The research is dealing with the problem of choosing right statistical criteria in order to analyze the concrete educological research information and to interpret the received results. The practical value of the research’s results could be described as: 1- the exact evaluation of the real situation, by researching the effectiveness of use of educational computer means at the lessons of mathematics, with the help of hypothesises; 2- the statistical criteria received at the time of the research can be used at the concrete future researches.

Objective of the research - to evaluate, using up-to-date statistical–genetic methods, the reproductive characteristics of pig breeds bred in Lithuania, to determine correlation of the characteristics with productivity traits, and to develop an optimised system of pigs genetic evaluation by BLUP method. Tasks of the research was: to determine influence of genetic and non-genetic factors in pigs reproductive characteristics, to evaluate the additive-genetic heritability parameters, and co-response of reproduction traits; to evaluate influence of reproductive characteristics on productivity traits, phenotype and genetic co-response; to develop an optimised pigs genetic evaluation system employing BLUP method, estimating pigs reproductive and productive characteristics, using the integrated multivariate model; to evaluate tendencies of pigs genetic improvement. Novelty of the research: using the method of unifactor and multifactor dispersion analysis, leverage of genetic and non-genetic factors on reproductive characteristics of pigs, breed in Lithuania, was determined; heritability parameters of reproductive characteristics were determined, using modern software; genetic and phenotype co-response of the reproductive characteristics was estimated; genetic correlation between reproductive characteristics and productivity traits was evaluated, using statistical-genetic methods, for the first time in Lithuania; optimised multivariate model for determination of reproductive and... [to full text]

The paper consists of two parts. In the first part the linear regression method is described, also employment possibilities and pupil achievement research are discussed. The second one deals with some factors and what influence they have on the eight class pupil’s mathematical achievement analysis.

The task of research: 1.To analyse and systematic body measures data; 2.to analyse and systematic control slaughter’s data; 3.to count correlation coefficients between different features. Methodology. It was found correlation coefficients between body measures, growth speed, carcass output and succulence. Correlation coefficients were count by using computer program – Excel. And correlation coefficient’s reliability was found by Snedekor. Conclusions: 1.Between separate body measures and growth fastness was determinated some connexion. The biggest correlation coefficients were between body measures and growth fastness in different periods of life r = 0,444 – 0,688 (P< 0,01). 2.The biggest correlation coefficients were determinated between hinder body parts measures and succulence r = 0,493 – 0,694 (P<0,01). 3.Because these high correlation coefficients show the firm belonging between determined features, so to fulfill the selection we need to take it to account. 4.It was noticed, that bulls which were dwars, they had bigger weight in different periods of their growth, instead the lofty ones. 5.The biggest growth fastness for Lithuanian Black and White breed bulls was definited from 12 – 15 months. They distinguished the biggest weight in this period. So, the most effective way to feed up these bulls would be till this period – 12 – 15 months.

