  Narrow-line Seyfert 1 galaxies (NLS1s) are an interesting subclass of active
galactic nuclei (AGN), which tipically does not exhibit any strong radio
emission. Seven percent of them, though, are radio-loud and often show a flat
radio-spectrum (F-NLS1s). This, along to the detection of $\gamma$-ray emission
coming from them, is usually interpreted as a sign of a relativistic beamed jet
oriented along the line of sight. An important aspect of these AGN that must be
understood is the nature of their parent population, in other words how do they
appear when observed under different angles. In the recent literature it has
been proposed that a specific class of radio-galaxies, compact-steep sources
(CSS) classified as high excitation radio galaxies (HERG), can represent the
parent population of F-NLS1s. To test this hypothesis in a quantitative way,in
this paper we analyzed the only two statistically complete samples of CSS/HERGs
and F-NLS1s available in the literature. We derived the black hole mass and
Eddington ratio distributions, and we built for the first time the radio
luminosity function of F-NLS1s. Finally, we applied a relativistic beaming
model to the luminosity function of CSS/HERGs, and compared the result with the
observed function of F-NLS1s. We found that compact steep-spectrum sources are
valid parent candidates and that F-NLS1s, when observed with a different
inclination, might actually appear as CSS/HERGs.
