Title of article :
A new uniform distribution with bathtub-shaped failure rate with simulation and application
Author/Authors :
Al abbasi, Jamal N Department of Statistics - Al Nahrain University - Baghdad, Iraq , Khaleel2, Mundher A Department of Mathematics - Faculty of Computer Science and Mathematics - University of Tikrit - Tikrit, Iraq , Abdal‑hammed, Moudher Kh Department of Business Administration - Faculty of Administration and Economics - University of Tikrit - Tikrit, Iraq , Loh, Yue Fang Department of Actuarial Science and Applied Statistics - Faculty of Business and Information Science - UCSI University - Kuala Lumpur, Malaysia , Ozel, Gamze Department of Statistics - Hacettepe University - Ankara, Turkey
Abstract :
Bathtub failure rate shape is widely used in industrial and medical applications. In this paper, a three-parameter lifetime distribution, so-called the generalized Weibull uniform distribution that extends the Weibull distribution, is proposed and studied. This distribution has bathtub-shaped or decreasing failure rate function which enables it to fit real lifetime data sets. Various structural properties of the new distribution are derived, including explicit expressions for the quantile function, moments, moment-generating function and order statistics. Parameter estimations are provided by a maximum likelihood estimation, and the performance of the maximum likelihood estimation is evaluated using a simulation study. An application to real-life data demonstrates that the proposed distribution can be very useful in fitting real data.
Keywords :
Weibull distribution , Reliability , Failure rate , Bathtub shape , Quantile function
