  This letter investigates the application of Haldane's statistical correlation
theory in classical systems. A modified statistical correlation theory has been
proposed by including non-linearity in the form of an exponent into the
original theory of Haldane. The dependence of the statistical correlation on
indistinguishability is highlighted. Using this modified theory, a
quasi-classical derivation of intermediate statistics is shown where
indistinguishability can be introduced into distinguishable systems in the form
of a statistical correlation. The final result is equivalent to the classical
fractional exclusion statistics (CFES), which was derived earlier using a
purely classical route. An extended non-linear correlation model based on power
series expansion is also proposed, which can produce various intermediate
statistical models.
