Using the model of gamma distribution in the problem of forming a time-limited test in a distance learning system

For the distance learning systems, consideration is given to generation of individual tasks with minimization of execution time. As a criterion, the convolution of two weighted normalized values associated with the deviation of the complexity of the generated test from the specified level and the quantile of the test execution time is used. The gamma distribution model is used to describe a model of a student's random response time to a task. An algorithm is proposed for estimating the parameters of the gamma distribution for each task. It is assumed that task complexities are determined either by an expert or by using corresponding algorithms based on the Rush model. The results of a numerical experiment are presented.