We study the generic properties of the electrostatic noise spectrum measured by an antenna immersed in a plasma with an isotropic electron velocity distribution function, at frequencies of the order of magnitude of the plasma frequency. We find that at high frequencies the noise level is proportional to the electron pressure for long wire antennae and to the electron flux for long double-sphere antennae. At low frequencies it depends mostly on the low-energy electrons. We also study the shape of the peak near the plasma frequency for distribution functions with Maxwellian or power law high-energy tails. We calculate the noise produced with a generalized Lorenzian (''kappa'') distribution function and compare the results with those obtained with different distributions having the same density and equivalent temperature. We deduce some prractical consequences for plasma wave measurements in space. ¿American Geophysical Union 1991