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Asymptotic tests for poisson distribution

by Manad Khamkong

Title:

Asymptotic tests for poisson distribution

Author(s):

Manad Khamkong

Advisor:

Pachitjanut Siripanich, advisor

Degree name:

Doctor of Philosophy

Degree level:

Doctoral

Degree discipline:

Statistics

Degree department:

School of Applied Statistics

Degree grantor:

National Institute of Development Administration

Issued date:

2010

Digital Object Identifier (DOI):

10.14457/NIDA.the.2010.89

Publisher:

National Institute of Development Administration

Abstract:

Poisson distribution is well used as a standard model for analyzing the count data in many fields such as environmental sciences, epidemiology, manufacturing applications, econometrics and finance. The importance for testing the fit of the observations arises from a Poisson distribution. In general, the tests related to the Index of Dispersion (ID) concerning the mean and variance is quite powerful against a wide variety of alternatives except when the ID is closer to 1 (Gurtler and ɺɺ Henze, 2000: 219; Karlis and Xekalaki, 2000: 381; Meintanis and Nikitin, 2008: 3729). However, there are many discrete distributions, which have a property of equal or almost equal dispersion (ID is close to 1). As a consequence, the tests related to the ID are not able to discriminate between the Poisson distribution and some other discrete distributions. In this dissertation, the two proposed alternative tests of fit for Poisson distribution are based on the characterization of skewness and the coefficient of variation, called SK and CSK, and are asymptotically normally distributed. The asymptotic level alpha of these statistics desired values of nominal levels. In theory, the comparative the powers of the proposed tests, in respect to other tests are too complicated and not worth to being considered because of their complication. Therefore, in practice, the asymptotic powers are investigated against some fixed alternatives in terms of the Absolute Inverse Coefficient of Variation, Abs(Inv_CV). The Abs(Inv_CV) is greater than the critical value of the test, which indicates that the power tends to 1. For discrete uniform alternative, the Abs(Inv_CV) of the procedure test of the CSK is greater than the SK except in family of under-dispersion distributions. Simulation studies suggest that the empirical Type I error rates of the proposed tests are expected at the 5% significance level when the sample of sizes are 50 and 100. Results of the empirical power studies show that a sample of size 100 is sufficient for tests involving the SK and CSK tests. The proposed tests are sensitive to mixed-dispersion alternatives for discrete uniform, beta-binomial and zero-inflated generalized Poisson distributions. In some situations the CSK test offers a more powerful test than the SK test and in other cases the power of these two tests are not appreciably different. The tests related to the ID are quite powerful against a wide variety of alternatives when the ID is further away from 1. However, the proposed tests do not perform as well for under-dispersion and over-dispersion alternatives, and seem to be nearly equivalent to the tests related to the ID when the range is 0.95 to 1.05. Then, the CSK test statistic is very practical, to test the observation departures from Poissonity when the alternative is unknown and the ID is closer to 1.

Description:

Thesis (Ph.D. (Statistics))--National Institute of Development Administration, 2010

Subject(s):

Poisson distribution
Distribution (Probability theory)

Resource type:

Dissertation

Extent:

xi, 100 leaves : ill. ; 30 cm.

Type:

Text

File type:

application/pdf

Language:

eng

Rights:

This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

URI:

http://repository.nida.ac.th/handle/662723737/386
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ทรัพยากรสารสนเทศทั้งหมดในคลังปัญญา ใช้เพื่อประโยชน์ทางการเรียนการสอนและการค้นคว้าเท่านั้น และต้องมีการอ้างอิงแหล่งที่มาทุกครั้งที่นำไปใช้ ห้ามดัดแปลงเนื้อหา และทำสำเนาต่อ รวมถึงไม่ให้อนุญาตนำไปใช้ประโยชน์เพื่อการค้า ไม่ว่ากรณีใด ๆ ทั้งสิ้น



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  • GSAS: Dissertations [166]

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Except where otherwise noted, content on this site is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International license.

Copyright © National Institute of Development Administration | สถาบันบัณฑิตพัฒนบริหารศาสตร์
Library and Information Center | สำนักบรรณสารการพัฒนา
Email: NIDAWR@nida.ac.th    Chat: Facebook Messenger    Facebook: NIDAWisdomRepository
 

 

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