STUDY ON INFERENCES AND APPLICATIONS OF ODD GENERALIZED EXPONENTIAL-RAYLEIGH DISTRIBUTION
CHAPTER ONE
INTRODUCTION
1.1Â Â Â Background of the study
The Rayleigh distribution was named after Lord Rayleigh (1842-1919) a British physicist as well as mathematician also known as John William Strutt. In 1895 he discovered the inert gas Argon (Ar), the research that earned him the 1904 Nobel Prize in Physics Venkatesh and Manikandan (2016).
The Rayleigh distribution has wide range of applications in the field of applied sciences, especially in modeling the lifetime of an object or service time. Battjes (1969) stated some areas where the distribution can also be applied, these includes sea waves, harbor, coastal and ocean engineering, heights and periods of wind waves. Despite its applicability, the distribution suffer’s the same problem other classical distributions suffered from, which is lack of flexibility due to the fact that it has only one parameter. For instance, Tahir and Cordeiro (2016) stated that, the well-known classical/baseline distributions such as exponential, Rayleigh, Weibull and gamma are limited in their characteristics and are unable to show wide flexibility. Because of this and several other problems; several researchers have worked and some are still trying to overcome these challenges by generalizing some of these classical distributions to come up with compound distributions.
According to Eugene et al. (2002) generalization of distributions started in the year 1925; Also, Ahuja and Nash (1967) introduced the generalized Gompertz-Verhulst family of distributions to study growth curve mortality. Gupta et al. (1998) added one parameter to the cumulative distribution function of the baseline distribution to define the exponentiated-G class of distributions and several others follows.
Also Gupta and Kundu (1999) pioneered the study of two-parameter generalization, in which they studied two-parameter Generalized Exponential (GE) distribution also called Exponentiated Exponential (EE) distribution, after which several other authors worked on GE distribution due to its attractive features, among which are Gupta and Kundu (1999), Kundu et al. (2005), Nadarajah (2006) and so on.
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STUDY ON INFERENCES AND APPLICATIONS OF ODD GENERALIZED EXPONENTIAL-RAYLEIGH DISTRIBUTION
