scholarly journals L2-CONVERGENCE OF A NEAREST NEIGHBOR ESTIMATOR OF THE INTENSITY FUNCTION OF A CYCLIC POISSON PROCES

2014 ◽  
Vol 13 (2) ◽  
pp. 49
Author(s):  
I W. MANGKU
Keyword(s):  
Poisson Process ◽  
Key Words ◽  
Nonparametric Estimation ◽  
Nearest Neighbor ◽  
Intensity Function ◽  
Key Words And Phrases ◽  
Subject Classifications ◽  
Single Realization ◽  
Func Tion

<p>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.<br />AMS 2010 subject classifications: 62E20, 62G05, 62G20.<br />Key words and phrases: cyclic Poisson process, cyclic intensity function, nonparametric estimation, nearest neighbor estimator, period, consis- tency, L2-convergence.</p>

scholarly journals Estimation of the local intensity of a cyclic Poisson process by means of nearest neighbor distances

2002 ◽  
Vol 1 (1) ◽  
pp. 1
Author(s):  
I W. MANGKU
Keyword(s):  
Poisson Process ◽  
Point Process ◽  
Poisson Point Process ◽  
Nearest Neighbor ◽  
Single Realization ◽  
Local Intensity ◽  
Strongly Consistent ◽  
Nearest Neighbor Distances

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.

scholarly journals Strong Consistency and Asymptotic Distribution of Estimator for the Intensity Function Having Form of Periodic Function Multiplied by Power Function Trend of a Poisson Process

2018 ◽  
Vol 8 (02) ◽  
Author(s):  
Nina Valentika ◽  
Wayan Mangku ◽  
Windiani Erliana
Keyword(s):  
Periodic Function ◽  
Poisson Process ◽  
Asymptotic Distribution ◽  
Power Function ◽  
Strong Consistency ◽  
Observation Interval ◽  
Intensity Function ◽  
Periodic Component ◽  
Single Realization ◽  
Non Homogeneous Poisson Process

This manuscript discusses the strong consistency and the asymptotic distribution of an estimator for a periodic component of the intensity function having a form of periodic function multiplied by power function trend of a non-homogeneous Poisson process by using a uniform kernel function. It is assumed that the period of the periodic component of intensity function is known. An estimator for the periodic component using only a single realization of a Poisson process observed at a certain interval has been constructed. This estimator has been proved to be strongly consistent if the length of the observation interval indefinitely expands. Computer simulation also showed the asymptotic normality of this estimator.

scholarly journals Penduga Konsisten dari Fungsi Sebaran dan Fungsi Kepekatan Peluang Waktu Tunggu Proses Poisson Periodik

2021 ◽  
Vol 3 (2) ◽  
pp. 128-139
Author(s):  
Fatimah Azzahra ◽  
I Wayan Mangku
Keyword(s):  
Poisson Process ◽  
Waiting Time ◽  
Intensity Function ◽  
Consistent Estimator ◽  
Density Functions ◽  
Parametric Form ◽  
Bounded Interval ◽  
Single Realization

ABSTRAKPenduga yang konsisten dari fungsi distribusi dan fungsi kepekatan peluang waktu tunggu dari proses Poisson periodik dibahas dalam artikel ini. Tidak ada asumsi bentuk parametrik tertentu dari fungsi intensitas proses Poisson periodik. Situasi dipertimbangkan ketika hanya ada realisasi tunggal dari proses Poisson periodik yang teramati dalam interval terbatas [0,n]. Hasil pembuktian menunjukkan bahwa penduga yang diusulkan konsisten ketika n-??. ABSTRACTThe consistent estimator of the distribution and the density functions of the waiting time of a cyclic Poisson process is considered and investigated. We do not assume any particular parametric form of the intensity function of the cyclic Poisson process. We consider the situation when there is only a single realization of the cyclic Poisson process is spotted in a bounded interval [0,n]. We proved that the propose estimators are consistent as n-??.

Narrative, Intertext and Allusion in the Qur'anic Presentation of Job

1999 ◽  
Vol 1 (1) ◽  
pp. 1-25 ◽  
Author(s):  
A. H. Johns
Keyword(s):  
Key Words ◽  
Complex Network ◽  
Key Words And Phrases ◽  
Divine Revelation ◽  
Western Tradition ◽  
Islamic Tradition ◽  
The Impact ◽  
The Way

Job (Ayyūb) is a byword for patience in the Islamic tradition, notwithstanding only six Qur'anic verses are devoted to him, four in Ṣād (vv.41-4), and two in al-Anbiyā' (vv.83-4), and he is mentioned on only two other occasions, in al-Ancām (v.84) and al-Nisā' (v.163). In relation to the space devoted to him, he could be accounted a ‘lesser’ prophet, nevertheless his significance in the Qur'an is unambiguous. The impact he makes is achieved in a number of ways. One is through the elaborate intertext transmitted from the Companions and Followers, and recorded in the exegetic tradition. Another is the way in which his role and charisma are highlighted by the prophets in whose company he is presented, and the shifting emphases of each of the sūras in which he appears. Yet another is the wider context created by these sūras in which key words and phrases actualize a complex network of echoes and resonances that elicit internal and transsūra associations focusing attention on him from various perspectives. The effectiveness of this presentation of him derives from the linguistic genius of the Qur'an which by this means triggers a vivid encounter with aspects of the rhythm of divine revelation no less direct than that of visual iconography in the Western Tradition.