Šiame magistro darbe nagrinėjamos papildomos informacijos panaudojimo galimybės konstruojant baigtinės populiacijos koreliacijos koeficiento įvertinius. Taikant imties plano svorių kalibravimo metodus sukonstruojami aštuoni nauji koreliacijos koeficiento įvertiniai. Įvertiniams konstruoti panaudotos kelios kalibravimo lygčių ir atstumo funkcijų kombinacijos. Kalibruotieji svoriai išvesti pasitelkiant Lagranžo neapibrėžtųjų daugiklių metodą. Naudojant Teiloro ištiesinimo ir visrakčio metodus sukonstruojami koreliacijos koeficiento įvertinių dispersijos įvertiniai. Darbe taip pat atliekamas matematinis modeliavimas, kuriuo siekiama palyginti naujai sukonstruotus įvertinius tarpusavyje ir su standartiniu įvertiniu. Įvertinių tikslumą lemia pakankamai didelė koreliacija tarp tyrimo kintamųjų ir jų papildomų kintamųjų, o du įvertiniai yra tikslūs ir esant mažai koreliacijai. Tiriama, kaip įvertinių tikslumą įtakoja imties dydis bei koreliacija tarp tyrimo ir papildomų kintamųjų. Matematinio modeliavimo eksperimentai atlikti, naudojant darbo autorės sukurtas MATLAB programas. / This master’s thesis analyzes the opportunities of auxiliary information usage while constructing the correlation coefficient estimators of the finite population. By applying the methods of weight calibration of sample design the new eight correlation coefficient estimators are derived. Several combinations of calibration equations and distance measures are used to construct estimators. Calibration weights were derived through Lagrange multiplier method. Using Taylor linearization and jackknife methods variance estimators of the correlation coefficient estimators were constructed. The paper also contains a mathematical simulation aimed at comparing the new derived estimators in between and with a standard estimator. The accuracy of estimators is determined by rather substantial correlation between study and auxiliary variables, whereas two of the estimators are accurate even in the presence of bad correlation. It is tested how sample size and correlation between study and auxiliary variables influences the accuracy of estimators. All the mathemathical simulation tests were performed employing MATLAB programs that have been created by the author of this work.

Viso pasaulio ir atskirų valstybių ekonomika pasižymi tuo, jog pagaminamos produkcijos kiekis kasmet kinta ir ilgu laikotarpiu būna nepastovus. Vienais metais produkcijos pagaminama daugiau, kitais mažiau. Pradėjusi mažėti gamybos apimtis sukelia daugybę šalutinių efektų: ima mažėti įmonių pajamos ir pelnai, mažiau pinigų lieka investicijoms, mažėja produktyvumas, didėja prekių atsargos sandėliuose, galiausiai tenka atleisti dalį darbuotojų ar sumažinti darbo užmokestį. Žmonės, gaunantys mažesnes pajamas, išleidžia mažiau pinigų ir taip priverčia įmones dar labiau riboti savo išlaidas. Tokiu būdu patenkama į užburtą ratą, kai priežastys tampa pasekmėmis ir jos tarpusavy kartojasi, tačiau ne visos ūkio šakos vienodai stipriai reaguoja į ekonomikos svyravimus. Darbo objektas – skirtingų ūkio sektorių jautrumas verslo ciklams. Darbo tikslas – nustatyti individualų skirtingų ūkio sektorių jautrumą verslo ciklams. Darbo uždaviniai: • Išanalizuoti verslo ciklo sąvoką, siekiant suvokti jo įtaką visai ekonomikai ir įmonėms • Nustatyti ciklinių svyravimų priežastis bei pasekmes, kurios atsiranda ekonomikai esant žemiausioje verslo ciklo fazėje • Remiantis moksliniais darbais bei specializuotų agentūrų informacija, išnagrinėti verslo ciklų indikatorius, nustatant jų reikšmę verslo ciklų analizėje • Išanalizuoti įmonėje dėl ekonomikos cikliškumo susidarantį užburtą ratą, kuris leistų suprasti procesus, vykstančius ciklų metu • Remiantis mokslininkų tyrimais, nustatyti daugiausiai ir... [toliau žr. visą tekstą] / The economy of all the world and different counties is characterized by the annual changes of production volume, that in the long-term is erratic. One year the amount of production is higher, others lower. The decrease in volume of production causes many side effects such as declining corporate earnings and profits, less money for investment, declining productivity, increasing inventory of goods in warehouses, then it leads firing workers or reducing wages. People with lower levels of income, spend less money and that makes companies even more to limit their costs. In this way, we get into the vicious circle, where causes become results and they inter-repeat, but not all economic sectors equally respond to economic fluctuations. Object – different economic sectors sensitivity to business cycles. The aim – to identify the individual sensitivity of different economic sectors to business cycles. Objectives: • To explore the concept of the business cycle, in order to understand it‘s impact on the economy and companies. • To find out the causes and the consequences of the cyclical fluctuations, that appears then the economy is in the lowest stage of the business cycle. • On the basis of scientific works and information of the specialized agencies, to analyze the business cycle indicators determining their value in business cycle analysis. • To analyze a vicious circle in the company, forming because of cycles of economy, which would allow to understand the processes during the... [to full text]

