Polskie Towarzystwo Statystycze Oddział we Wrocławiu ŚLĄSKI Silesia Statistical Review Nr 3 (9) Wydawictwo Uiwersytetu Ekooiczego we Wrocławiu Wrocław 205
RADA NAUKOWA Walety Ostasiewicz, Tadeusz Bedarski, Iva Belko, Luisa Caal, Staisław Heilper, Staislava Hroová, Agiola Pollastri, Jerzy Śleszyński, Reihard Viertl, Halia Woźiak, Michele Zega, Eilia Zikova KOMITET REDAKCYJNY Zofia Rusak (redaktor aczely) Edyta Mazurek (sekretarz aukowy) Tadusz Borys, Katarzya Ostasiewicz, Grażya Trzpiot RECENZENCI WSPÓŁPRACUJĄCY Z CZASOPISMEM Helea Jasiulewicz, Wojciech Kordecki, Dorota Kuchta, Aa Malia, Zofia Mielecka-Kubień, Dauta Mierzwa, Staisława Ostasiewicz, Barbara Podolec, Katarzya Sawicz, Juliusz Siedlecki, Jerzy Wawrzyek, Jausz Wywiał Iforacje o aborze artykułów i zasadach recezowaia zajdują się a stroie iteretowej Wydawictwa www.silesiastatreview.ue.wroc.pl www.wydawictwo.ue.wroc.pl Czasopiso jest ideksowae w astępujących bazach: BazEko www.kagur.uek.krakow.pl/bazy_ae/bazeko/owy/idex.php CEEOL www.ceeol.co EBSCO www.ebscohost.co Woly dostęp do wersji elektroiczej: silesiastatreview.ue.wroc.pl Cetru Otwartej Nauki www.bibliotekaauki.ceo.pl Dolośląska Biblioteka Cyfrowa www.dbc.wroc.pl www.ibuk.pl www.ksiegaria.ue.wroc.pl
Spis treści Od Redakcji 5 Muhaad Shafiq, Reihard Viertl: Geeralized Kapla Meier Estiator for Fuzzy Survival Ties 7 Jausz Łyko, Atoi Soluk: Próba foralej defiicji dobrobytu 5 Teresa Kupczyk, Waldear Kordecki: Statistical correlatios betwee the Kowledge Ecooy Idex ad Geder (i)equality Idex 29 Aa Kowalska: Pooc państwa w zakresie dożywiaia dzieci i łodzieży w Polsce 43 Agieszka Tarowska: Możliwości edukacyje i wychowawcze a obszarach wiejskich województwa dolośląskiego a tle kraju 57 Daia Gąska: Progozowaie bakructwa za poocą klasyfikatorów rozytych realizujących ideę aksyalego argiesu 7 Joaa Dębicka, Agieszka Marciiuk: Aaliza porówawcza hipoteczych ret ałżeńskich w krajach Uii Europejskiej 89 Staisława Ostasiewicz: Statystycza aaliza ryzykowych sytuacji decyzyjych Tadeusz Gerstekor: Uwagi o wzorze a oety rozkładu prawdopodobieństwa Pólyi 3 Katarzya Ostasiewicz, Walety Ostasiewicz: Reshapig ecooics to ecopass quality of life issues 37 Edyta Mazurek: Kosekwecje zia ulgi prorodziej w polski systeie podatkowy 6 Walety Ostasiewicz: Professor Zdzisław Heryk Hellwig (26.05.925 8..203) 77 Walety Ostasiewicz: O trwały rozwoju 83 Walety Ostasiewicz: Celebratig the 90 th Birthday of Professor Oscar Sheyi 209 Katarzya Ostasiewicz: Probley z próbai, dyskryiacją rasową i edukacją: ekooetria i zagadieia społecze w pracy Jaesa J. Heckaa (agroda iieia Nobla, 2000) 22 Witold Więsław: Pierwsza polska rozprawa z rachuku prawdopodobieństwa 25 Agata Girul: Ważiejsze dae społeczo-gospodarcze o województwach 283
ŚLĄSKI 4 Spis treści Suaries Muhaad Shafiq, Reihard Viertl: Uogólioy estyator Kaplaa Meiera dla rozytego czasu przeżycia 4 Jausz Łyko, Atoi Soluk: A attept of the foral defiitio of well-beig 27 Teresa Kupczyk, Waldear Kordecki: Statystycze związki poiędzy wskaźikie gospodarki opartej a wiedzy (Kowledge Ecooy Idex) a stopie ie/rówości kobiet i ężczyz (Geder Equality Idex) 42 Aa Kowalska: State aid for childre ad youth i ters of feedig i Polad 55 Agieszka Tarowska: Educatioal ad childcare opportuities i rural areas of Lower Silesia voivodship copared to the whole coutry 69 Daia Gąska: Bakruptcy predictio with Maxiu