Joseph Dzhun

Joseph Dzhun
File:Jun kaf1.jpg
Born	13 July 1940
Nationality	Ukrainian
Alma mater	National University “Lviv Polytechnic”
Known for	the creation of non-classical theory of errors and the development of non-classical information processing procedures
Awards	awarded by the medal “For military prowess”
Scientific career
Fields	mathematics, mathematical processing of astronomical, space and large amounts of statistical information
Institutions	Head of Mathematical Modelling Department, Faculty of Cybernetics, IUEH

Professor Joseph V. Dzhun (Джунь Йосип Володимирович) is an academician of International Pedagogical Academy, Doctor of Physics and Mathematics, astronomer, well-known expert in the field of robust statistics and error analysis, the author of many scientific works devoted to non-classical procedures of mathematical processing of astronomical, space, geophysical and other statistical information.

It is eager to know for the people who is interested in new mathematical methods of large volumes of statistical data processing, astrometry, geophysics, geodesy, and history of science in Ukraine.

Rivne Institute of Economics and Humanities of the Ministry of Education and Science

Activities

Scientist and astronomer Joseph Dzhun – a representative of E.P. Fedorov’s scientific school – is a specialist in the theory of errors and mathematical processing of astronomical, space and statistical information of great values. His major scientific works are devoted to testing, substantiation of new axiomatic foundations and development of non-classical procedures in the theory of the methods of the data mathematical analysis. The works of J.V. Dzhun are significant contribution to the started by E.P. Fedorov new section of astrometry, which may be defined as “Nonclassical methods of astronomical information mathematical processing”. Just these methods for decades defined nature of most researches in the latitudinal astrometry and they were pioneer methods. Similar researches were appeared abroad much later. These new methods have two main aspects: the usage of spectral analysis for the detection of the “signal” on the background of noises and for studying of the frequency structure dependent (systematic) errors and the usage of non-classical means of construction of point and interval estimation of non-Gauss distributions of the random errors and their analysis.

One cannot imagine the modern astrometry without application of such new means of studying of the errors such as spectral analysis, or without Jeffreys’ sophisticated evaluation procedures. But in the 1960s in astrometry the usage of these methods only was initiated. To estimate all meanings of “breakthrough” which was made by S. P. Fedorov and his followers, it would firstly say about these conceptions, the astronomical observations errors, which were kept in that time. These conceptions were started more than 200 years ago by Gauss and had this axiomatic basis:

• there are no errors in systematic observations;
• conditions of observations are constant;
• casual errors are normally distributed.

