Two sets of random vectors cannot both be Gaussian if they are nonlinearly related. Thus, Autoregressive (AR)parameters and reflection coefficient (resp. cepstrum coefficient) estimators cannot both be Gaussian for a finite number of samples. However, most estimators of AR parameters and reflection coefficients (resp. cepstrum coefficients) are Gaussian asymptotically. Thus, the distribution of AR parameter and reflection coefficient (resp. cepstrum coefficient) estimates are close to Gaussian for large samples. This paper studies the ``closeness'' between the Gaussian distribution and the ``non-linear transformation of Gaussian AR parameters'' distribution. A new distance is defined which is based on the Taylor expansion of the non-linear transformation. This ``Taylor'' distance called $M$-distance is used to measure the deviations from the Gaussian distribution of reflection coefficient and cepstrum coefficient statistics. A comparison is presented between this distance and Kullback's divergence. The main advantage of the M-distance with respect to other distances is a very simple closed form expression of the deviations from normality. This closed form expression shows that the convergence of the reflection and cepstrum coefficient distribution to its asymptotic Gaussian distribution (when the number of samples tends to infinity) depends on the position of AR model poles in the unit circle.