  The densities of Yang-Lee zeros for the Ising ferromagnet on the $L\times L$
square lattice are evaluated from the exact grand partition functions
($L=3\sim16$). The properties of the density of Yang-Lee zeros are discussed as
a function of temperature $T$ and system size $L$. The three different classes
of phase transitions for the Ising ferromagnet, first-order phase transition,
second-order phase transition, and Yang-Lee edge singularity, are clearly
distinguished by estimating the magnetic scaling exponent $y_h$ from the
densities of zeros for finite-size systems. The divergence of the density of
zeros at Yang-Lee edge in high temperatures (Yang-Lee edge singularity), which
has been detected only by the series expansion until now for the square-lattice
Ising ferromagnet, is obtained from the finite-size data. The identification of
the orders of phase transitions in small systems is also discussed using the
density of Yang-Lee zeros.
