Julius Kruopis – the pioneer of applied statistics in Lithuania

Abstract

Julius Kruopis was born on 21.02.1941 in Utena district. In 1963 he graduated from Vilnius University,  Faculty of Physics and Mathematics. In 1964–1966 he worked as a  trainee lecturer at the Department of Probability Theory and Number Theory of the Faculty of Mathematics of Vilnius University. In 1966–1969 he studied at the post-graduate course of the Steklov Institute of Mathematics of the USSR (supervisor was the famous Russian mathematician Professor Login Bolshev) and defended the thesis of a candidate of mathematical sciences (the current equivalent is PhD thesis). 
Returning to Lithuania after postgraduate studies, J. Kruopis worked as a senior lecturer at the Department of Probability Theory and Number Theory of the Faculty of Mathematics of Vilnius University, and in 1971 transferred to the newly established Department of Applied Mathematics (he worked as an associate professor since 1972). In 1991 this department was renamed the Department of Mathematical Statistics. Since 2013, J. Kruopis has been an affiliated professor of the Department of Mathematical Statistics.
In 1980–1986 J. Kruopis headed the Department of Applied Mathematics. He established and fostered new traditions, and aimed for the majority of students' theses to have a clear applied nature. He led such works himself and encouraged other teachers to do the same. From the very first days of scientific work, the talent of J. Kruopis became evident through  mathematical and statistical modeling of real processes.
PhD thesis ``Estimation of Markov processes parameters'' by J. Kruopis, defended in 1969 in Moscow (supervised by prof. L. Bolshev), has a clear applied character. Statistical modeling of tick-borne encephalitis virus infection and immunity formation processes was performed. Methods of queueing theory and mathematical statistics were used for modeling and statistical estimation of model parameters.  A detailed analysis of the obtained results was carried out using real data. In addition, the thesis presents the assessment of the transition probabilities of Markov processes with migration. The findings are used for demographic and reliability data analysis.
Having returned to Lithuania, Julius developed a very wide range of activities in the application of statistical methods in many companies and factories. He consulted engineers of Kaunas radio factory, Panevėžys factory of kinescopes   ``Ekranas'' and joint  stock company ``AB Lietkabelis'', Vilnius drill,  ``Venta'', ``Vilma'', radio components factories,  Šiauliai TV factory,  Dniepropetrovsk tire factory ``Dnieproshina'', Moscow Aviation Institute, and others.  Julius Kruopis grasped the essence of technological processes very quickly. A particularly long and fruitful cooperation was established with the Kaunas radio plant. Under the leadership of Julius, a number of factories managers and engineers defended PhD theses.
Especially valuable are his works in the application of statistical methods. These  applications are mainly related to optimization of  control systems, regulation and management of technological processes (acceptance control of materials and details, intermediate control of manufactured details and nodes, outgoing production control, metrological control of measuring devices, product reliability control, etc.).
Although J. Kruopis work is dominated by works on statistical applications, there are also theoretical works on mathematical statistics. For example, the problem of making an optimal decision when choosing a distribution from several possible alternative distributions was examined. There are several works by J. Kruopis related to the application of statistical methods in reliability theory and survival analysis.  Although J. Kruopis always considered himself primarily a statistician, he also achieved important results in probability theory.
In 1986 J. Kruopis introduced shifted Poisson approximation, which unlike the usual Poisson approximation has two parameters and, therefore, is comparable to normal approximation. Moreover, for integer-valued random variables, the accuracy of shifted Poisson approximation can be measured in total variation metric. In contrast, the accuracy of normal approximation to discrete random variables is measured in weaker uniform metric only.
A large part of J. Kruopis research in Probability Theory is related to so-called Signed Compound Poisson approximations – a topic very new in the early eighties. J. Kruopis introduced so-called left-hand-side and right-hand-side factorial cumulants and practically solved the problem of the choice of parameters for such approximations.
J. Kruopis is the co-author of several monographs: ``Quality of mechatronic products. Selective control'', ``Nonparametric tests for complete data'', ``Nonparametric tests for censored data''. While working at the university, J. Kruopis supervised a large number of undergraduate, bachelor, and master theses.  Under his supervision Vanda Bikelienė (Asymptotic distribution of sums of samples from finite populations, 1981) and  Natalja Kosareva  (Asymptotic analysis of statistics distributions in the scheme of sets of particles arrangement with equal probabilities, 1986) defended their doctoral theses in mathematics.
J. Kruopis wrote the first textbook on mathematical statistics in Lithuania.
In the last years of his work at the university, he wrote a comprehensive four-part textbook ``Mathematical Statistics'' with V. Bagdonavičius and e-book ``Mathematical statistics Problems with Solutions'' together with V. Bagdonavičius and R. Levuliene.
One of the main features of J. Kruopis as the head of the department was his great trust in the young lecturers of the department. He did not support the usual practice of other departments where lectures were given by senior and more experienced lecturers, while novice assistants only conducted exercises. J. Kruopis always sought that from the first days of work at the department, all teachers had at least one full course of lectures-exercises-exams.
J. Kruopis instilled his passion for mathematics and its applications not only in students but also in his children, who both graduated from the Faculty of Mathematics and Informatics. Julius was a person of quick, constructive thinking, always restrained, tactful and modest. Both students and colleagues liked him very much.