New Probability Distributions in Astrophysics: IX. Truncation for Exponential, Half Gaussian and Sech-Square Distributions with Application to the Galactic Height

Abstract

What distribution function best fits that of the stars’ heights above the Galactic plane? Can truncated distributions improve the fit? In order to answer the above questions, we derive the probability density function, the distribution function, the average value, the rth moment, the median, an expression to generate random variate and the maximum likelihood estimator, for the truncated exponential, truncated half-normal and the truncated sech-square distributions. The results are applied to the galactic height for open clusters and for Gaia’s stars in order to understand whether the truncated distributions are useful or not to astronomers.