Neapibrėžtumo analizė techninių sistemų modeliavimo rezultatams yra ypač aktuali, kai modeliuojamas pavojingų sistemų darbas, saugą užtikrinančių sistemų funkcionavimas, nagrinėjami avarijų scenarijai ar kiti, su rizika susiję klausimai. Tokiais atvejais, ypatingai reaktorių saugos analizės srityje, yra labai svarbu, kad gauti modeliavimo rezultatais būtų robastiški. Šiame darbe yra atliekama Ignalinos AE tikimybinio saugos vertinimo modelio neapibrėžtumo ir jautrumo analizė. Neapibrėžtumo ir jautrumo analizė atlikta naudojantis skirtingais statistinio vertinimo metodais, taikant programų paketą SUSA. Gauti rezultatai palyginti su tikimybinio modeliavimo sistemos Risk Spectrum PSA tyrimo rezultatais. Palyginimas parodė, jog skirtingais metodais ir programiniais paketais parametrų reikšmingumas įvertintas vienodai. Statistinė neapibrėžtumo ir jautrumo analizė, taikant Monte Karlo modeliavimo metodą, leido nustatyti parametrus turėjusius didžiausią įtaką modelio rezultatui. / The uncertainty estimation is the part of full analysis for modelling of safety system functioning in case of the accident, for risk estimation and for making the risk-based decision. In this paper the uncertainty and sensitivity analysis of Ignalina NPP probabilistic safety assessment model was performed using SUSA software package. The results were compared with the results, performed using software package Risk Spectrumm PSA. Statistical analysis of uncertainty and sensitivity allows to estimate the influence of parameters on the calculation results and find those modelling parameters that have the largest impact on the result. Conclusions about for importance of a parameters and sensitivity of the result are obtained using a linear approximation of the model under analysis.

Baigiamajame magistro darbe yra nagrinėjamas Baltijos šalių – Lietuvos, Latvijos ir Estijos BVP, jo kitimo tendencijos bei pagrindiniai makroekonomikos rodikliai – galutinio vartojimo išlaidos, prekių ir paslaugų importas bei eksportas, investicijos, užimtųjų darbo rinkoje skaičius bei BVP defliatorius. Išnagrinėti šių rodiklių apibrėžimai bei ekonominė prasmė, taip pat apžvelgta sukaupta mokslininkų patirtis modeliuojant juos. Siekiant išsiaiškinti ryšius tarp šių rodiklių atlikta koreliacijų bei Grangerio priežastingumo analizė. Modeliuojant, visų pirma, rasti ilgalaikiai sąryšiai tarp kintamųjų, o po to kiekvienai šaliai specifikuotas paklaidų korekcijos modelis bei įvertintas šio modelio tikslumas. Išnagrinėjus praktinius ir teorinius aspektus, pateikiamos baigiamojo darbo išvados ir pasiūlymai. Darbą sudaro 5 dalys: įvadas, analitinė - metodinė dalis, tiriamoji dalis, išvados ir pasiūlymai, literatūros sąrašas. Darbo apimtis – 112 p. teksto be priedų, 60 iliustr., 35 lent., 28 bibliografiniai šaltiniai. Atskirai pridedami darbo priedai. / The gross domestic product of the Baltic States – Lithuania, Latvia and Estonia, has been examined in the master thesis. Trends of the GDP and the main macroeconomic indicators – gross final consumption expenditure, imports and exports of goods and services, investment, labor force and GDP deflator have been analyzed. The definitions of these indicators and an economic sense, as well as researchers' experience in modeling, have been examined. In order to establish the relationship between these variables, analysis of the correlation and Granger causality test has been performed. In particular, modeling started with the finding of the long – term relationship between selected indicators. After that the error correction model has been specified and the accuracy of this model has been estimated. After the examination of the practical and theoretical aspects, the conclusions and recommendations have been presented. Structure: introduction, analytical – methodical part, research part, conclusions and suggestions, references. Thesis consists of: 112 p. text without appendixes, 60 pictures, 35 tables, 28 bibliographical entries. Appendixes included.

