## distribution function

in polymers
https://doi.org/10.1351/goldbook.D01815
A normalized function giving the relative amount of a portion of a @M03667@ substance with a specific value, or a range of values, of a random @V06600@ or variables.
Notes:
1. Distribution functions may be discrete, i.e. take on only certain specified values of the random @V06600@(s), or continuous, i.e. take on any intermediate value of the random @V06600@(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 @V06600@ is less than or equal to a given value. Alternatively they may be differential distribution functions (or @P04856@ functions), i.e. give the (maybe infinitesimal) proportion of the population for which the random @V06600@(s) is (are) within a (maybe infinitesimal) interval of its (their) range(s).
3. @NT07086@ requires that: (i) for a discrete differential distribution function, the sum of the function values over all possible values of the random @V06600@(s) be unity; (ii) for a continuous differential distribution function, the integral over the entire range of the random @V06600@(s) be unity; (iii) for an integral (cumulative) distribution function, the function value at the upper limit of the random @V06600@(s) be unity.
Source:
Purple Book, 1st ed., p. 55 [Terms] [Book]