2013ApJ...765..128Z

The initial mass function for stars is usually fitted by three straight lines, which means it has seven parameters. The presence of brown dwarfs (BDs) increases the number of straight lines to four and the number of parameters to nine. Another common fitting function is the lognormal distribution, which is characterized by two parameters. This paper is devoted to demonstrating the advantage of introducing a left truncated beta probability density function, which is characterized by four parameters. The constant of normalization, the mean, the mode, and the distribution function are calculated for the left truncated beta distribution. The normal beta distribution that results from convolving independent normally distributed and beta distributed components is also derived. The chi-square test and the Kolmogorov-Smirnov test are performed on a first sample of stars and BDs that belongs to the massive young cluster NGC 6611, and on a second sample that represents the masses of the stars of the cluster NGC 2362.