The Weibull Distribution with Estimable Shift Parameter

Abstract

In this paper, a new lifetime distribution known as the Shifted Weibull (SHW) distribution with a shift parameter that does not necessarily determine the lower boundary of the support variable is proposed and studied. The study is motivated by the Shifted Exponential (SHE), Shifted Exponential-G (SHE-G) family of distributions and centred on shift parameter that is estimable. Some properties were derived. Estimation techniques namely; the maximum likelihood, least squares, weighted least squares, maximum product spacing, Cramer-von-Mises, Anderson-Darling and the right-tailed Anderson-Darling estimations are used. Two real data sets were deployed to show the usefulness and superiority of the proposed distribution relative to the parent distribution and other competing distributions. The weighted least squares estimator gave the best classical estimates of the parameters compared to other methods considered.