A quiescent filament was observed near the center of the disk (N5, W5) with the MSDP spectrograph of the 50 cm refractor of the Pic-du-Midi Observatory on June 17, 1986. We focus our study on the statistical moments of the Dopplershift, V 1, and the intensity, I 1, at the center of a chord of the H α profile (±0.256 Å), versus the minimum intensity I 0. We use a statistical model simulating a number n max of threads (of optical thickness τ 0 and source function S 0), seen over the chromosphere. The threads j along the same line-of-sight i are identical except for the velocity v j (gaussian distribution v 0, σ v). We search for the best fit between the observed and simulated quantities: V 1, σ ( V 1), I 1, σ( I 1), and the histogram of the I 0 values over the field of view. A good fit is obtained with: (a) threads characterized by τ 0 = 0.2, S 0 = 0.06 (unit of the continuum at disk center), mean upward velocity v 0 = 1.7 km s-1 and gaussian-type velocity distribution σ v = 3.5 km s-1. Other possible values of τ 0 and σ v are discussed; (b) underlying chromosphere deduced from observed quiet Sun (outside the filament) by modifying the chromospheric velocities: additional mean upward velocity 0.7 km s-1, standard deviation reduced by a factor F c ∼ 0.7. The results are discussed in connection with the values deduced from prominence observations.