And it was not just that these axioms were forgotten or simply ignored. A.A. Korsun’ in the work [3] gives pointed explanation of situation, citing the S.P. Fedorov’s unpublished manuscript: “Classical methods of the observations processing and analysis made by the scientists who themselves used these methods in the practice of their calculations. It is enough to mention at least Gauss. His desire to obtain the most reliable conclusions from his own observations led Gauss to engage in development of the method of the smallest squares. But gradually such unity become broke. A particular distribution of work was appeared: the scientists, who don’t put into practice these methods, research such methods development and theoretical substantivation. But those scientists who directly make the processing of observations, use finished means sometimes without understanding of their basis and consequently do not always use them best. Hence there are discrepancies in the approach to the given observations analysis and the difficulty of understanding between the groups of scientists, statisticians and physicists, as H. Jeffreys calls them. “E.P. Fedorov felt acutely need of significant changes in approaches to the errors analysis, which was stipulated as by limitation of the classical theory of the errors as of axiomatic impossibility of their postulates. The essence of the problem was that these postulates were constantly discussing with the astrometric reality. Firstly, it is Gauss’ assumption about that we can completely eliminate the systematic errors influence from the results of observations: “it is important to emphasize that in the following studies we will talk only about the random errors that do not have a constant component” [1]. As one can see, Gauss solved this problem simply removing it from consideration. At the same time the problem of systematic errors is one of the most urgent matter in astrometry. You can reduce the impact of different means of the systematic errors, but we can never completely eliminate these errors from the results of observations. Gauss guessed about it himself: “What means may require the computer specialist from the theory of probability theory in observations processing which are not entirely free from the systematic errors? The publication of the special study about these means, we will set for other case” [1]. Clearly, that this case didn’t occur. Only in 250 years after Gauss’ work these means were firstly put into effect in E.P. Fedorov’s school. Fedorov’s students, without wasting time on theoretical discussions as to the problem importance, demonstrated graphically the power and practical expediency of usage of the spectral means of the dependent errors analysis and opened the gateway for similar works as in our country and abroad. We can say that with the help of these works it can got over one of the causes of crisis of the errors theory. Another source of the crisis was the Gauss’ statement about that random errors have to obey to normal distribution. But this statement clashed with astrometry practice. At first time, this discrepancy was noticed by American astronomer and mathematician S. Newcomb, who in 1886 analyzing the errors of 684 observations of Mercury passing by the solar disc, noted a significant non-conformity of distribution of these errors according to the Gauss’ law [11]. Later, Newcomb proposed at first time in his work [12] linearly weighted assessment, which actually opened the era of robust assessments reopen in the midst of 20 century [5]. Later many other prominent statisticians, including Karl Pearson (1902), Student (1927), H. Jeffreys (1939), analyzing the samples of high quality came to the conclusion about the impressive typical nature of frequency of real distributions deviations from the theoretical ones according to Gauss [9]. Jeffreys in the work [8] exposed the normal law to well-grounded criticism, and showed its non-conformity to the actual state of things. But in 60s, such criticism was ignored as in universities as by the most part of the researchers. It was assumed that one can ignore the deviations from the ideal Gauss’ model as insignificant methods, and that the statistical methods are optimal in the strict model, and remain roughly the same as in the approximate model. Outstanding statisticians P. Huber and J. Tukey forewarned about such hopes often are baseless, even minor deviations from the Gauss’ model have resulted stronger effects [5]. Having entered to the postgraduate study in 1964 due to the E.P. Fedorov’s reference, J. Dzhun began his scientific work examining of the Jeffreys’ conclusion about the Pearson’s character of the errors distribution of the VII type on the base of usage great material of international and domestic latitude services.

Distributions of the astronomical observations random errors were investigated only for the fact that can “confirm” (for the nth time) their normal character. E.P. Fedorov had quite different opinion as regards the random component research. Although it seemed that it was a simple test of the statistical hypothesis, but just mentioned above E.P. Fedorov’s recommendation affirms his gift of foresight. Actually the question was about experimental processing of the scientific hypotheses about the mathematical form of a new universal random errors distribution, a new model of chaos. In 1964, nobody suspected that 20 years later the well-known mathematicians-statisticians: P. Huber, F. Humpel, E. Ronchetti, P. Pousseeuw, W. Stahel [6,5], discussing the Pearson’s VII type nature of the general law of the random errors, will refer to the H. Jeffreys works as the pioneer ones and emphasized his excessive prudence in definition of the law deviations from standard one.

E.P. Fedorov recommended to J. Dzhun use high-quality series that were produced with the “clear” errors of astronomical observations for analysis of distributions. It had in mind parallel latitudinal series of international and domestic services of the Earth pole motion, which made according to the same program for two or three instruments. The significance of these series of regular observations was that they provided an opportunity to get a real random component, which produced mostly by the instrumental errors of astronomical observations. The distributions of differences of individual latitudes of two instruments obtained with the same Talkott’s pairs were investigated. These differences completely exclude effect of the so-called polar component (motion of the Earth poles), effect of local geophysical factors and refractive effects common for both devices, and most importantly, any effect of the most unpleasant errors of the star catalogs for classical astrometry was completely excepted. The distributions of latitudes differences of such famous series of the parallel latitudinal observations were investigated (the letter n marks their volumes):

