A left and right truncated lognormal distribution for the stars

TL;DR

This paper introduces a truncated lognormal distribution model for stellar initial mass functions, demonstrating its advantages through statistical tests on star samples.

Contribution

It proposes a four-parameter truncated lognormal distribution for stars and derives its key statistical properties, improving modeling accuracy.

Findings

The truncated lognormal model fits star data better than traditional models.

Derived formulas for normalization, mean, variance, and distribution function.

Statistical tests confirm the model's effectiveness on real star samples.

Abstract

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.