{"id":{"repo_id":"greece","oai_identifier":"oai:10442/1601"},"canonical_url":"https://search.dev.ndltd.org/etd/greece/oai:10442/1601","repository":{"repo_id":"greece","name":"Greek National Archive of PhD Theses","base_url":"https://phdtheses.ekt.gr/eadd_oai/request"},"display":{"title":"ΜΟΝΟΔΙΑΣΤΑΤΕΣ ΚΑΙ ΠΟΛΥΔΙΑΣΤΑΤΕΣ ΚΑΤΑΝΟΜΕΣ POLYA ΚΑΙ ΑΝΑΣΤΡΟΦΗ POLYA ΤΑΞΕΩΣ Κ","abstract":"IN THIS PH.D. DISSERTATION WE DERIVE AND STUDY NEW UNIVARIATE AND MULTIVARIATE DISCRETE DISTIBUTIONS OF ORDER K. WE INTRODUCE THE FOLLOWING DISTRIBUTIONS OF ORDER K, TYPE II: HYPERGEOMETRIC, NEGATIVE HYPERGEOMETRIC, INVERSE HYPERGEOMETRIC, INVERSE NEGATIVE HYPERGEOMETRIC, POLYA, INVERSE POLYA AND UNIFORM DISTRIBUTION OF ORDER K ON THE INTEGERS 1,....,K. WE DERIVE THE MOMENT GENERATING FUNCTIONS, MEANS AND VARIANCES OF THESE DISTRIBUTIONS, WE ESTABLISH SEVERAL ASYMPTOTICRELATIONSHIPS OF THEM AND WE OBTAIN THE MOMENT ESTIMATORS OF THEIR PARAMETERS.GENERALIZING THESE DISTRIBUTIONS TO THE MULTIVARIATE CASE, WE DERIVE AND STUDYTHE FOLLOWING MULTIVARIATE DISTRIBUTIONS OF ORDER K, HYPERGEOMETRIC, NEGATIVE HYPERGEOMETRIC, INVERSE HYPERGEOMETRIC, INVERSE NEGATIVE HYPERGEOMETRIC, POLYA,INVERSE POLYA AND BOSE-EINSTEIN. WE ALSO INTRODUCE AND STUDY A UNIFIED MULTIVARIATE DISTRIBUTION OF ORDER K, WHICH INCLUDES ALL THE ABOVE MENTIONED DISTRIBUTIONS.","abstract_html":"IN THIS PH.D. DISSERTATION WE DERIVE AND STUDY NEW UNIVARIATE AND MULTIVARIATE DISCRETE DISTIBUTIONS OF ORDER K. WE INTRODUCE THE FOLLOWING DISTRIBUTIONS OF ORDER K, TYPE II: HYPERGEOMETRIC, NEGATIVE HYPERGEOMETRIC, INVERSE HYPERGEOMETRIC, INVERSE NEGATIVE HYPERGEOMETRIC, POLYA, INVERSE POLYA AND UNIFORM DISTRIBUTION OF ORDER K ON THE INTEGERS 1,....,K. WE DERIVE THE MOMENT GENERATING FUNCTIONS, MEANS AND VARIANCES OF THESE