Maximum likelihood estimates for exponential type density families

We consider a parametric family of density functions of the type exp(-|x|^α/2) for modeling acoustic feature vectors used in automatic recognition of speech. The parameter α is a measure of the impulsiveness as well as the nongaussian nature of the data. While previous work has focused on estimating the mean and the variance of the data here we attempt to estimate the impulsiveness α from the data on a maximum likelihood basis. We show that there is a balance between α and the number of data points N that must be satisfied before maximum likelihood estimation is carried out. Numerical experiments are performed on multidimensional vectors obtained from speech data