MOMENT APPROXIMATIONS FOR PROBABILITY DENSITY-FUNCTIONS

The problem of reconstructing a probability density function from a small number of measured integral moments of the random variable is discussed. The situation where the random variable is the concentration of a scalar contaminant within a turbulent shear flow is considered in detail. Advantage is taken of a theoretical prediction for the distribution of moments in self-similar shear flows such as jets, wakes, and boundary layers to motivate the use of a Jacobi polynomial expansion for the inversion problem. A comparison is made between the uses of the Jacobi and Legendre polynomial expansions and a maximum entropy formulation with experimental data. © 1990.