  The initial mass function for the stars is often modeled by a lognormal
distribution. This paper is devoted to demonstrating the advantage of
introducing a left and right truncated lognormal probability density function,
which is characterized by four parameters. Its normalization constant, mean,
the variance, second moment about the origin and distribution function are
calculated. The chi-square test and the Kolmogorov--Smirnov test are performed
on four samples of stars.
