  The search for astronomical pulsed signals within noisy data, in the radio
band, is usually performed through an initial Fourier analysis to find
"candidate" frequencies and then refined through the folding of the time series
using trial frequencies close to the candidate. In order to establish the
significance of the pulsed profiles found at these trial frequencies, pulsed
profiles are evaluated with a chi-squared test, to establish how much they
depart from a null hypothesis where the signal is consistent with a flat
distribution of noisy measurements. In high-energy astronomy, the chi-squared
statistic has widely been replaced by the $Z^2_n$ statistic and the H-test as
they are more sensitive to extra information such as the harmonic content of
the pulsed profile. The $Z^2_n$ statistic and H-test were originally developed
for the use with "event data", composed of arrival times of single photons,
leaving it unclear how these methods could be used in radio astronomy. In this
paper, we present a version of the $Z^2_n$ statistic and H-test for pulse
profiles with Gaussian uncertainties, appropriate for radio or even optical
pulse profiles. We show how these statistical indicators provide better
sensitivity to low-significance pulsar candidates with respect to the usual
chi-squared method, and a straightforward way to discriminate between pulse
profile shapes. Moreover, they provide an additional tool for Radio Frequency
Interference (RFI) rejection.
