A gradient potential induced by a strongly focused laser beam can perturb the diffusion dynamics of particles in solutions and result in biased photon counting statistics in fluorescence fluctuation spectroscopy (FFS). In this paper, the theories of the photon counting histogram (PCH) and fluorescence intensity distribution analysis (FIDA) approaches are extended independently to fit the biased experimental data and retrieve the unbiased parameters, i.e., the average number of the sample particles in the focal volume N, their brightness epsilon, and polarizability alpha. The extended theories are tested using Monte Carlo simulations for single- and double-component systems. It is also proved numerically and analytically that the extended PCH and FIDA approaches are completely equivalent. Practical implementations and possible applications of extended PCH and FIDA are discussed.