DISTRIBUTIONS, WE ESTABLISH SEVERAL ASYMPTOTICRELATIONSHIPS OF THEM AND WE OBTAIN THE MOMENT ESTIMATORS OF THEIR PARAMETERS.GENERALIZING THESE DISTRIBUTIONS TO THE MULTIVARIATE CASE, WE DERIVE AND STUDYTHE FOLLOWING MULTIVARIATE DISTRIBUTIONS OF ORDER K, HYPERGEOMETRIC, NEGATIVE HYPERGEOMETRIC, INVERSE HYPERGEOMETRIC, INVERSE NEGATIVE HYPERGEOMETRIC, POLYA,INVERSE POLYA AND BOSE-EINSTEIN. WE ALSO INTRODUCE AND STUDY A UNIFIED MULTIVARIATE DISTRIBUTION OF ORDER K, WHICH INCLUDES ALL THE ABOVE MENTIONED DISTRIBUTIONS.","abstract_has_math":false,"creators":["Τρυψιάννης, Γρηγόριος"],"institution":"Πανεπιστήμιο Πατρών","degree_name":null,"degree_level":null,"degree_discipline":null,"degree_department":null,"school":null,"contributors":[],"advisors":[],"committee_chairs":[],"committee_members":[],"year":1991,"date_issued":"1991","date_published":"1991","updated_at":"2026-07-24T02:25:02Z","subjects":["HYPERGEOMETRIC","INVERSE HYPERGEOMETRIC","INVERSE POLYA","NEGATIVE HYPERGEOMETRIC","NEGATIVE INVERSE HYPERGEOMETRIC","POLYA","UNIFIED HYPERGEOMETRIC DISTRIBUTION OF ORDER K","UNIFORM DISTRIBUTION ON THE INTEGERS 1,...,K","ΑΝΑΣΤΡΟΦΗ POLYA","ΑΝΑΣΤΡΟΦΗ ΥΠΕΡΓΕΩΜΕΤΡΙΚΗ","ΑΡΝΗΤΙΚΗ ΑΝΑΣΤΡΟΦΗ ΥΠΕΡΓΕΩΜΕΤΡΙΚΗ","ΑΡΝΗΤΙΚΗ ΥΠΕΡΓΕΩΜΕΤΡΙΚΗ","ΕΝΟΠΟΙΗΜΕΝΗ ΥΠΕΡΓΕΩΜΕΤΡΙΚΗ ΚΑΤΑΝΟΜΗ ΤΑΞΕΩΣ Κ","ΚΑΤΑΝΟΜΕΣ ΤΑΞΕΩΣ Κ-ΜΟΝΟΔΙΑΣΤΑΤΕΣ & ΠΟΛΥΔΙΑΣΤΑΤΕΣ ΥΠΕΡΓΕΩΜΕΤΡΙΚΗ","ΟΜΟΙΟΜΟΡΦΗ ΚΑΤΑΝΟΜΗ ΕΠΙ ΤΩΝ ΑΚΕΡΑΙΩΝ 1,...,Κ","Φυσικές Επιστήμες","Natural Sciences","Μαθηματικά","Mathematics"],"languages":["gre"],"rights":[],"rights_urls":[],"identifier_entries":[{"key":"dc:identifier","label":"Identifier","values":["10.12681/eadd/1601"],"render_values":[{"text":"10.12681/eadd/1601","href":"https://doi.org/10.12681/eadd/1601","code":true}]}]},"links":{"outbound_url":"http://hdl.handle.net/10442/hedi/1601","outbound_label":"Handle","outbound_source":"dc:identifier"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:creator","label":"Author","values":["Τρυψιάννης, Γρηγόριος"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date","label":"Dc