Discrete Weibull distribution
The continuous Weibull distribution has a close relationship with the Gumbel distribution which is easy to see when log-transforming the variable. A similar transformation can be made on the discrete-weibull.
Define where (unconventionally) and define parameters and . By replacing in the cmf:
We see that we get a location-scale parametrization:
- Nakagawa, Toshio and Osaki, Shunji (1975). "The discrete Weibull distribution". Reliability, IEEE Transactions on. 24: 300–301.
- Scholz, Fritz (1996). "Maximum Likelihood Estimation for Type I Censored Weibull Data Including Covariates". ISSTECH-96-022, Boeing Information & Support Services. Retrieved 26 April 2016.