Features of the Distribution of the Estimate of the Time of Arrival of the Random Radio Pulse with Inexactly Known Duration

We found the analytical expressions for the central moments of the estimate of the time of arrival of the random pulse with inexactly known duration. This estimate was synthesized by the maximum likelihood method. We show that the anomalous errors, which are possible under not too big output signal-to-noise ratio, can result in the considerable change of the distribution of the obtained estimate, particularly increasing the coefficient of excess by several thousand units. By methods of statistical simulation, we determined the borders of applicability for the asymptotically exact formulae for the third- and fourth-order cumulant coefficients.