• observations on the Cookson’s floating zenith telescope and Bamberg’s zenith telescope at the International latitudinal station in Mizusava (Japan) 1940.0 − 1949.7 (n = 4008); 1957–1961 (n = 2127).
• observations on the Zeiss and Bamberg’s zenith telescopes in Santiago 1949,9–1954,5 (n = 7057). Analysis of these distributions convincingly confirmed the depth and far-reachingness of H. Jeffreys’s assumptions about the nature of non-Gauss character of the errors real distributions. All investigated distributions were poorly described with the Gauss’ law, but much better with the Pearson VII type distribution, which has the density obtained by Harold Jeffreys:

$y={\frac {\Gamma (m+1)}{{\sqrt {2\prod (m-0.5)}}\Gamma (m+0.5)\sigma }}\left[1+{\frac {m^{2}}{2(m-0.5)^{3}}}\left({\frac {x-\lambda }{\sigma }}\right)^{2}\right]^{-m}\qquad m>1.5,$

where λ and σ responds to the center and standard of the normal law, and can be considered as a measure of deviation of distribution (1) from the Gauss law where $m=\infty$. It should be noted, that density (1) is not only the solution of the well-known differential equation for Pearson’s families:

File:Form 2 ed.jpg

where $c_{0}$, $c_{1}$, $c_{2}$ – some functions from the central moments. Jeffreys prepared a form of the new, universal law of the errors. Instead of Gauss distribution, which has independent parameters, he suggested modification of the Pearson distribution of VII type (1), which has a Fisher diagonal informational matrix. The value of the parameter m of distribution (1) for the mentioned above three series is not drawing closer to infinity, and were:

File:Form 3 1 ed.jpg

These data convincingly confirmed the H. Jeffreys’ opinion about the Pearson’s character of VII type of the random errors distribution. Jeffreys in the work [9] made a conclusion that the index m for similar (free of dependent errors) observations should be within 3≤m≤5, and thus one can use the law with index m=4 for the reductions observations. The values of m found by us are based near the right part of the indicated interval, in total it affirms about presence of some correlation of these differences was then confirmed by the spectral analysis.

Started by J.V. Dzhun wide research of distribution of the chain differences of the nearest individual latitudes for visual (VZT – visual zenithal tube), floating (FZT - floating zenithal tube) and photographic Z tube (PZT – photographic zenithal tube) in Mizusava, also showed their impressive correspondence to the Pearson VII type distribution. The data in the table below, where n is the amount of difference for each instrument; $\beta _{2}$ is the kurtozis;, $P_{r}$ s $P_{VII}$ are found with the help of the criterion $\chi ^{2}$ probability that the data of difference are the samples in accordance with the normal Pearson VII type of general totality:

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No comments, as the saying is. In general, the gigantic material of observations which includes more than 70 thousand of latitudes was processed. For each sample the Pearson’s VII type curve significantly better reflected the realities of statistical distributions. So far as the meanings of the kurtozis are significantly different for different types of observations, J.V. Dzhun offered a simple robust estimation to calculate the normal points of latitude, which is based on the following weight function for the processing of latitudinal series:

File:Form 5 ed.jpg

where $\sigma ^{2}$ is dispersion; $\varepsilon =\beta _{2}-3$ ; ${\overline {\lambda }}\ \$ - estimation of the parameter $\lambda$ (in the first approaching takes $\lambda$=${\overline {\chi }}\ \$ where ${\overline {\chi }}\ \$ - is average). It is important to mention, that this system of balances, which takes into account the most significant peculiarity of the errors distributions, was offered for the first time in astrometry almost 20 years before the Pearson’s VII type distribution character of the random errors distribution was recognized by the leading foreign statisticians [5]. Professor P.V. Novitskii (St. Petersburg), the author of a number of scientific works on the theory and practice of error analysis of electrical quantities measurements estimated the meaning of that balance function: “The peculiarity of distributions with large positive excess is that scattering of estimations of the center coordinate, standard deviations and excess defined with the help of the experimental data quickly increases with the increase of excess. Exactly for analysis of such distributions the methods of so-called “robust assessment”, which were reduced to assigning of different balances of observations depending on their deviation from the center and many authors of this modern tendency in statistics (Huber, Laner, Wilkinson and others) suggested the new and new heuristic methods of these balances assignment. J.V. Dzhun proposed and developed a different method of robust estimation, when the balances do not set in heuristic way but they defined according to the strict analytical method developed by him. It appeared that the balance function is very steep, and the sign of its curvature is determined by the excess distribution. This scientific discovery transforms robust estimation from heuristic attempts in the real science”.

