A Re-Examination Of A Five Parameter Lindley Distribution

Abstract

In this project,Generalized Five Parameter Lindley distribution(G5L) has been proposed as a new generalization of Lindley capable of modeling di erent shapes with increasing, decreasing,constant and bathtub failure rates.It has been constructed using nite mixture as the tool and Gamma as the special function.Construction of G5L,has been expressed in terms of Pdf,Cdf,Survival function,Hazard function,Reverse hazard function,Residual lifetime function,Mean residual life function,Equilibrium distribution,Survival function of equilibrium distribution and Hazard function of equilibrium distribution.G5L was applied to real data from Nichols and Padgett on breaking stress of Carbon bers(2006) to draw shapes and test goodness of t.Parameters were then estimated using Moment matching method(Mom) and Maximum likelihood estimation(MLE).The results obtained proved that G5L provided better t than other generalizations of Lindley hence more exible. Therefore,G5L is recommended for modeling lifetime data that fails to follow other generalizations of Lindley because of its extensiveness.