Date","values":["1991"]},{"key":"dc:publisher","label":"Institution","values":["Πανεπιστήμιο Πατρών","University of Patras"]},{"key":"dc:type","label":"Dc Type","values":["PhD Thesis"]}]},{"id":"subjects_keywords","label":"Subjects and Keywords","entries":[{"key":"dc:subject","label":"Dc Subject","values":["HYPERGEOMETRIC","INVERSE HYPERGEOMETRIC","INVERSE POLYA","NEGATIVE HYPERGEOMETRIC","NEGATIVE INVERSE HYPERGEOMETRIC","POLYA","UNIFIED HYPERGEOMETRIC DISTRIBUTION OF ORDER K","UNIFORM DISTRIBUTION ON THE INTEGERS 1,...,K","ΑΝΑΣΤΡΟΦΗ POLYA","ΑΝΑΣΤΡΟΦΗ ΥΠΕΡΓΕΩΜΕΤΡΙΚΗ","ΑΡΝΗΤΙΚΗ ΑΝΑΣΤΡΟΦΗ ΥΠΕΡΓΕΩΜΕΤΡΙΚΗ","ΑΡΝΗΤΙΚΗ ΥΠΕΡΓΕΩΜΕΤΡΙΚΗ","ΕΝΟΠΟΙΗΜΕΝΗ ΥΠΕΡΓΕΩΜΕΤΡΙΚΗ ΚΑΤΑΝΟΜΗ ΤΑΞΕΩΣ Κ","ΚΑΤΑΝΟΜΕΣ ΤΑΞΕΩΣ Κ-ΜΟΝΟΔΙΑΣΤΑΤΕΣ & ΠΟΛΥΔΙΑΣΤΑΤΕΣ ΥΠΕΡΓΕΩΜΕΤΡΙΚΗ","ΟΜΟΙΟΜΟΡΦΗ ΚΑΤΑΝΟΜΗ ΕΠΙ ΤΩΝ ΑΚΕΡΑΙΩΝ 1,...,Κ","Φυσικές Επιστήμες","Natural Sciences","Μαθηματικά","Mathematics"]}]},{"id":"language_rights","label":"Language and Rights","entries":[{"key":"dc:language","label":"Dc Language","values":["gre"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier","label":"Identifier","values":["10.12681/eadd/1601","http://hdl.handle.net/10442/hedi/1601"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description","label":"Description","values":["IN THIS PH.D. DISSERTATION WE DERIVE AND STUDY NEW UNIVARIATE AND MULTIVARIATE DISCRETE DISTIBUTIONS OF ORDER K. WE INTRODUCE THE FOLLOWING DISTRIBUTIONS OF ORDER K, TYPE II: HYPERGEOMETRIC, NEGATIVE HYPERGEOMETRIC, INVERSE HYPERGEOMETRIC, INVERSE NEGATIVE HYPERGEOMETRIC, POLYA, INVERSE