Mathematical Models of Geometric Sizes of Cereal Crops’ Seeds as Dependent Random Variables

Abstract

Dimensions of 100 randomly selected wheat seeds of the Smuglyanka variety, rye seeds of the Puhovchanka variety and barley seeds of the Pejas variety were determined by measuring their length (l), width (b) and thickness (h). Results of the measurements were processed by the methods of mathematical statistics; parameters of distributions of individual sizes as random variables were calculated. On the basis of values of variation coefficient, the density function of normal distribution (Gaussian distribution) was taken as a model of individual sizes of seeds. Models of two-dimensional distributions of seed sizes as independent random variables were presented. Correlation coefficients between geometric sizes of seeds were calculated. Obtained values of the correlation coefficients indicate that the geometric sizes of seeds should be considered as dependent random variables. Mathematical models of geometric sizes of studied cereal crops’ seeds as dependent random variables in the form of density functions of their normal distribution were proposed. By values of the sums of squared deviations as a fitting criterion, it was established that the mathematical models of geometric sizes of seeds as dependent random variables in the form of density functions of their normal distribution provide better data approximation than the mathematical models of geometric sizes of some cereal crops’ seeds as independent random variables.

Keywords

• wheat
• seeds
• geometric parameters
• simulation
• the random value
• the distribution function