A STUDY ON EXPONENTIATED-NEW WEIGHTED EXPONENTIAL DISTRIBUTION
A STUDY ON EXPONENTIATED-NEW WEIGHTED EXPONENTIAL DISTRIBUTION
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Date
2018-06
Authors
DADA, KEMI VICTORIA
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Abstract
Statistical probability distributions are vital in explaining real world situations. It has been shown overtime that extreme value distributions are found to be useful in various field of studies such as engineering, financial sector, biological sciences etc. Generalizing existing distributions is being studied frequently so as to enhance and improve on the flexibility of an existing distribution. In this work, a three-parameter distribution known as Exponentiated New Weighted Exponential distribution was proposed by introducing an exponentiated (shape) parameter to an existing distribution, it can be used to model real life situations. Structural statistical properties of the proposed distribution such as the hazard, survival, moments and moment generating function were derived. The order statistics and quantile function were also studied. The method of maximum likelihood estimation procedure was used in estimating the parameters of the proposed distribution. The kernel density estimates and the classical Kolmogorov-Smirnov two sample test was also utilized to see how the estimated kernel density function from the proposed distribution mimic the parent distribution and also to check if the data sets used (waiting time of bank customers and accelerated life test) and the sample drawn from the fitted ENWED are indeed from the same distribution. Finally, to prove the flexibility and performance of the proposed distribution, we applied two real life data sets to the proposed distribution, exponentiated-new weighted exponential distribution and to competing distributions such as weighted exponential distribution, new-weighted exponential distribution and exponentiated weighted exponential distribution. The results indicate that the newly proposed distribution outperformed the competing distributions.
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A THESIS 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, NIGERIA
Keywords
A STUDY ON EXPONENTIATED-NEW WEIGHTED,, EXPONENTIAL DISTRIBUTION,