POLYA AND UNIFORM DISTRIBUTION OF ORDER K ON THE INTEGERS 1,....,K. WE DERIVE THE MOMENT GENERATING FUNCTIONS, MEANS AND VARIANCES OF THESE DISTRIBUTIONS, WE ESTABLISH SEVERAL ASYMPTOTICRELATIONSHIPS OF THEM AND WE OBTAIN THE MOMENT ESTIMATORS OF THEIR PARAMETERS.GENERALIZING THESE DISTRIBUTIONS TO THE MULTIVARIATE CASE, WE DERIVE AND STUDYTHE FOLLOWING MULTIVARIATE DISTRIBUTIONS OF ORDER K, HYPERGEOMETRIC, NEGATIVE HYPERGEOMETRIC, INVERSE HYPERGEOMETRIC, INVERSE NEGATIVE HYPERGEOMETRIC, POLYA,INVERSE POLYA AND BOSE-EINSTEIN. WE ALSO INTRODUCE AND STUDY A UNIFIED MULTIVARIATE DISTRIBUTION OF ORDER K, WHICH INCLUDES ALL THE ABOVE MENTIONED DISTRIBUTIONS.","ΣΤΗΝ ΕΡΓΑΣΙΑ ΑΥΤΗ ΕΙΣΑΓΟΝΤΑΙ ΚΑΙ ΜΕΛΕΤΩΝΤΑΙ ΝΕΕΣ ΜΟΝΟΔΙΑΣΤΑΤΕΣ ΚΑΙ ΠΟΛΥΔΙΑΣΤΑΤΕΣ ΚΑΤΟΝΟΜΕΣ ΤΑΞΕΩΣ Κ. ΣΥΓΚΕΚΡΙΜΕΝΑ ΕΙΣΑΓΟΝΤΑΙ ΟΙ ΚΑΤΟΝΟΜΕΣ ΤΑΞΕΩΣ Κ, ΥΠΕΡΓΕΩΜΕΤΡΙΚΗ, ΑΡΝΗΤΙΚΗ ΥΠΕΡΓΕΩΜΕΤΡΙΚΗ, ΑΝΑΣΤΡΟΦΗ ΥΠΕΡΓΕΩΜΕΤΡΙΚΗ, ΑΡΝΗΤΙΚΗ ΑΝΑΣΤΡΟΦΗ ΥΠΕΡΓΕΩΜΕΤΡΙΚΗ, POLYA, ΑΝΑΣΤΡΟΦΗ POLYA, ΚΑΙ ΟΜΟΙΟΜΟΡΦΗ ΚΑΤΑΝΟΜΗ ΕΠΙ ΤΩΝ ΑΚΕΡΑΙΩΝ 1,...,Κ. ΓΙΑ ΤΙΣ ΚΑΤΑΝΟΜΕΣ ΑΥΤΕΣ ΥΠΟΛΟΓΙΖΕΤΑΙ ΠΛΗΘΟΣ ΑΡΙΘΜΗΤΙΚΩΝ ΧΑΡΑΚΤΗΡΙΣΤΙΚΩΝ, ΔΙΝΟΝΤΑΙ ΑΣΥΜΠΤΩΤΙΚΕΣ ΣΧΕΣΕΙΣ ΑΥΤΩΝ ΜΕ ΓΝΩΣΤΕΣ ΚΑΤΑΝΟΜΕΣ ΤΑΞΕΩΣ Κ ΚΑΙ ΠΡΟΣΔΙΟΡΙΖΟΝΤΑΙ ΟΙ ΕΚΤΙΜΗΤΕΣ ΤΩΝ ΠΑΡΑΜΕΤΡΩΝ ΤΟΥΣ. ΓΕΝΙΚΕΥΟΝΤΑΣ ΑΥΤΕΣ ΤΙΣ ΚΑΤΑΝΟΜΕΣ ΣΤΙΣ Μ- ΔΙΑΣΤΑΣΕΙΣ, ΕΙΣΑΓΟΥΜΕ ΤΙΣ ΠΟΛΥΔΙΑΣΤΑΤΕΣ ΚΑΤΑΝΟΜΕΣ ΤΑΞΕΩΣ Κ, ΥΠΕΡΓΕΩΜΕΤΡΙΚΗ, ΑΡΝΗΤΙΚΗ ΥΠΕΡΓΕΩΜΕΤΡΙΚΗ, ΑΝΑΣΤΡΟΦΗ ΥΠΕΡΓΕΩΜΕΤΡΙΚΗ, POLYA, ΑΝΑΣΤΡΟΦΗ POLYA, BOSE-EINSTEIN. ΣΤΗ ΣΥΝΕΧΕΙΑ ΓΙΝΕΤΑΙ ΑΝΤΙΣΤΟΙΧΗ ΜΕΛΕΤΗ ΤΩΝ ΚΑΤΑΝΟΜΩΝ ΑΥΤΩΝ. ΤΕΛΟΣ ΕΙΣΑΓΕΤΑΙ ΜΙΑ ΕΝΟΠΟΙΗΜΕΝΗ ΠΟΛΥΔΙΑΣΤΑΤΗ ΚΑΤΑΝΟΜΗ ΤΑΞΕΩΣ Κ, ΕΙΔΙΚΕΣ ΠΕΡΙΠΤΩΣΕΙΣ ΤΗΣ ΟΠΟΙΑΣ ΑΠΟΤΕΛΟΥΝ ΟΛΕΣ ΟΙ ΚΑΤΑΝΟΜΕΣ ΠΟΥ ΑΝΑΦΕΡΘΗΚΑΝ ΠΙΟ ΠΑΝΩ."]