a new four-parameter lifetime distribution: mixing generalized linear failure rate distribution with geometric distribution

A new four-parameter distribution is introduced. it appears to be the rst dis- tribution that exclusively allows for monotonically increasing, bathtub-shaped, and upside-down bathtub-shaped hazard rates. it encompasses many known lifetime distributions as special cases. some mathematical properties of the new distribu- tion, including estimation procedures using the method of maximum likelihood, are derived