t r ) pada persamaan (12) dan (13) tidak saling bebas.…”

Section: Fungsi Nilai Harapan Dan Fungsi Ragamunclassified

Interval Kepercayaan Untuk Fungsi Nilai Harapan dan Fungsi Ragam Proses Poisson Periodik Majemuk

2022

Self Cite

View full text Add to dashboard Cite

show abstract

“…Kemudian pada Mangku [5] dilakukan modifikasi terhadap penduga fungsi nilai harapan yang disusun pada Ruhiyat [9] agar bisa ditentukan pendekatan asimtotik bagi bias dan ragamnya. Pada Makhmudah [4] diteliti tentang pendugaan fungsi ragam proses Poisson periodik majemuk. Pada Wibowo [12] diteliti tentang pendugaan fungsi nilai harapan proses Poisson periodik majemuk dengan tren linear.…”

Section: Pendahuluanunclassified

Evaluasi Numerik Penduga Fungsi Nilai Harapan Dan Fungsi Ragam Proses Poisson Majemuk Dengan Intensitas Eksponensial Fungsi Linear

Utami

Mangku

Purnaba

2018

JMA

View full text Add to dashboard Cite

Performances of estimators for the mean and variance functions of a compound Poisson process having intensity obtained as an exponential of linear function are investigated using Monte Carlo simulations. The intensity function of this process is assumed to be 𝑒𝑥𝑝(𝛼+𝛽𝑠) with 0<𝛽<∞, where 𝛽 is assumed to be known. In [8], estimators of the mean and variance functions of this process have been constructed and have been proved to be unbiased, weakly and strongly consistent. The objectives of this research are to check distributions of these estimators using Monte Carlo simulation and to check the convergence to 1−𝛼 of the probabilities that the parameters are contained in the confidence intervals constructed in [11]. Results of the research are as follows. Distribution of estimators for the mean and variance functions are approximately normal. For a given significance level 𝛼, the larger the size of observation interval, the closer the probabilities that the parameters are contained in the confidence intervals to 1−𝛼.

show abstract

“…So it is necessary to develop a new model where the frequency component in CPP is assumed to have the form of NHPP. Furthermore, if in an event that has an event that tends to be repeated so that it has cyclic or periodic properties, then the model must be changed to the form of NHPP with an intensity function in the form of periodic functions ( [7], [8] and [9]). Because this intensity function has a repetitive function in the next period, this model is good for describing phenomena that occur periodically.…”

Section: Introductionmentioning

confidence: 99%

Algorithm for Generating Compound Poisson Process Which has Nonhomogeneous Poisson process and Exponential Distribution Components

Abdullah¹,

Susilo²,

Mangku³

et al. 2020

Proceedings of the 1st International Multidisciplinary Conference on Education, Technology, and Engineering (IMCETE 2019)

Self Cite

View full text Add to dashboard Cite

Compound Poisson process (CPP) is one of the models of stochastic processes in which this model can model a real phenomenon that has an element of uncertainty in the process. CPP has two main components, those is a Poisson process on the component of the poses of an event that occurs and a sequence component of the magnitude as a result of the process of events that occur. This research aims to develop an algorithm to generate random numbers from CPP with a component in the Poisson process in the form of a nonhomogeneous Poisson process (NHPP) and a component in the magnitude of the effect in the form of an exponential distribution (CPP-NHPP-ED). The method used is using the acceptance and rejection method in the form of Thinning process techniques. The results of the study obtained several algorithms, namely the algorithm for CPP-HPP-ED, CPP-NHPP-ED type 1, and CPP-NHPP-ED type 2. These algorithms can be used for computer simulation analysis that can be applied to various fields of science and engineering.

show abstract

Estimating the Variance Function of a Compound Cyclic Poisson Process

Cited by 9 publications

References 0 publications

Interval Kepercayaan Untuk Fungsi Nilai Harapan dan Fungsi Ragam Proses Poisson Periodik Majemuk

Interval Kepercayaan Untuk Fungsi Nilai Harapan dan Fungsi Ragam Proses Poisson Periodik Majemuk

Evaluasi Numerik Penduga Fungsi Nilai Harapan Dan Fungsi Ragam Proses Poisson Majemuk Dengan Intensitas Eksponensial Fungsi Linear

Algorithm for Generating Compound Poisson Process Which has Nonhomogeneous Poisson process and Exponential Distribution Components

Contact Info

Product

Resources

About