distribution function

in polymers
A normalized function giving the relative amount of a portion of a @[email protected] substance with a specific value, or a range of values, of a random @[email protected] or variables.
  1. Distribution functions may be discrete, i.e. take on only certain specified values of the random @[email protected](s), or continuous, i.e. take on any intermediate value of the random @[email protected](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.
  2. Distribution functions may be integral (or cumulative), i.e. give the proportion of the population for which a random @[email protected] is less than or equal to a given value. Alternatively they may be differential distribution functions (or @[email protected] functions), i.e. give the (maybe infinitesimal) proportion of the population for which the random @[email protected](s) is (are) within a (maybe infinitesimal) interval of its (their) range(s).
  3. @[email protected] requires that: (i) for a discrete differential distribution function, the sum of the function values over all possible values of the random @[email protected](s) be unity; (ii) for a continuous differential distribution function, the integral over the entire range of the random @[email protected](s) be unity; (iii) for an integral (cumulative) distribution function, the function value at the upper limit of the random @[email protected](s) be unity.
Purple Book, 1st ed., p. 55 [Terms] [Book]