Reliability parameter estimation of the Inverse Flexible Weibull Distribution for type-I censored samples

Censoring is a phenomenon usually encountered in the analysis of lifetime system. It became commonly used in the last few decades because of its flexibility in removing failed units from tests. In this paper, the Inverse Flexible Weibull Distribution (IFWD) proposed in [1] is studied using maximum likelihood technics based on three different algorithms: Newton Raphson (NR), Levenberg Marquardt (LM) and Trust Region reflective (TR). The proposed parameter estimation method is introduced and proved to work from theoretical and practical point of view. On one hand, we apply Maximum likelihood estimation method using complete simulated and real data. On the other hand, we study for the first time the model using simulated and real data for type I censored samples. The observed Fisher information matrix, as well as the asymptotic variance-covariance matrix of the MLE are derived. The estimation results are approved by a statistical test.