Reliability functions of generalized log-normal model

It is well known that the failure rate of the normal distribution is increasing and that of the log-normal distribution is nonmonotonic with one turning point. In this paper, we investigate the monotonicity of the failure rate and the mean residual life function of the generalized log-normal distribution. It turns out that, in the case of generalized log-normal distribution, the monotonicity of the failure rate takes different form depending on the range of the extra parameter λ