Estimating the turning points of the beta generalized exponential failure rate

This note concerns the interval estimation of the turning point of the failure rate based on the newly proposed beta generalized exponential distribution. The point estimate of the turning point is obtained using the maximum likelihood estimation. Since there is no closed form of the turning point of the BGE failure rate function, we propose to construct the confidence interval of the turning point using simulation methods. Two real life data sets are used to illustrate the proposed procedures.