  We analyze a dense cluster of solar radio spikes registered at ~ 4.5 -- 6 GHz
by the Purple Mountain Observatory spectrometer (Nanjing, China) operating in
the 4.5 -- 7.5 GHz range with the 5 ms temporal resolution. To handle with the
data from the spectrometer we developed a new technique utilizing a nonlinear
multi-Gaussian spectral fit based on chi-squared criteria to extract individual
spikes from the originally recorded spectra. Applying this method to the
experimental raw data we eventually identified about 3000 spikes for this
event, which allows for a detailed statistical analysis. Various statistical
characteristics of the spikes have been evaluated, including intensity
distributions, spectral bandwidth distributions, and distribution of the spike
mean frequencies. The most striking finding of this analysis is distributions
of the spike bandwidth, which are remarkably asymmetric. To reveal the
underlaying microphysics we explore the local trap model with the renormalized
theory of spectral profile of the electron cyclotron maser (ECM) emission peak
in a source with random magnetic irregularities. The distribution of the solar
spikes relative bandwidth calculated within the local trap model represents an
excellent fit to the experimental data. Accordingly, the developed technique
may offer a new tool of studying very low levels of the magnetic turbulence in
the spike sources, when the ECM mechanism of the spike cluster is confirmed.
