A Two-Parameter Lindley-Binomial Distribution: Properties and Applications

The binomial distribution is a common and well known distribution that many situations and applications of binomial distribution can be found. In the real life anything that can be thought of a success or a failure can be considered as a Binomial distribution. However, this kind of instances does not fit to binomial distribution well at all the time. Therefore, in order to improve the ability of fitting various models, two-parameter Lindley distri- bution is used to combine with binomial distribution. In this thesis, a new generalized discrete distribution, that is named as two-parameter Lindley-binomial distribution, is introduced by compounding two-parameter Lindley distribution with binomial distribution. Several prob- abilistic properties of this proposed distribution such as the shape of proba- bility mass function, generating functions etc., are derived. Estimations for the parameters are obtained through method of moments, maximum like- lihood estimation and expectation-maximization algorithm. This proposed distribution is used to fit two real data sets and to test its goodness of fit. We also compared the performance of proposed distribution with that of bi- nomial and beta-binomial distributions. The results obtained from examples demonstrate some advantage of the distribution proposed in this thesis.

Name thesis:degree_name

Master of Science (MSc)

Level thesis:degree_level

Master's

Discipline thesis:degree_discipline

Statistics

Grantor dc:publisher

Faculty of Graduate Studies and Research, University of Regina

Year dc:date.issued

2021

Author dc:creator

• Zhang, Xiaoqing

Advisor dc:contributor.advisor

• Deng, DianLiang

Committee member dc:contributor.committeemember

• Volodin, Andrei

Language dc:language.iso

en

DOI

https://doi.org/10.82465/3907

OAI identifier oai:identifier

oai:uregina.scholaris.ca:10294/14492