  A class of discrete probability distributions contains distributions with
limited support, i.e. possible argument values are limited to a set of numbers
(typically consecutive). Examples of such data are results from subjective
experiments utilizing the Absolute Category Rating (ACR) technique, where
possible answers (argument values) are $\{1, 2, \cdots, 5\}$ or typical Likert
scale $\{-3, -2, \cdots, 3\}$. An interesting subclass of those distributions
are distributions limited to two parameters: describing the mean value and the
spread of the answers, and having no more than one change in the probability
monotonicity. In this paper we propose a general distribution passing those
limitations called Generalized Score Distribution (GSD). The proposed GSD
covers all spreads of the answers, from very small, given by the Bernoulli
distribution, to the maximum given by a Beta Binomial distribution. We also
show that GSD correctly describes subjective experiments scores from video
quality evaluations with probability of 99.7\%. A Google Collaboratory website
with implementation of the GSD estimation, simulation, and visualization is
provided.