Margi Fuzzy Classifiers 88 Joaa Dębicka, Agieszka Marciiuk: Coparative aalysis of arriage reverse auity cotracts i the coutries of the Europea Uio 0 Staisława Ostasiewicz: Statistical aalysis of risky situatios 30 Tadeusz Gerstekor: Rearks o the forula for the oets of the Pólya probability distributio 35 Katarzya Ostasiewicz, Walety Ostasiewicz: Przystosowaie ekooii do badań ad jakością życia 58 Edyta Mazurek: Effects of chages i the Pro-faily Tax Relief i The Polish Tax Syste 75 Walety Ostasiewicz: O the sustaiable developet 208
PROFESSOR ZDZISŁAW HENRYK HELLWIG (26.05.925 8..203) ŚLĄSKI Walety Ostasiewicz Uiwersytet Ekooiczy we Wrocławiu ISSN 644-6739 e-issn 2449-9765 DOI: 0.56/sps.205.3.2. Short biography Professor Doctor habilitatus h.c.h.c. Z.H. Hellwig was bor o 26 May 925 i the sall tow of Dokszyce, ot far fro Wilo. Both of his parets were teachers. His father, Hery Hellwig, taught Gera ad his other taught Matheatics. Prof. Z. Hellwig was educated at Kig Zygut August Giazju i Wilo. However his secodary school graduatio certificate ( atura i Polish) he oly obtaied after the Secod World War i Wrocław, i 947. I the sae year he erolledi the Wyższa Szkoła Ekooicza (Uiversity of Ecooics) i Wrocław, fro which he graduated i 950 with a Bachelor s Degree. I 952 he received his Master s Degree ( agister i Polish) i Theory of Statistics at The Pricipal School of Plaig ad Statistics (SGPiS ) i Warsaw. Bachelor ad Master degreecertificates Whilsta studet of the secod year i the Higher Coercial School (Wyższa Szkoła Hadlowa i Polish), he started to work at this school as a juior assistat.
ŚLĄSKI 78 Walety Ostasiewicz O the basis of the paper Liear regressio ad its applicatios i ecooics, he defeded i 958 his Ph.D. degree i Ecooic Scieces (officially the ae of this degree was Kadydat Nauk Ekooiczych, that is Cadidate of Ecooic Scieces). I 967 he becae Professor of Ecooics, ad i 972 he was oiated as (full) Professor i Ecooics. I 962 Prof. Z. Hellwig was oiated as Head of Departet of Statistics ad held this post util 995, the year whe he retired. Although Professor Hellwig retired fro his chair, he cotiued to work quite regularly i his office. I 2005 the first coferece o actuarial statistics was orgaized i Polad, dedicated to Professor Hellwig o the occasio of his 80 th birthday. This coferece was atteded by practically all the proiet Polish statisticias. May ideas, cocepts ad ethods bear the ae of Hellwig. The ost faous of the are listed below.. Iforatio capacity or the iforatio easure coveyed by a set of ecooic variables (i Polish: pojeość iforacyja), published i 968. The iforatio easure coveyed by the -eleet subsets { Xk, X,..., k X 2 k } of the set of potetial variables { X, X2,..., X } has bee defied by the followig forula (istatly recogizable by ay Polish statisticia): H( k,,) i= j= r 2 ki =, r where k = ( k, k2,..., k), ad r kk is the correlatio coefficiet be-twee i j X k i ad X, r k i is the correlatio coefficiet betwee Y ad X k i. k j kk i j 2. Idex of stochastic depedece (published i 969) The other sigificat Hellwig s achieveet is the easure of stochastic depedece. For the case of two diesioal rado vector ( XY, ) this easure has bee defied as follows: 2. d = ( i[ f ( x, y), f ( x) f ( y)] dxdy)