Previous works on classification committees have shown that an efficient committee should consist of networks that are not only very accurate, but also diverse. In this work, aiming to explore trade-off between the diversity and accuracy of committee networks, the steps of neural network training, aggregation of the networks into a committee, and elimination of irrelevant input variables are integrated. To accomplish the elimination, an additional term to the Negative correlation learning error function, which forces input weights connected to the irrelevant input variables to decay, is added.

Šis darbas skirtas Italijos verslininkų pasitenkinimo darbu analizei, naudojantis kokybinių požymių daugiamatės statistikos metodais. Duomenys yra iš Italijos Veneto regiono verslininkų tyrimo, kurį 2006 metais pradėjo Padujos universiteto Statistikos departamentas. Imtį sudaro 1216 stebėjimų iš beveik 113000 Veneto regiono (Šiaurės rytų Italija) verslininkų populiacijos. Priklausomasis kintamasis, t.y. pasitenkinimas darbu, išmatuotas ranginėje keturių taškų Likert skalėje su šiomis kategorijomis: „nepatenkintas“, „nei patenkintas, nei nepatenkintas“, „pakankamai patenkintas“ ir „patenkintas“. Paaiškinamuosius kintamuosius sudaro demografinės, firmos charakteristikos, tapimo verslininku motyvus, darbą, laisvalaikį ir ateities perspektyvas atspindintys kintamieji. Beveik visi kintamieji, taip pat ir priklausomasis, yra kategoriniai. Todėl pagrindinis šio darbo tikslas yra išsirinkti geriausiai tokio tipo duomenims tinkantį modelį. Aptariama galimybė naudotis tiesine regresija, atlikus optimalųjį matavimo skalės transformavimą (optimal scaling), logistine regresija, prieš tai apjungus priklausomojo kintamojo rangus, daugianariu logit modeliu, analizuojant kiekvienos kategorijos tikimybę atskirai ir rangine regresija su logit ir cloglog sąryšio funkcijomis. Potencialių pasitenkinimo darbu veiksnių skaičius- pakankamai didelis (daugiau negu 30), todėl itin svarbus uždavinys yra parinkti aiškinančiuosius kintamuosius, vengiant multikolinearumo problemos. Siekiant sumažinti... [toliau žr. visą tekstą] / The paper presents job satisfaction analysis among Italian entrepreneurs using multivariate statistical techniques. Data are taken from Veneto region (North-East part of Italy) businessmen research started by Department of Statistics of Padova University at 2006. Sample consists of 1216 observations (real population is almost 113 000 entrepreneurs at this region). The outcome variable for the job satisfaction is measured on an ordered, categorical, four-point Likert scale – „dissatisfied‘“, „neither satisfied nor dissatisfied“ , „quite satisfied“ and „satisfied“. Explanatory variables include demographic items, firm characteristics, variables representing the reasons of having started the own business, items associated with work, leisure activities and future perspectives. Quite all variables, as well as the dependent one, beeing categorical, the main objective of this work is to select an appropriate model for such type of data among possible alternatives. Discussions are made on possibility to applicate linear regression with optimal scaling, binary logit for dichotomized dependent variable, multinomial logit for analysis of every single category and ordinal logistic regression with several link functions (logit and cloglog). The number of possible determinants of job satisfaction beeing quite large (there were more than 30 questionnaire items associated with job satisfaction) it was of a great importance choosing which explanatory variables should be included in the models... [to full text]