EXTENSION OF BURR V DISTRIBUTION: ITS PROPERTIES AND APPLICATION TO REAL-LIFE DATA

EXTENSION OF BURR V DISTRIBUTION: ITS PROPERTIES AND APPLICATION TO REAL-LIFE DATA

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Abstract

More than a decades ago, a new general family of continuous distribution known as beta-G

Distribution was proposed. This new generator has been used to propose some distributions in

recent years with simplified mathematical treatment. An extension of Burr V (BV) distribution

was therefore proposed, using the logit of the beta random variable and some of its properties

studied. The Probability Density Function (PDF) of the Beta Burr V (BBV) was defined and

verified. Hazard Rate Function, Survival Function and Asymptotic Behaviour of the distribution

were obtained, the distribution was also found to be bimodal. The method of maximum

likelihood was proposed to estimate the parameters of the distribution. The performance of the

new distribution was evaluated using a real-life data. The extended distribution was found to be

superior and quite flexible when subjected to scrutiny with burr V, beta Dagum and Beta Power

Exponential distributions by fitting it to two real empirical datasets, thus; it was found that it can

serve as a good alternative distribution to model positive real data in many areas.

CHAPTER ONE: INTRODUCTION

1.1       Background to the Study

Extended or generalized distributions have been extensively studied in recent years. Amoroso

(1925) was the pioneer researcher to start generalizing continuous distributions, discussing the

generalized gamma distribution to fit observed distribution of income rate. Since then, numerous

authors have developed various classes of generalized distributions. Well-known distributions

have been generated or extended in many ways. Some of the well-established generators are

Marshal-Olkin generated family (MO-G) by Marshall and Olkin (1997), the beta-G by Eugene et

al. (2002), Jones (2004), gamma-G (type 1) by Zografos and Balakrishnan (2009),

Kumaraswamy-G (Kw-G for short) by Cordeiro and De Castro (2011), gamma-G (type 2) by

Ristic and Balakrishnan (2012), gamma-G (type 3) by Torabi and Hedesh (2012), McDonald-G

(Mc-G) by Alexander et al. (2012), log-gamma-G by Amini et al. (2014), exponentiated

generalized-G by Cordeiro et al. (2013), Weibull-G by Bourguignion, et al. (2014) among

others. Recent developments have been geared to define new families by introducing shape

parameters to control skewness, kurtosis and tail weights thus providing great flexib


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