massefunktion

Massefunktion is a term used chiefly in mathematics and astrophysics to denote a function that assigns "mass" in some sense to outcomes or objects. In probability theory the term corresponds to the probability mass function (pmf) of a discrete random variable: for a variable X the pmf pX(x) = P(X = x) gives the probability that X takes the value x. A pmf is non‑negative for every x and sums to 1 over the variable’s support. The pmf is related to the cumulative distribution function (CDF) by summation, and it is the discrete analog of the probability density function used for continuous variables. Common discrete distributions defined by a pmf include the binomial, Poisson and geometric distributions; expectations and moments are computed by summing x times the pmf or powers thereof.

In astrophysics and cosmology, a massefunktion (mass function) describes the number density of objects as a function of mass, typically expressed as the number per unit volume per unit mass interval. A prominent example is the stellar initial mass function (IMF), which gives the initial distribution of masses for a population of stars and is often approximated by power laws (e.g., the Salpeter IMF ∝ m^−2.35 for certain mass ranges). Mass functions are used to model star formation, galaxy evolution and the mass distribution of dark matter halos.

The term may appear in other applied fields where a distribution of discrete or continuous "mass" or weight across categories is of interest.