Skip to Main Content
 

Global Search Box

 
 
 
 

Files

File List


dissertation (05-15).pdf (2.05 MB)

ETD Abstract Container

Abstract Header

Study of Generalized Lomax Distribution and Change Point Problem

Alghamdi, Amani Saeed
http://rave.ohiolink.edu/etdc/view?acc_num=bgsu1526387579759835

Abstract Details

2018, Doctor of Philosophy (Ph.D.), Bowling Green State University, Mathematics/Mathematical Statistics.
Generalizations of univariate distributions are often of interest to serve for real life phenomena. These generalized distributions are very useful in many ¿elds such as medicine, physics, engineer-ing and biology. Lomax distribution (Pareto-II) is one of the well known univariate distributions that is considered as an alternative to the exponential, gamma, and Weibull distributions for heavy tailed data. However, this distribution does not grant great ¿exibility in modeling data. In this dissertation, we introduce a generalization of the Lomax distribution called Rayleigh Lo-max (RL) distribution using the form obtained by El-Bassiouny et al. (2015). This distribution provides great ¿t in modeling wide range of real data sets. It is a very ¿exible distribution that is related to some of the useful univariate distributions such as exponential, Weibull and Rayleigh dis-tributions. Moreover, this new distribution can also be transformed to a lifetime distribution which is applicable in many situations. For example, we obtain the inverse estimation and con¿dence intervals in the case of progressively Type-II right censored situation. We also apply Schwartz information approach (SIC) and modi¿ed information approach (MIC) to detect the changes in parameters of the RL distribution. The performance of these approaches is studied through simu-lations and applications to real data sets. According to Aryal and Tsokos (2009), most of the real world phenomenon that we need to study are asymmetrical, and the normal model is not a good model for studying this type of dataset. Thus, skewed models are necessary for modeling and ¿tting asymmetrical datasets. Azzalini (1985) in-troduced the univariate skew normal distribution and his approach can be applied in any symmet-rical model. However, if the underlying (base) probability is not symmetric, we can not apply the Azzalini’s approach. This motivated the study for more ¿exible alternative. Shaw and Buckley (2007) introduced a quadratic rank transmutation map (QRTM) which can be applied in any (symmetric or asymmetric) distribution. Recently, many distributions have been suggested using the QRTM to derive the transmuted class (TC) of distributions. This provides great ¿exibility in performing real datasets. We extend our work in RL distribution to derive the transmuted Rayleigh Lomax (TR-RL) distribution using the QRTM. Mathematical and statistical properties, such as moment generating function, L-moment, probability weight moments are de-rived and studied. We also establish the relationship between the TR-RL , the RL, and other useful distributions to show that our proposed distribution includes them as special cases. TR-RL is ¿tted to a well known dataset, the goodness of ¿t test and the likelihood ratio test are presented to show how well the TR-RL ¿ts the data.
Arjun Gupta, Ph. D. (Committee Co-Chair)
Wei Ning, Ph. D. (Committee Co-Chair)
John Chen, Ph. D. (Committee Member)
Jane Chang, Ph. D. (Other)
129 p.
Statistics
Confidence Intervals; Inverse estimator; Order statistics; Proportional hazard family; Change point; Rayleigh Lomax distribution; Information criterion; Binary segmentation

Recommended Citations

Citations

  • Alghamdi, A. S. (2018). Study of Generalized Lomax Distribution and Change Point Problem [Doctoral dissertation, Bowling Green State University]. OhioLINK Electronic Theses and Dissertations Center. http://rave.ohiolink.edu/etdc/view?acc_num=bgsu1526387579759835

    APA Style (7th edition)

  • Alghamdi, Amani. Study of Generalized Lomax Distribution and Change Point Problem . 2018. Bowling Green State University, Doctoral dissertation. OhioLINK Electronic Theses and Dissertations Center, http://rave.ohiolink.edu/etdc/view?acc_num=bgsu1526387579759835.

    MLA Style (8th edition)

  • Alghamdi, Amani. "Study of Generalized Lomax Distribution and Change Point Problem ." Doctoral dissertation, Bowling Green State University, 2018. http://rave.ohiolink.edu/etdc/view?acc_num=bgsu1526387579759835

    Chicago Manual of Style (17th edition)

bgsu1526387579759835
1,921
© 2018, all rights reserved.
This open access ETD is published by Bowling Green State University and OhioLINK.