While most of experts believed that the errors observations distribution made in similar conditions should be normal and that the Pearson’s VII type character of distributions stipulated by the dominant influence of fluctuation of observations accuracy. But basic researches of the form of observations errors distribution fulfilled during 15–20 min., during the time when the conditions of astronomical observations are not able change significantly, and they also do not confirmed their Gauss nature. These studies, carried out by J.V. Dhun on the base of the powerful - criterion, forced for the first time to reevaluate the depth of criticism of theoretical capacity of the normal law as set forth in the Jeffreys’ work [8].

Carried out by J.V. Dzhun series of investigations became the basis of his candidate thesis “Analysis of parallel latitudinal observations fulfilled according to the general program”, which he defended in February 4, 1975 at the conference of academic council of the Institute of Mathematics, USSR Academy of Sciences. But the named researches include only classical methods of astronomical observations. In that time the new methods for studying of the Earth poles motion, such as: laser location of Artificial Satellites of the Earth and the Moon, Doppler observations of Artificial Satellites of the Earth, interferometry with the longest bases. The natural question is arose: Is the Pearson’s VII type character of the random errors distribution only specific peculiarity of classical observations? Can one disseminate it to the new means of astronomical and space observations, which differ by large amounts in particular. In this case, as H. Jeffreys emphasized, that the meaning of the correct theory of data processing unceasingly increase. Indeed, while the astrometric series created by work of the enthusiastic astronomers, these series, as a rule, were small by their volumes and their errors, in general, would be described with the help of the Gauss distribution. The situation essentially changed with the introduction of the new means of astronomical observations: it was abrupt, unusual increase of astroinformation caused by automation space experiments. These volumes have grown to thousands, tens of thousands, hundreds of thousands of times. The hypothesis about normal distribution of differences О–С deflects always and almost with 100% probability with such volumes of samples. In these conditions the situation warned by Jeffreys starts to realise [10]. He said that when the amount of observations is less than 400–500, it is not worth to attach importance to present deviations from the Gauss distribution. But according to this limit of the volumes the realm of non-Gauss or very strong non-Gauss distributions, as a rule, of the Pearson VII type is existed. The new studies of J.V. Dzhun are convincingly confirmed all above-mentioned, including the studies of distributions of differences O–C, resulting from laser treatment of locations Artificial Satellites of the Earth according to the international (short) program MERIT. V.K. Taradij presented these results to J.V. Dzhun. J.V. Dzhun examined the distributions of differences O–C for six arcs of the laser locations of the Artificial Satellites of the Earth (575≤n≤880) and total distribution (n = 4475). The meaning of the parameter m For five arcs value m the meaning of the parameter m of Pearson’s VII type distribution changed within 2,725≤ m ≤7,840 for one of the arcs of O–C difference obey to the Pearson VII type distribution ($\beta _{2}$= 2,82 ± 0,18). The meaning m=4.192 was got for the total distribution.

In addition, opening in 1985 and re-developing and regardless of American mathematician V. Gentleman [7] the theory of the method $L_{p}$-estimates, J.V. Dzhun also defined the parameters of $L_{p}$ assessment of the parameters of all indicated sections of the Pearson type VII and II types, which were necessary for their practical application, including:

• the simple mathematical expressions for definitions of the moments of the Pearson VII and II types distribution were found;
• the limits of the Rao–Cramer disparities for assessment of the parameters of the of the same distributions with the appropriate caution were received. It was already the further development of the theory of assessment of the Pearson distributions so far as Jeffries did not present these limits in their complete form;
• a new method more effective than the method of receiving method of maximum likelihood assessment of the distributions Pearson’s the VII and II type by the direct (without differentiation) minimization of the verisimilitude function proposed by H. Jeffreys, a method that greatly simplifies assessment, using the means of the modern computers. All the complexity of this matter is in that one should search for the optimum of the piece and explosive function. That is the solution of this matter requires a professional data classification, correct determination of the intervals histogram values;
• the theory of optimal selection of intervals classification of statistical distributions histograms is worked out.

