### probability density function

**(PDF)**
(shows probability of taking a particular value from a continuous range)

A **probability density function** (**PDF**)
is a type of function used in the mathematical subfield of **probability**
to describe the relative probability of
occurrence of some value that can take on
*real number* values (uncountable numbers,
i.e., including numbers like π
that are not integers or rational numbers).
An example PDF would be a function giving the probability of a person
having some specific height.

More technically, a PDF is a function of a
**continuous random variable** (that can have any real number
value, at least over some interval)
that gives the relative likelihood of the
variable taking the given value.
Such a probability distribution has the quality that
the probability of any specific number is zero
(to be "exactly six feet tall" is totally improbable,
given measurement of sufficient precision),
but shows the probability of occurrence within an interval
(e.g., being within 1/100 of an inch of six feet tall).
This is calculated by integrating the PDF over the interval.
If the result of such integration gives the actual probability,
the function is termed a **normalized PDF** (**NPDF** or **N-PDF**), in which
case, integrating the function over all real numbers
(from negative to positive infinity) yields 1.
Short of that, a function that gives relative probabilities
(e.g., the true ratio of the number of people within 1/100 of
an inch of six feet versus similarly for five feet),
then it is termed an **unnormalized PDF** and the equivalent
NPDF can be derived by taking the unnormalized PDF and incorporating
an additional
constant factor (**normalizing constant** aka **normalization constant**)
consisting of the reciprocal of the area under the entire curve
of the unnormalized PDF.

Similarly, a **probability mass function (PMF)**
is like a PDF except that rather than mapping
a continuous random variable, it maps a
**discrete random variable**,
i.e., a finite (or countable) number of values,
such as the probability that a coin flip will be heads or tails.

(*mathematics,statistics,function*)
**Further reading:**

http://en.wikipedia.org/wiki/Probability_density_function

**Referenced by pages:**

Akaike information criterion (AIC)

Bayesian statistics

conditional stellar mass function (CSMF)

dense core mass function (DCMF)

Gaussian function

globular cluster luminosity function (GCLF)

halo mass function

initial mass function (IMF)

luminosity function (LF)

Maxwell-Boltzmann distribution

probability mass function (PMF)

planetary nebula luminosity function (PNLF)

RMS

Index