A luminosity function is an empirical unnormalized probability density function that yields the number of some time of item at each given luminosity, such as galaxies (galaxy luminosity function) or globular clusters (globular cluster luminosity function).
An example demonstrating a typical form of such functions is the Schechter luminosity function for galaxies (aka Schechter function, an example of a galaxy luminosity function), which is a "modified" power law:
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.