Informatics and Applications
2019, Volume 13, Issue 4, pp 11-17
USING THE MODEL OF GAMMA DISTRIBUTION IN THE PROBLEM OF FORMING A TIME-LIMITED TEST IN A DISTANCE LEARNING SYSTEM
- A. V. Bosov
- A. V. Naumov
- G. A. Mkhitaryan
- A. P. Sapunova
Abstract
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.
[+] References (13)
- Naumov, A. V., A. S. Dzhumurat, and A. O. Inozemtsev.
2014. Sistema distantsionnogo obucheniya matematiche- skim distsiplinam CLASS.NET [Distance learning system for mathematical disciplines CLASS.NET]. Vestnik komp'yuternykh i informatsionnykh tekhnologiy [Herald of Computer and Information Technologies] 10:36-44.
- Rasch, G. 1980. Probabilistic models for some intelligence and attainment tests. Chicago, IL: University of Chicago Press. 224 p.
- Van der Linden, W.J., D.J. Scrams, and D. L. Schnipke. 1999. Using response-time constraints to control for differential speededness in computerized adaptive testing. Appl. Psych. Meas. 23(3): 195-210.
- Kuravsky, L. S., P. A. Marmalyuk, V. I. Alkhimov, and
G. A. Yuryev. 2013. Novyy podkhod k postroeniyu in- tellektual'nykh i kompetentnostnykh testov [A new ap-proach to the construction ofintellectual and competence tests]. Modelirovanie i analiz dannykh [Modelling Data Analysis] 1:4-28.
- Naumov, A. V., and A. O. Inozemtsev. 2013. Algoritm formirovaniya individual'nykh zadaniy v sistemakh dis- tantsionnogo obucheniya [Algorithm to generate individual tasks in the remote learning systems]. Vestnik komp'yuternykh i informatsionnykh tekhnologiy [Herald of Computer and Information Technologies] 74(6):35-42.
- Kibzun, A. I., and A. O. Inozemtsev. 2014. Using the maximum likelihood method to estimate test complexity levels. Automat. Rem. Contr. 75(4):607-621.
- Kuravsky, L. S., P. A. Marmalyuk, G. A. Yuryev, P. N. Dumin, and A. S. Panfilova. 2015. Veroyatnostnoe modelirovanie protsessa vypolneniya testovykh zadaniy na osnove modifitsirovannoy funktsii Rasha [Probabilistic modeling of the test tasks based on the modified Rush function]. Voprosy psikhologii [Psychology Issues] 4:109-118.
- Kuravsky, L. S., A. A. Margolis, P. A. Marmalyuk, A. S. Panfilova, G. A. Yuryev, and P. N. Dumin. 2016. A probabilistic model of adaptive training. Appl. Math. Sci. 10(48):2369-2380.
- Naumov, A. V., andG. A. Mkhitaryan. 2016. On the problem of probabilistic optimization of time-limited testing. Automat. Rem. Contr. 77(9):1612-1621.
- Naumov, A. V., G. A. Mkhitaryan, and E. E. Cherygova. 2019. Stokhasticheskaya postanovka zadachi formirovaniya testa zadannogo urovnya slozhnosti s mi- nimizatsiey kvantili vremeni vypolneniya [Stochastic formulation of the problem of forming a test of a given level of complexity with minimization of the quantile of runtime]. Vestnik komp'yuternykh i informatsionnykh tekhnologiy [Herald of Computer and Information Technologies] 2:37-46.
- Kibzun, A. I., A. V. Naumov, and V. I. Norkin. 2013. On reducing a quantile optimization problem with discrete distribution to a mixed integer programming problem. Automat. Remot. Contr. 74(6):951-967.
- Kan, Yu. S., and A.I. Kibzun. 2009. Zadachi stokhasticheskogo programmirovaniya s veroyatnostnymi kriteriyami [Problems of stochastic programming with probabilistic criteria]. Moscow: Fizmatlit. 372 p.
- Naumov, A. V., and S. V. Ivanov. 2011. On stochastic linear programming problems with the quantile criterion. Automat. Rem. Contr. 71(2):353-369.
[+] About this article
Title
USING THE MODEL OF GAMMA DISTRIBUTION IN THE PROBLEM OF FORMING A TIME-LIMITED TEST IN A DISTANCE LEARNING SYSTEM
Journal
Informatics and Applications
2019, Volume 13, Issue 4, pp 11-17
Cover Date
2019-12-30
DOI
10.14357/19922264190402
Print ISSN
1992-2264
Publisher
Institute of Informatics Problems, Russian Academy of Sciences
Additional Links
Key words
distance learning system; statistical analysis; adaptive systems; quantile optimization
Authors
A. V. Bosov  , A. V. Naumov  , G.A. Mkhitaryan , and A. P. Sapunova
Author Affiliations
Institute of Informatics Problems, Federal Research Center "Computer Science and Control" of the Russian Academy of Sciences, 44-2 Vavilov Str., Moscow 119333, Russian Federation
Moscow State Aviation Institute (National Research University), 4 Volokolamskoe Shosse, Moscow 125933, Russian Federation
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