A normalized function giving the relative amount of a portion of a
polymeric substance with a specific value, or a range of values, of a random
variable or variables.
Notes:
-
Distribution functions may be discrete, i.e. take on only certain specified values
of the random variable(s), or continuous, i.e. take on any intermediate value of the random variable(s), in a given range. Most distributions in polymer science are intrinsically discrete,
but it is often convenient to regard them as continuous or to use distribution functions
that are inherently continuous.
-
Distribution functions may be integral (or cumulative), i.e. give the proportion of
the population for which a random variable is less than or equal to a given value. Alternatively they may be differential distribution
functions (or probability density functions), i.e. give the (maybe infinitesimal) proportion of the population for
which the random variable(s) is (are) within a (maybe infinitesimal) interval of its (their) range(s).
- Normalization requires that: (i) for a discrete differential distribution function, the sum of
the function values over all possible values of the random variable(s) be unity; (ii) for a continuous differential distribution function, the integral
over the entire range of the random variable(s) be unity; (iii) for an integral (cumulative) distribution function, the function
value at the upper limit of the random variable(s) be unity.
Source:
Cite as:
IUPAC. Compendium of Chemical Terminology, 2nd ed. (the "Gold Book"). Compiled by
A. D. McNaught and A. Wilkinson. Blackwell Scientific Publications, Oxford (1997).
XML on-line corrected version: http://goldbook.iupac.org (2006-) created by M. Nic,
J. Jirat, B. Kosata; updates compiled by A. Jenkins. ISBN 0-9678550-9-8.
https://doi.org/10.1351/goldbook.
