On Two-sided Length Biased Inverse Gaussian Distribution

Abstract

The new lifetime distribution based on the non-classical parametrization model called the two-sided length biased inverse Gaussian distribution is introduced. The physical phenomena of this situation can be explained in the case when a crack develops from two sides. Some statistical properties of the distribution such as reciprocal properties and the first four moments are investigated. The conventional point estimation, method of moment, is developed to estimate the parameters of the distribution together with asymptotic analysis of the proposed estimators. In order to evaluate the performance of the suggested estimators, Monte Carlo simulation studies are conducted. Furthermore, real data sets in a practical setting are used to illustrate the presented estimation method. Concluding remarks and discussions are also provided.