Estimation of the Hyperexponential Density with Applications in Sensor Networks

This paper solves the problem of estimation of the parameters of a hyperexponential density and presents a practical application of the solution in sensor networks. Two novel algorithms for estimating the parameters of the density are formulated. In the first algorithm, an objective function is constructed as a function of the unknown component means and an estimate of the cumulative distribution function (cdf) of the hyperexponential density. The component means are obtained by minimizing this objective function, using quasi-Newton techniques. The mixing probabilities are then computed using these known means and linear least squares analysis. In the second algorithm, an objective function of the unknown component means, mixing probabilities, and an estimate of the cdf is constructed. All the 2M parameters are computed by minimizing this objective function, using quasiNewton techniques. The developed algorithms are also compared to the basic EM algorithm, and their relative advantages over the EM algorithm are discussed. The algorithms developed are computationally efficient and easily implemented, and hence, are suitable for low-power and sensor nodes with limited storage and computational capacity. In particular, we demonstrate how the structure of these algorithms may be exploited to be effectively utilized in practical situations, and are hence ideal for sensor networks. Index Terms Hyperexponential density, Bursty traffic engineering, Parameter estimation, Nonlinear optimization, Sensor networks, Rainfall prediction.