Abstract A method has been presented for calculating the first, second, and third moments of the displacement of an internuclear distance in a polyatomic molecule, 〈Δr〉, 〈Δr2〉, and 〈Δr3〉. The moments, which depend on the frequencies of normal vibrations, the cubic potential constants, and the temperature of the system, have been related to the extent of distortion of the probability distribution function of the internuclear distance from a Gaussian function caused by the anharmonicity in the potential function. An approximate expression has been obtained for the phase parameter κ in the molecular intensity of gas electron diffraction in terms of the moments. Numerical results are given for CO2, CS2, SO2, H2O, D2O, CH4, and CD4 by the use of experimental or estimated cubic potential constants. The phase parameters for bonded distances agree with simple estimates based on “diatomic approximation” to the accuracy of current experimental studies, while the phase parameters for nonbonded distances are similar in magnitude to those for bonded distances in spite of their larger mean-square amplitudes of vibration.