A New Left Truncated Distribution for Modeling Failure time data: Estimation, Robustness study and Application

Truncation arises in many practical situations such as Epidemiology, Material science, Psychology, Social Sciences and Statistics where one wants to study about data which lie above or below a certain threshold or with in a specified range. Left-truncation occurs when observations below a given threshold are not present in the sample. It usually arises in employment, engineering, hydrology, insurance, reliability studies, survival analysis etc. In this article, we develop and analyze a new left truncated distribution by truncating an asymmetric and heavy tailed distribution namely Esscher transformed Laplace distribution from the left so that the resulting distriution lies with in (b,$\infty$). Various distributional and reliability properties of the proposed distribution are investigated. A real data analysis is done using failure time data.