An Exponential-Type Distribution for Modeling Failure Rate.

Abstract

In this paper we introduced the Truncated Exponential Skew Symmetric Gumbel II (TESSG II) distribution which generalizes the Gumbel II distribution using the method proposed by Nadarajah et al (2013). Unlike the Gumbel II distribution which exhibits a monotone decreasing failure rate, the new distribution is useful for modeling unimodal (Bathtub-shaped) failure rates which has a wider class of applications in solving real life problems. Structural properties of the new distribution namely, density function, hazard function, moments and moment generating function were obtained. The maximum likelihood was employed to estimate parameters of the new distribution. Real data set for failures of Air conditional system of Jet air planes were used to validate its tractability, we discovered that the Truncated Exponential Skew Symmetric Gumbel II (TESSG II)  has a better fit than Gumbel II distribution.

Keywords: Quantile function, Bathtub-shaped failure rate, Renyl entropy, moments