I am currently developing a new flexible discrete distribution with two parameters. However, I am unable to obtain the unique estimators using MLEs and moments method. Multiple solutions obtained from the R software with same logLikelihood values. The method of moments also a dead end. Why does this happen? By the way, the distribution is a legit distribution with sum of probability equates to one.
1. Log-likelihood estimates are guaranteed to be unique only if the likelihood function is log-concave in parameters. This is not always the case; see e.g. "
Examples of Nonunique Maximum Likelihood Estimators" by Dharamdhikari and Joag-Dev.
2. Method of moments will not work if your discrete distribution is on infinite support and the sequence of partial sums for one of the moments (say q^th moment) \sum_i p_i x^q_i does not converge.
- Badges
- Science topic
- Similar topics
- Mathematics