A luminosity function is an empirical unnormalized probability density function that yields the number of stars or galaxies at each given luminosity.
A common form is the Schechter luminosity function for galaxies (aka Schechter function, an example of a galaxy luminosity function), a "modified" power law providing a format for such functions:
n(x)dx = ΦSunxae-xdx
Some typical values of the plug-in parameters:
Other variations of luminosity functions are globular cluster luminosity functions, galaxy cluster luminosity functions, and luminosity functions of particular bands, or lines, or the lines of a specific molecule (e.g., carbon monoxide).
Luminosity functions also are assumed to evolve, e.g., to vary with redshift.