Professor Zdzisław Heryk Hellwig 79 For the discrete case this easure has bee defied by the followig forula: d r s i( p, pq ) ij i j i= j= = (i( rs, )) Both of the were further ivestigated i a uber of papers by ay scholars.. ŚLĄSKI 3. Distace rado variable I 967 Z. Hellwig itroduced a ew statistical cocept, aely the cocept of distace variable. It has bee defied as follows. 0 0 0 0 Let X = ( X, X,..., X ), X = ( X, X,..., X ),..., X = 2 2 ( X, X 2,..., X } be a siple rado saple fro the distributio give by cdf F( x,..., x ) or by the desity fuctio f ( x,..., x ). The distace rado variable, deoted by sybol C,, is defied as follows: where C = i( Y, Y,..., Y ),, 2 0 j 2 Yj = ( Xi Xi ) j =,2,,. i= Ituitively, variable C, eas the shortest distace betwee a 0 2 rado vector X ad a set of rado vectors X, X,..., X. The geeral expressio for the cuulative distributio fuctio was established by Bolesław Kopociński (the well-kow Polish atheaticia). His forula is the followig: C =, R 2 F ( c) ( V ( x, x,..., x, c)) dx,... dx. V ( x... x, c) = f ( x + u, x + u,..., x + u ) du... du Where A 2 2 with A= {( u..., u ) u + u +... + u < c}. 2 2 2 2
ŚLĄSKI 80 Walety Ostasiewicz The liit distributio, whe, is the followig: F c = e f x x x dx dx, K ( c) C ( ) (, 2,..., )... R /2 ( ) =Π / Γ ( / 2 + ). K c c Giter Trybuś (94-203), oe of Hellwig s first disciples, thoroughly ivestigated the theoretical ad practical probles related to the distace variable. He devoted a whole oograph tothe ivestigatio of the explicit forulae of the distributios of distace variable calculated for saple drovig fro a uber of populatios. 4. Idex of socio-ecooic developet Suppose there is give observatio vector xi = ( xi, xi 2,..., xi ) which cotais the values of features characterisig the evaluated coutries with respect to their level of socio-ecooic developet. There is give the referece vector x0 = ( x0, x0,..., x0 ) which has bee called the patter of ecooic developet, characterizig a ideal coutry. The level of developet of each coutry is calculated accordig to the followig forula: ci di =, i =,2,, N, c o where N is the uber of coutries evaluated with respect to their status of developet, ad the quatities c i ad c o are defied as follows: 2 ci = ( xij xoj ) j= N 2 2 ( i ), N i = co = c + c c with = N c ci. N For illustratio, here is a excerpt fro Hellwig s work, A ethod for the selectio of a copact set of varaiables published i Social idicators: probles of defiitio ad of selectio, Reports ad papers i the social scieces, No. 30, UNESCO, 974. i=
Professor Zdzisław Heryk Hellwig 8 5. Visioary activities Professor Hellwig had a uusual prophetic abilities. Whe oly a few people i Polad were seriously thikig about the future of a electroic brai, Professor Hellwig orgaized a educatioal ad study cetre for coputer prograig ad data processig. Uder his leadership there were published for the advertiseet of Lower Silesia Busiess School first tie i Polad a series of textbooks o prograig laguages, scietific coputatios usig a co-puter achie. Whe Polad was udergoig the chage of political syste, Z. Hellwig proposed to orgaize the Lower Silesia Busiess School for the study ad teachig of fiacial atheatics ad actuarial statistics. Reeberig this iitiative, there was orgaized i 2000,for the first tie i Polad, Actuarial Coferece coeoratig Hellwig s 80 th birthday. I spite of soe stublig blocks, practically all of the ost proiet Polish statisticias ad atheaticias took part i this coferece. ŚLĄSKI