Use of Polynomial Splines In Modeling Air Traffic Management Statistics

We have found polynomial splines, expressed as sums of basic splines convenient for generating values of random variables defined as sums, and for identifying distributions from sample data. Simulations of air traffic management scenarios often involve random variables that are sums of several random variables. For example, multi-stage detect-decideact sequences used in our safety can involve total time variables that are the sums of several random variables with individual distributions, and the distributions can be analytic and empirical. One scenario encountered in our research included six distributions, two with one Gamma distribution, three with a different Gamma distribution, and one with a normal distribution. Other tasks in air traffic management require identifying continuous distributions of random variables from sets of samples. This paper explains these uses of polynomial splines, and describes a collection of Java methods for them.