},{"key":"dc:title","label":"Title","values":["ΜΟΝΟΔΙΑΣΤΑΤΕΣ ΚΑΙ ΠΟΛΥΔΙΑΣΤΑΤΕΣ ΚΑΤΑΝΟΜΕΣ POLYA ΚΑΙ ΑΝΑΣΤΡΟΦΗ POLYA ΤΑΞΕΩΣ Κ","UNIVARIATE AND MULTIVARIATE POLYA AND INVERSE POLYA DISTRIBUTIONS OF ORDER K"]}]}],"canonical_facts":{"dc:creator":["Τρυψιάννης, Γρηγόριος"],"dc:date":["1991"],"dc:description":["IN THIS PH.D. DISSERTATION WE DERIVE AND STUDY NEW UNIVARIATE AND MULTIVARIATE DISCRETE DISTIBUTIONS OF ORDER K. WE INTRODUCE THE FOLLOWING DISTRIBUTIONS OF ORDER K, TYPE II: HYPERGEOMETRIC, NEGATIVE HYPERGEOMETRIC, INVERSE HYPERGEOMETRIC, INVERSE NEGATIVE HYPERGEOMETRIC, POLYA, INVERSE POLYA AND UNIFORM DISTRIBUTION OF ORDER K ON THE INTEGERS 1,....,K. WE DERIVE THE MOMENT GENERATING FUNCTIONS, MEANS AND VARIANCES OF THESE DISTRIBUTIONS, WE ESTABLISH SEVERAL ASYMPTOTICRELATIONSHIPS OF THEM AND WE OBTAIN THE MOMENT ESTIMATORS OF THEIR PARAMETERS.GENERALIZING THESE DISTRIBUTIONS TO THE MULTIVARIATE CASE, WE DERIVE AND STUDYTHE FOLLOWING MULTIVARIATE DISTRIBUTIONS OF ORDER K, HYPERGEOMETRIC, NEGATIVE HYPERGEOMETRIC, INVERSE HYPERGEOMETRIC, INVERSE NEGATIVE HYPERGEOMETRIC, POLYA,INVERSE POLYA AND BOSE-EINSTEIN. WE ALSO INTRODUCE AND STUDY A UNIFIED MULTIVARIATE DISTRIBUTION OF ORDER K, WHICH INCLUDES ALL THE ABOVE MENTIONED DISTRIBUTIONS.","ΣΤΗΝ ΕΡΓΑΣΙΑ ΑΥΤΗ ΕΙΣΑΓΟΝΤΑΙ ΚΑΙ ΜΕΛΕΤΩΝΤΑΙ ΝΕΕΣ ΜΟΝΟΔΙΑΣΤΑΤΕΣ ΚΑΙ ΠΟΛΥΔΙΑΣΤΑΤΕΣ ΚΑΤΟΝΟΜΕΣ ΤΑΞΕΩΣ Κ. ΣΥΓΚΕΚΡΙΜΕΝΑ ΕΙΣΑΓΟΝΤΑΙ ΟΙ ΚΑΤΟΝΟΜΕΣ ΤΑΞΕΩΣ Κ, ΥΠΕΡΓΕΩΜΕΤΡΙΚΗ, ΑΡΝΗΤΙΚΗ ΥΠΕΡΓΕΩΜΕΤΡΙΚΗ, ΑΝΑΣΤΡΟΦΗ ΥΠΕΡΓΕΩΜΕΤΡΙΚΗ, ΑΡΝΗΤΙΚΗ ΑΝΑΣΤΡΟΦΗ ΥΠΕΡΓΕΩΜΕΤΡΙΚΗ, POLYA, ΑΝΑΣΤΡΟΦΗ POLYA, ΚΑΙ ΟΜΟΙΟΜΟΡΦΗ ΚΑΤΑΝΟΜΗ ΕΠΙ ΤΩΝ ΑΚΕΡΑΙΩΝ 1,...,Κ. ΓΙΑ ΤΙΣ ΚΑΤΑΝΟΜΕΣ ΑΥΤΕΣ ΥΠΟΛΟΓΙΖΕΤΑΙ ΠΛΗΘΟΣ ΑΡΙΘΜΗΤΙΚΩΝ ΧΑΡΑΚΤΗΡΙΣΤΙΚΩΝ, ΔΙΝΟΝΤΑΙ ΑΣΥΜΠΤΩΤΙΚΕΣ ΣΧΕΣΕΙΣ ΑΥΤΩΝ ΜΕ ΓΝΩΣΤΕΣ ΚΑΤΑΝΟΜΕΣ ΤΑΞΕΩΣ Κ ΚΑΙ ΠΡΟΣΔΙΟΡΙΖΟΝΤΑΙ ΟΙ ΕΚΤΙΜΗΤΕΣ ΤΩΝ ΠΑΡΑΜΕΤΡΩΝ ΤΟΥΣ. ΓΕΝΙΚΕΥΟΝΤΑΣ ΑΥΤΕΣ ΤΙΣ ΚΑΤΑΝΟΜΕΣ ΣΤΙΣ Μ- ΔΙΑΣΤΑΣΕΙΣ, ΕΙΣΑΓΟΥΜΕ ΤΙΣ ΠΟΛΥΔΙΑΣΤΑΤΕΣ ΚΑΤΑΝΟΜΕΣ ΤΑΞΕΩΣ Κ, ΥΠΕΡΓΕΩΜΕΤΡΙΚΗ, ΑΡΝΗΤΙΚΗ ΥΠΕΡΓΕΩΜΕΤΡΙΚΗ, ΑΝΑΣΤΡΟΦΗ ΥΠΕΡΓΕΩΜΕΤΡΙΚΗ, POLYA, ