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The Dirac's chord method may be suitable in different areas of physics forthe representation of certain six-dimensional integrals for a convex body usingthe probability density of the chord length distribution. For a homogeneousmodel with a nonconvex body inside a medium with identical properties ananalogue of the Dirac's chord method may be obtained, if to use so-calledgeneralized chord distribution. The function is defined as normalized secondderivative of the autocorrelation function. For nonconvex bodies this secondderivative may have negative values and could not be directly related with aprobability density. An interpretation of such a function using alternatingsums of probability densities is considered. Such quasi-probabilitydistributions may be used for Monte Carlo calculations of some integrals for asingle body of arbitrary shape and for systems with two or more objects andsuch applications are also discussed in this work.

Extension of Dirac's chord method to the case of a nonconvex set by use of quasi-probability distributions