A WEIBULL-NORMAL DISTRIBUTION: ITS PROPERTIES AND APPLICATIONS

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dc.contributor.authorIEREN, TERNA GODFREY
dc.date.accessioned2017-07-18T08:10:42Z
dc.date.available2017-07-18T08:10:42Z
dc.date.issued2017-01
dc.descriptionA DISSERTATION SUBMITTED TO THE SCHOOL OF POSTGRADUATE STUDIES, AHMADU BELLO UNIVERSITY, ZARIA IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE AWARD OF MASTER OF SCIENCE DEGREE IN STATISTICS DEPARTMENT OF STATISTICS, FACULTY OF PHYSICAL SCIENCES AHMADU BELLO UNIVERSITY, ZARIA, NIGERIAen_US
dc.description.abstractTheNormal distribution is a very important and well known probability distribution for dealing with problems in several areas of life, however there are numerous situations when the assumption of normality is not validated by the data. In this work, we propose a new model calledWeibull-Normal distribution, an extension of the normal distribution by adding two skewness parameters to the normal distribution using the Weibull generator proposed by Bourguignon et al., (2014). This study has derived explicit expressions for some of its basic statistical properties such as moments, moment generating function, the characteristics function, reliability analysis and the distribution of order statistics. The implications of the plots for the survival and hazard functions indicate that the Weibull-Normal distribution would be appropriate in modeling time or age-dependent events, where survival and failure rate decreases with time or age. Also, the plots for the pdf of the distribution showed that it is negatively skewed. The method of maximum likelihood estimation is used to estimate the parameters of our proposed model. The usefulness of the Weibull-normal distribution has been illustrated by some applications to two real data sets. The results showed that new distribution (Weibull-Normal distribution) performs better (provides better fits) than the generalizations of the normal distribution such as Kumaraswamy-Normal, Beta-Normal, Gamma-Normal, Kummer Beta- Normal and the normal distributions when the data set is negatively skewed however, the results from the second data confirmed that this distribution is more flexible and appropriate for modeling negatively skewed data sets.en_US
dc.identifier.urihttp://hdl.handle.net/123456789/9081
dc.language.isoenen_US
dc.subjectWEIBULL-NORMAL DISTRIBUTION,en_US
dc.subjectPROPERTIES AND APPLICATIONS,en_US
dc.titleA WEIBULL-NORMAL DISTRIBUTION: ITS PROPERTIES AND APPLICATIONSen_US
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