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Discriminating between the extended exponential geometric distribution and the gamma distribution

by Prasong Kitidamrongsuk

Title:

Discriminating between the extended exponential geometric distribution and the gamma distribution

Author(s):

Prasong Kitidamrongsuk

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.2010.58

Publisher:

National Institute of Development Administration

Abstract:

The proposed test called ELT is a goodness of fit test for discriminating between the family of the extended exponential geometric (EEG) distributions and the family of the Gamma distributions. The corresponding test statistic is developed based on the empirical Laplace transform () ktx e (, ) txwhere the argument value maximizes n X () ; t L t and is replaced by its MLE . It is verified that converges in distribution to (0 , 1). Performance of the proposed test is compared via Monte Carlo studies to that of the Kolmogorov – Smirnov (KS) test and the test based on the empirical moment generating function (EMGF) proposed by Epps et al. (1982) in two aspects, namely, estimated values of Type I error rates and power of the tests for various situations. It is found that the ELT and EMGF test can control the Type I error rate much better than the KS test in all situations. In addition, the ELT test seems to be more conservative than the EMGF test, that is, values of empirical Type I error rate ( () ) of ELT test are less than those of EMGF test in many situations especially when values of shape parameter are small ( = 0.1). However, the differences are small and close to zero as gets large. Further, under the alternative distribution of a Gamma family, empirical power values of the KS test are somewhat higher than those of the ELT and EMGF tests when sample size is small, but as increases, empirical power values of the ELT and EMGF tests increase and are much higher than those of the KS test. It is noticed that empirical power values of the ELT are slightly larger than the EMGF tests in many cases but the differences are not significant at 5% level.

Description:

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

Subject(s):

Distribution (Probability theory)
Exponential families (Statistics)
Laplace transformation

Resource type:

Dissertation

Extent:

xi, 93 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/662723737/387
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ทรัพยากรสารสนเทศทั้งหมดในคลังปัญญา ใช้เพื่อประโยชน์ทางการเรียนการสอนและการค้นคว้าเท่านั้น และต้องมีการอ้างอิงแหล่งที่มาทุกครั้งที่นำไปใช้ ห้ามดัดแปลงเนื้อหา และทำสำเนาต่อ รวมถึงไม่ให้อนุญาตนำไปใช้ประโยชน์เพื่อการค้า ไม่ว่ากรณีใด ๆ ทั้งสิ้น



This item appears in the following Collection(s)

  • 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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