A Note on Distinguishing Random Trees Populations

ABSTRACT

Several new results are presented for a class of univariate distributions for which the maximum likelihood estimate of the population mean is the sample mean. It is shown that the convolution of any two such distributions also belongs to this class of functions. It is also shown that the marginal distribution for the sample mean captures all of the Fisher information for the population mean contained in the full distribution. Parameters orthogonal to the mean are found for special cases of these distributions. If the distribution is conditioned on the sample mean, the conditional distribution depends on the parameters only through parameters orthogonal to the mean.