The main object of this book is to make statistical inferences (recurrence relations, estimation and prediction) for inverse Weibull model using generalized order statistics. This book has been organized and presented in six Chapters. Basic concepts and some other definitions and notations are given. A review of some of the work done concerning the generalized order statistics (progressive censored data, ordinary order statistics and lower k-record values) on the recurrence relations, the Bayesian and non- Bayesian approaches are given. We are concerned with the problem of estimation of the...

Models with bathtub-shaped failure rate function are useful in reliability analysis and particularly in reliability related decision making and cost analysis. A modified Weibull distribution (MWD) was recently proposed by Lai et al.(2003) as a generalization of the two-parameter Weibull distribution. This distribution has both the two-parameter Weibull and the type I extreme value distributions as special cases. This lifetime distribution is able to model data with bathtub-shaped hazard rate, which is an important feature for engineering reliability analysis. Parameter estimation is...

Mathematics is most often associated with the task of solving equations. Indeed, many problems in biology, economics, physics, and engineering involve equations and mathematics is the one to provide methods for solving them. But any equation of the form f(x) = 0 can be transformed into a new problem by a simple transformation: F(x) = f(x)+x = x. Points that remains invariant under the action of a function are called fixed points. When interested in the existence of solutions to generalized real life problems the question can be translated into asking about whether the problem has fixed...