Comparative Study of Maximum Likelihood, Maximum Product Spacing and Bayesian
Approaches for the DUS-EV Model with Stress-Strength Applications
Rakhi Chandran, Chacko V.M
Abstract
Numerous new probability distributions have been introduced to model lifetime and failure time data more
accurately. The extreme value distribution plays a significant role in reliability and survival studies because of its
relationship with the Weibull distribution. Different methods are available in the statistical literature to propose
new distributions. Among the techniques, the DUS transformation has gained popularity in reliability and survival
analysis, since it does not consider additional parameters, but provides a better fit to the data. We present the DUS
transformation of the extreme value distribution (DUS-EV), characterized by the parameters λ and α, and study
its statistical properties. We observe that the DUS-EV distribution exhibits an increasing failure rate, making it
suitable for modeling aging phenomena. Parameter estimation is performed through the classical and Bayesian
approaches, including maximum likelihood, maximum product spacing, and the M-H algorithm. A simulation
study validates the estimation procedures. A real dataset comprising time intervals between telephone calls to a
company's switchboard is employed to illustrate the suggested distribution's applicability. The results show that
the DUS-EV distribution fits better than other well-known distributions. Moreover, stress-strength estimation for
both single-component and multi-component systems are performed. The accuracy of our present model's
estimation procedures is evaluated using a simulation study, and the model is used to analyze strength data.
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