Professor P.V. Novitskii’s statement about the importance of the last problem solution which was settled rather empirical or heuristic means by the mathematicians affirms: “J.V. Dzhun, using the entropy approach, firstly received the theoretical, strictly reasonable formula for the optimal number of histogram columns at any value of excess, and the formula to calculate the indicator of distribution degree according to excess value. The modern mathematical statistics has neither one nor another. Ascertainment of such retio gives an opportunity for effective identification of experimental distributions.”

In order to strictly mathematically define the limits of the method of the least squares practical use in modern astrometry, J.V. Dzhun deduced, basing on the methods of information theory, the special entropy factor for assessment of statistical capacity of the Markov’s postulate about the balance in each situation depending on the value of the parameter m of real distribution. He showed that when and n >100 it is necessary to apply classical methods for data processing. In order to show the universality of the Pearson’s VII type distribution as a new mathematical model of chaos, J.V. Dzhun performed wide studies of the gravity, geodesic and geophysical observations errors. All these studies clearly confirmed without alternative the universality of the Pearson’s VII type. Before the J.V. Dzhun’s works the deviation from the normal law were determined as a curiosity, as a single fact. Sometimes the reputable journals refused to publish his works because they did not want “to confuse” the amateurs of respectable classical theory of processing. But the mathematical fundamentality and breadth of research done by J.V. Dzhun, forced even the skeptics to believe that the Pearson’s distribution of the VII type is not a curiosity, not a single impressive fact, and it is a universal distribution of the errors, a new foundation for the theory of errors and initiating non-classical procedures of the mathematical data processing and more, can become the basis of a new, non-Fisher’s mathematical statistics. Its elaboration will be one of the largest and most complex mathematical problems of the new millennium.

Professor P.V. Novitskii, full member of the Metrological Academy of Sciences, the creator of information theory of the measuring devices, estimated the value of the .V. Dzhun’s works: “The basis of the proposed new approach is a refusal from universality of the normal errors distribution. He forms this postulate: “Each instrument or method (observation) has its own individual excess, i. e., individual law of distribution, which must be defined and used in processing. It is hard to overestimate the novelty and importance of this new approach. Naturally, for practical use of this postulate one must be found the models that allow to describe the laws of distribution with the variables in a wide range of values of excess. Research of interval of excess changes were conducted before. The well-known works in which the range of the excess changes was investigated on the base of the several thousand observations data (H. Jeffreys, 1939 – 4–5 000 observations, I.W. Alekseyeva, 1975–20 000 observations). The matter one can consider definitively settled in the works of J.V. Dzhun.

J.V. Dzhun for the first time in the world scientific literature examined the huge array of astronomical, space, gravimetric, geophysical, and geodetic series of errors, beginning from F.V. Bessel to the present day. He analyzed statistics for more than 130000 observations and showed that the errors sections usually have a range of excess changes from −0.18 to 6.00. Hence, to describe the curves distribution, he recommends to use the Pearson’s law (with the constant excess). And being himself one of the founders of the $L_{p}$-methods, in spite of original boom of $L_{p}$ – estimates, he firstly analysed their shortcomings, caused by irregularity of $L_{p}$-distribution and theoretical impossibility, therefore, construction of the limits of the construction of the Rao–Cramer inequality for dispersion estimation of its parameters.

