This paper provides necessary and sufficient conditions for a solution to likelihood equations for an exponential family of distributions, which includes Gamma, Rayleigh and singly truncated normal distributions. Furthermore, the maximum likelihood estimator is obtained as a limit case when the equations have no solution. These results provide a way to test departures from Rayleigh and singly truncated normal distributions using the likelihood ratio test. A new easy way to test departures from a Gamma distribution is also introduced.
|Journal||Annals of the Institute of Statistical Mathematics|
|Publication status||Published - 1 Jan 1997|
- Exponential families
- Rayleigh and singly truncated normal distributions