Application of the variance-covariance matrix in natural exponential family to identify noise in signal

In this paper, we introduce the notion of trace variance function which is the trace of the variance-covariance matrix. This trace variance function characterizes the Natural Exponential Family (NEF). We apply this characterization in order to estimate the distribution which belonging to some NEF. The proposed estimator of this trace variance function converges almost surely towards the trace function. We applied the proposed estimator to identify the noise in a received signal.