The mentioned researches of J.V. Dzhun made the basis of his doctoral thesis: “Mathematical Processing of Astronomical and Space Information in Non-Gauss Errors of Observations”, which was defended in November 5, 1992. All the results of these studies were published. Their importance is also that they convincingly changed the whole attitude statistical Pirson’s school. Well-known astronomer, Doctor of physical and mathematical sciences I.G. Kolchinskii whites about the J. Dzhun’s thesis: “It is made an important conclusion, that the Pirson’s distribution of the VII type has some interesting properties, due to one can compose “the foundation of the theory of nonclassical errors”. Especially important to me, is a conclusion ... about theoretical and practical usefulness of this distribution not only in astrometry, but in the theory of errors. In connection with this conclusion of J.V. Dzhun we want to note that in the J.V. Dunin–Barkovskii and N.V. Smirnov’ book “Theory of probability and mathematical statistics in the technicks” (1955) the authors, analyzing the approaches of Russian school of mathematics “which reflecting essential features of the real processes” site against the works of English school, where the founder K. Pearson gives by his curves “superficial description of the empirical distribution pattern (pp. 128–129). This formal approach is typical for idealistic English school, it was connected with refusal of the dispersion real conditions analysis. Theoretical and probable substantiation of some of the types of distributions proposed by Pearson, was got later by different way and due to the works of A.A. Markov, S.N. Bershtein, A.N. Kolmogorov and other Soviet scientists. Just this way meets the basic parameters of the Marxist–Leninist theory. I do not want to hurl accusations to the Soviet scientists, who like many others, were the victims of conjuncture. The thesis of J.V. Dzhun clarified a question and showed how unwary it is pin a label on someone”.

“One of the most important problem that were solved in the voluminous work of J.V. Dzhun, was testing the ability of two competing theories of the fundamental concepts of the errors:

Gauss’ conceptions:

- observations random errors obey to the normal distribution;

- the systematic errors completely excluded from the results of observations.

Jeffreys’ concept:

- observations random errors comply with the Pearson’s distribution of the VII type;

- the random independent errors have the parameter of the Pearson’s distribution of the VII type m=4 in the similar conditions of observations, but in the real conditions of astronomical observations they have most likely 2,2≤ m ≤ 2,7.

All works made by J.V. Dzhun convincingly demonstrated statistical capacity of just Jeffries’ concept.

Taking into consideration the results received by J.V. Dzhun, one can think about the general idea of the distribution model of the random errors, that is a model in which there is no “signal”, i.e. there are no dependent errors.

In the fundamental work [4] it was noted that H. Jeffreys’ assumption about the distribution law of the similar observations must have m = 4 is too cautious. P. Huber suggested [5] that the multiple observations free from dependent errors will have the Student distribution in the range $t_{3}$, that is the Pearson VII type from m=2 (instead of m = 4 as considered H. Jeffreys). Distribution of $t_{3}$ has excess $\varepsilon =6$, and this is precisely the law which Laplas recommended in his early works for the theory of the errors. Laplace due to Gauss authority is neglected thoughtlessly by his great guess. The statement about that the distribution of the similar observations (where there are no dependent errors) should be the Pearson’s distribution of the VII type with definite m, is still more paradoxical even to the modern astronomer. According to Gauss weighting function of all normallydistributed observations is constant and equal to $\sigma ^{-2}$. And how to imagine the similar observations with different values of the weighting function? One can only partly explain the presence of the strong Pearson’s distributions of VII type by the fluctuations of observations accuracy. K. Pearson conducted observation of the artificial star in completely controlled similar conditions. This experiment is described in the work [13]. Analyzing these distributions H. Jeffreys showed in the work [9] their Pearson’s character. Thus, these facts testify that the conditions of the central limit theorem do not take into account the most significant peculiarity of the physical world.

There is another aspect that emphasizes the importance of the results received by J.V. Dzhun. We can say about diagnostics of the quality (capability) of any theory. A. Migdal wrote “The question of the theory with experiment comparison is very difficult. It is a very exciting question as for me the physic theorist” [1]. The astronomer can say the same about this question because studying of differences O–C is the only objective means of deep diagnosing of the quality of our theory and our tools in general. According to A. Frans’ apt opinion “any theory creates and come into the world only to suffer from the facts” [2].

The meaning close to m=2 of distribution (1) for differences O–C will testify about the high quality of the theory and tools. It will be the ideal to which every astrometryst who wants to ascertain in perfection of his theory and applied tools should strive.

