  We study H-alpha, far- and near-ultraviolet luminosity functions (LF) of the
sample of 795 luminous compact star-forming galaxies with z<0.65. The
parameters of optimal functions for LFs are obtained using the maximum
likelihood method and the accuracy of fitting is estimated with the chi-squared
method. We find that these LFs cannot be reproduced by the Schechter function
because of an excess of very luminous galaxies. On the other hand, the Saunders
function, the log-normal distribution and some new related functions are good
approximations of LFs. The fact that LFs are not reproduced by the Schechter
function can be explained by the propagating star formation. This may result in
an excess of luminous starbursts with the mass of a young stellar population
above 2*10^8 M_Sun as compared to the LF of the quiescent galaxies. The most
luminous compact galaxies are characterised by H-alpha luminosities of >
5*10^{42} erg/s and star formation rates of > 40 M_Sun/yr.
