Characterization and estimation of weighted nakagami erlang and rayleigh distributions

Abstract

newlineStatistical inference is the procedure of drawing conclusion about a population on the newlinebases of the sample observations. It mainly takes the form of estimation of certain newlinepopulation parameters and of testing various hypotheses regarding the value of certain newlinepopulation parameters. It is the role of statistics to assess the accuracy with which newlinesample properties of the characteristic of interest approximate the corresponding newlinepopulation properties. Even with such assessment, there is a risk of making a wrong newlinedecision. Thus, statistical inference is also concerned with the appraisal of the risks newlineand consequences, to which one might be exposed by making generalizations beyond newlinethe sample, especially when such generalizations lead to decisions and actions. newlineMainly two paradigms are employed for drawing inferences about the parameter. One newlineis classical and the other is Bayesian paradigm. In classical method, it is assumed that newlinethere is an unknown but objectively fixed parameter. It chooses the value of parameter newlinewhich maximizes the likelihood of observed data. Bayesian paradigm treats the newlineunknown parameter as a random variable and the prior uncertainty regarding the same newlineis modeled in the form of a prior distribution. The prior distribution is then updated by newlinecombining it with the likelihood function through the Bayes theorem resulting into newlinewhat we call posterior distribution. The posterior distribution is certainly an updated newlineversion of the information obtained by combing the prior distribution with the data. newlineStatistical distributions and models are employed in a plethora of applied fields newlinenamely economics, engineering, health and biological sciences. In this age of newlineeconomical and faster personnel computers, practitioners of statistics and scientists newlinefrom different walks of life find it easy to fit a probability model to describe the newlinedistributions of a real life data set. As a matter of fact, statistical distributions are newlineemployed to model a large number of practical problems. Effective implementation o.....