Concluding the description of the main scientific achievements of J.V. Dzhun it is should be noted that he is the only representative of E.P. Fedorov School, who was not afraid to move from Kyiv to the province and now he is one of the leading scientists in Rivne region. He is a member of the organisation committee of the Confederation of scientists of Rivne region, nominated as a representative of clerisy in to the L.D. Kuchma president's team, during his visit to Poland. J.V. Dzhun prepared a special letter about the connections possible activation of Rivne region with Poland in technical and scientific spheres.

For many years, Joseph Dzhun successfully combines science with industrial problems of Rivne region. Two new lasers surveying instruments of the Laser Attachment-1 and Laser Zenith Instrument-1 on the plant “Gazotron” (device Laser Attachment-1 has a silver award of the Exhibition of Achiements of the National Economy, and electrical cindery installations шлаковое литье ао (ICC-100 and ICC-200) where the high-tech methods of alloyed steel and copper smelting were created due to his direct participation in Rivne region. These installations work successfully in our time and give the necessary details for the national economy. In Scientific Research Institute of the Technologies of the Machine Building J.V. Dzhun created the Laboratory of the Metal Research, which provides entering and outgoing control of the high-technology electrical cindery installations production. In 1992, on behalf of the Vice Premier J.V. Dzhun visited about 40 major plants in Ukraine in order to reorientation of the Ukrainian tool production without additional investments. J.V. Dzhun enjoys authority with the pedagogical staff and students, is an internationally recognized scholar. The scientists from abroad come to him to take an advice.

In 1998–2000, using the world's most important macroeconomic series and based on the works of American economist E. Peters, J.V. Dzhun convincingly substantiated the law of the random oscillations of the series distribution of the Pearson’s type VII and got for them the value m within 1,858 ≤ m ≤ 2,980.

Now the main sphere of J.V. Dzhun’s scientific interest is applied mathematics and statistics, consequent improvement and expanding of usage of the modern robust procedures in assessment of fundamental astronomical and physical constants and in the processing of geophysical, gravity and other statistical information.

Experienced teacher, full member of the International Pedagogical Academy J.V. Dzhun is a head of the department of statistics and information technologies of International University of Economics and Humanities named after Academician Stepan Demianchuk (Rovno). He works in good staff and he is full of new ideas for further development of science and integration of Ukrainian scientific achievements into the world science.

The main dates of life and activity

1957 Graduated from secondary school of the village Vysoka Pich, Zhytomyr district, Zhytomyr region, got a silver medal;

1957–1962 The student of Lviv Institute of Politechnics (now State University “Lviv Politecnics”);

1962–1964 Mechanic, then junior researcher of the Graviametric observatory of Academy of Sciences of USSR in Poltava;

1964–1967 Postgraduate student of the Main Asrtonomical Observatory of Academy of Sciences of Ukraine;

1967–1968 Assistant of the Department of Engineering Geodesy of Ukrainian Institute of the Water Economy Engineers (now “Technical University”), Rivne town;

1968–1970 Active service in the Soviet Army, position of a platoon of sound ranging leader;

1970 Was awarded by the Medal for Military Valour and the Letter of Recommendation of the Commander of the Carpathian military district for the 1st place in the competition among the similar subunits.

1970–1977 Senior teacher of Ukrainian Institute of the Water Economy Engineers, Rivne town.

1975 A degree of the Сandidate of Physical and Mathematical Science was conferred;

1977–1987 Assistant Professof of the Department of Engineering Geodesy of Ukrainian Institute of Water Economy, Rivne town;

1980 A degree of the Assistant Professor of the Department of Engineering Geodesy was conferred; водное хозяйство

1987–1997 The Head of the Research Laboratory of Metal Research of Research Institute of the Machinebuilding Technologies, Rivne town;

1992 A degree of the Doctor of Physical and Mathematical Science was conferred;

From 1997 to now The Head of the Department of Statistics and Information Technologies of the Rivne Institute of Economics and Humanities;

1998 Member of the editorial board of the journal “EKONOMIKA FIRIEM, 1998” of Bratislava University, Slovakia;

1999 Member of the Organisation Committee of the Confiredarion of the Scientists of Rivne region, Rivne town;

1999 Full member of the International Academy of Pedagogical Sciences, Moscow.

References

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