Abstract: In a classic paper, Teicher (1961) showed that certain location and scale families of distributions are characterized by maximum likelihood estimators of their respective families. In particular, the distributions that are characterized in this manner are the exponential and normal distributions as scale parameter families, and the normal distribution as a location family. We have extended these results to the gamma distribution as a scale parameter family and to the multivariate normal distribution as a location parameter family. Similar results are obtained for elliptically contoured families and Laplace distributions.
Key words and phrases: Gamma distribution, normal distribution, Laplace distribution, functional equations, location families, scale families, elliptically contoured families.