Modeling extreme value data with an upside down bathtub-shaped failure rate model

Abstract

The Pareto model corresponds to the power law widely used in physics, biology, and many other fields. In this article, a new generalized Pareto model with a heavy right tail is introduced and studied. It exhibits an upside-down bathtub-shaped failure rate (FR) function. The moments, quantiles, FR function, and mean remaining life function are examined. Then, its parameters are estimated by maximum likelihood, least squared error, and Anderson–Darling (a weighted least squared error) approaches. A simulation study is conducted to verify the efficiency and consistency of the discussed estimators. Analysis of Floyd River flood discharges in James, Iowa, USA, from 1935 to 1973 shows that the proposed model can be quite useful in real applications, especially for extreme value data.

Keywords

• pareto model
• maximum likelihood estimation
• heavy right tail
• extreme value data