Полиязычие в образовании как кондиция развития Кыргызстана

2019 ◽  
pp. 24-26
Author(s):  
Гүлия Эрмат кызы
Keyword(s):  
Economic Growth ◽  
Key Words ◽  
Communication Skills ◽  
Language Skills ◽  
Local Population ◽  
Foreign Languages ◽  
Educational Reforms ◽  
Key Words And Phrases ◽  
Kyrgyz Republic ◽  
General Overview

Аннотация: В статье предлагается общий обзор двуязычия в Кыргызской Республике и необходимости изучения иностранных языков для развития толерантной личности. Особое внимание уделяется языковым навыкам обучающихся как одному из важных условий развития страны в целом. Соблюдение координации в преподавании иностранного, русского и родного языков является одним из главных стимулов поддержания и повышения интереса к изучению языков. Владение несколькими языками дает человеку способность осуществлять коммуникативную деятельность и стремиться к расширению лингвистического мировоззрения. Многоязыковая коммуникативная способность населения также может рассматриваться как одно из условий экономического роста в республике. Ключевые слова: Двуязычие, полиязычие, культура, национальность, конкурентоспособность, стратегия, образовательные реформы, коммуникативные навыки, лингвистическое сознание, гражданская интеграция Аннотация: Макалада Кыргыз Республикасындагы орун алган билингвизм боюнча жалпы сереп сунушталып, коомдогу толеранттуулукту илгерилетүүдө чет тилдерди үйрөнүү зарылчылыгы баяндалат. Өлкөнүн бүтүндөй өнүгүү жолунда, маанилүү шарттардын бири – бул англис, орус жана кыргыз тилдерин окутуудагы болгон координациянын сакталышы эсептелинет. Адамдын бир нече тилдерди билүүсү, ага болгон кызыгуу менен гана чектелип кала бербестен, жеке коммуникативдик жөндөмдү андан ары кеңейтүүгө өбөлгө түзөт. Жергиликтүү калктын коммуникативдик потенциалы өлкөнүн экономикалык өсүүсүнө түздөн-түз таасирин тийгизип, жарандык интеграцияга мүмкүнчүлүк түзүлөт. Түйүндүү сөздөр: Билингвизм, полилингвизм, маданият, улут, атаандаштык, стратегия, билим берүү реформасы, коммуникативдик аң-сезим, жарандык интеграция. The article offers a general overview of bilingualism in the Kyrgyz Republic and the need to learn foreign languages for advancing tolerance in a society. Special attention is paid to the language skills of people as one of the important development conditions of the country itself. Compliance with coordination in the teaching of the English, Russian and Kyrgyz languages is one of the main ways to maintain and increase interest in the study of languages. Knowledge of several languages gives a person an ability to carry out communicative activities and strive to expand own linguistic worldview. Multilingual communicative capacity of the local population can also be considered as one of the conditions for economic growth in the country. Key words and phrases: Bilingualism, polylinguism, culture, nationality, competitiveness, strategy, educational reforms, communication skills, linguistic consciousness, civil integration.

The basic issue surrounds whether the law has been broken. We have been told Mary has been charged with theft under s 1 of the Theft Act. We are to assume that the three statements provided containing all of the information in this scenario have been produced just for us to read and work on. For the purposes of this exercise we will assume that these statements were produced in ways not calling into doubt their admissibility or credibility. This means therefore that we only have to concentrate on their probative value. (What do they prove?) The seven point approach of Twining and Miers will be used. 1 Standpoint: the standpoint of the Chart is that of the author of this book demonstrating the Wigmore Chart Method for the purposes of demonstrating the method and argument construction. 2 Stages 2, 3 and 4: relate to setting up the propositions and then key listing and charting. The impossibility of approaching each task in an isolated way is immediately perceived as we are going to work from statements. We have to find out the facts before we can draft the UP, PP, and interim probanda. Task: so that you can appreciate the levels of analysis go back to the statements and highlight the key words and phrases that begin to allow you to break into them and locate the story, and the law. Then try to give answers to the following questions: (1) What are the relevant facts? (2) What key phrases in the statements give you clues as to the application of the law? (3) Can you construct the deductive argument for the prosecution? (4) Can you construct the inductive argument for the prosecution? (5) Can you construct the opposing inductive argument for the defence? (6) Are there any conditions of doubt in your mind surrounding the wording of s1(1) of the Theft Act which may apply? (For example questions surrounding the presence of both mens rea and actus reus.) DO NOT PROCEED UNTIL YOU HAVE ANSWERED QUESTIONS (1)–(6).

2012 ◽  
pp. 253-254
Keyword(s):  
Key Words ◽  
Levels Of Analysis ◽  
Mens Rea ◽  
Key Words And Phrases ◽  
Deductive Argument ◽  
Inductive Argument ◽  
Probative Value ◽  
Actus Reus ◽  
The Law ◽  
Key Phrases

Weak limit results for the extremes of a class of shot noise processes

1995 ◽  
Vol 32 (03) ◽  
pp. 707-726 ◽  
Author(s):  
Patrick Homble ◽  
William P. McCormick
Keyword(s):  
Poisson Process ◽  
Shot Noise ◽  
Impulse Response Function ◽  
Weak Limit ◽  
Intensity Function ◽  
Important Class ◽  
Homogeneous Poisson Process ◽  
Periodic Intensity ◽  
Non Homogeneous Poisson Process ◽  
Over Time

Shot noise processes form an important class of stochastic processes modeling phenomena which occur as shocks to a system and with effects that diminish over time. In this paper we present extreme value results for two cases — a homogeneous Poisson process of shocks and a non-homogeneous Poisson process with periodic intensity function. Shocks occur with a random amplitude having either a gamma or Weibull density and dissipate via a compactly supported impulse response function. This work continues work of Hsing and Teugels (1989) and Doney and O'Brien (1991) to the case of random amplitudes.

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