Mode
One of the numerical characteristics of the probability distribution of a random variable. For a random variable with density (cf. Density of a probability distribution), a mode is any point
where
is maximal. A mode is also defined for discrete distributions: If the values
of a random variable
with distribution
are arranged in increasing order, then a point
is called a mode if
and
.
Distributions with one, two or more modes are called, respectively, unimodal (one-peaked or single-peaked), bimodal or multimodal. The most important in probability theory and mathematical statistics are the unimodal distributions (cf. Unimodal distribution). Along with the mathematical expectation and the median (in statistics) the mode acts as a measure of location of the values of a random variable. For distributions which are unimodal and symmetric with respect to some point , the mode is equal to
and to the median and to the mathematical expectation, if the latter exists.
Comments
References
[a1] | A.M. Mood, F.A. Graybill, "Introduction to the theory of statistics" , McGraw-Hill (1963) |
[a2] | L. Breiman, "Statistics with a view towards applications" , Houghton Mifflin (1973) pp. 34–40 |
Mode. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Mode&oldid=16879