The Numerical Simulation for Asymptotic Normality of the Intensity Obtained as a Product of a Periodic Function with the Power Trend Function of a Nonhomogeneous Poisson Process

Maulidi, Ikhsan; Ihsan, Mahyus; Apriliani, Vina

doi:10.24042/djm.v3i3.6374

Cited by 2 publications

(2 citation statements)

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“…Erliana et al [11], Maulidi, et al [12] and Mulidi et al [13] discussed the power function trend of a non-homogeneous Poisson process. Mangku [14], Maulidi et al [15], and Abdullah et al [16] estimated the intensity of a cyclic Poisson process with the power function of a non-homogeneous Poisson process.…”

Section: Introductionmentioning

confidence: 99%

A Study on the Estimator Distribution for the Expected Value of a Compound Periodic Poisson Process with Power Function Trend

Safitri

Mangku

Sumarno

2022

InPrime:Ind.Jour.Pure.Applied.Math

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This article discusses the estimation for the expected value, also called the mean function, of a compound periodic Poisson process with a power function trend. The aims of our study are, first, to modify the existing estimator to produce a new estimator that is normally distributed, and, second, to determine the smallest observation interval size such that our proposed estimator is still normally distributed. Basically, we formulate the estimator using the moment method. We use Monte Carlo simulation to check the distribution of our new estimator. The result shows that a new estimator for the expected value of a compound periodic Poisson process with a power function trend is normally distributed and the simulation result shows that the distribution of the new estimator is already normally distributed at the length of 100 observation interval for a period of 1 unit. This interval is the smallest size of the observation interval. The Anderson-Darling test shows that when the period is getting larger, the p-value is also getting bigger. Therefore, the larger period requires a wider observation interval to ensure that the estimator still has a normal distribution.Keywords: moment method; normal distribution; Poisson process; the smallest observation interval. AbstrakPada artikel ini dibahas tentang pendugaan fungsi nilai harapan Proses Poisson periodik majemuk dengan tren fungsi pangkat. Tujuan penelitian kami adalah, pertama, memodifikasi penduga yang telah ada untuk menghasilkan penduga baru yang memiliki distribusi normal. Kedua, menentukan ukuran interval pengamatan terkecil sehingga penduga yang diusulkan masih berdistribusi normal. Pada dasarnya, penduga yang kami usulkan diformulasi menggunakan metode momen. Kami menggunakan metode simulasi Monte Carlo untuk memeriksa sebaran distribusinya. Hasil menunjukkan bahwa penduga yang baru untuk fungsi nilai harapan Proses Poisson periodik majemuk dengan tren fungsi pangkat memiliki distribusi normal. Hasil simulasi menunjukkan bahwa penduga baru telah berdistribusi normal pada panjang interval pengamatan 100 untuk periode sebesar 1 satuan. Interval pengamatan ini merupakan ukuran interval pengamatan terkecil. Selain itu, hasil uji Anderson-Darling menunjukkan bahwa ketika periode semakin besar maka p-value juga semakin besar. Oleh karena itu, periode yang lebih besar memerlukan interval pengamatan yang lebih panjang untuk menjamin penduga yang kami usulkan tetap berdistribusi normal.Kata Kunci: metode momen; distribusi normal; proses Poisson; interval pengamatan terkecil. 2020MSC: 62E17

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Section: Introductionmentioning

confidence: 99%

A Study on the Estimator Distribution for the Expected Value of a Compound Periodic Poisson Process with Power Function Trend

Safitri

Mangku

Sumarno

2022

InPrime:Ind.Jour.Pure.Applied.Math

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“…[15] has given strong consistency of these estimators. In addition, the asymptotic normality of the estimator has also been formulated and given a numerical simulation of the consistency of the estimator [16]. The results obtained in that study are the estimator of the periodic component which converges to the normal distribution by providing certain conditions.…”

Section: Introductionmentioning

confidence: 99%

The Confidence Interval of the Estimator of the Periodic Intensity Function in the Presence of Power Function Trend on the Nonhomogeneous Poisson Process

Maulidi

Wibowo

Valentika

et al. 2021

CAUCHY

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The nonhomogeneous Poisson process is one of the most widely applied stochastic processes. In this article, we provide a confidence interval of the intensity estimator in the presence of a periodic multiplied by trend power function. This estimator's confidence interval is an application of the formulation of the estimator asymptotic distribution that has been given in previous studies. In addition, constructive proof of the convergent in probability has been provided for all power functions.

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The Numerical Simulation for Asymptotic Normality of the Intensity Obtained as a Product of a Periodic Function with the Power Trend Function of a Nonhomogeneous Poisson Process

Cited by 2 publications

References 5 publications

A Study on the Estimator Distribution for the Expected Value of a Compound Periodic Poisson Process with Power Function Trend

A Study on the Estimator Distribution for the Expected Value of a Compound Periodic Poisson Process with Power Function Trend

The Confidence Interval of the Estimator of the Periodic Intensity Function in the Presence of Power Function Trend on the Nonhomogeneous Poisson Process

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