PROBABILITY-DISTRIBUTION WITH RESPECT TO EXPANSION OR CONTRACTION OF IMAGE SIZE

Often, in handwriting a character, a natural expansion or contraction occurs even if the writer intends to write the character in a specified size. This paper considers the expansion-contraction phenomenon which appears statistically in drawing a figure in general. A theoretical investigation is presented from the theory of probability, and the shape of the probability distribution governing the phenomenon is analyzed mathematically. The approach also gives an answer from the viewpoint of the theory of probability to the problem where the length is expanded or contracted unintentionally, even if a constant length is intended. This paper shows a typical mathematical approach in which the determination of the shape of the probability density function is reduced to the solution of the special functional equation. It is considered to be interesting also from the viewpoint of the theory.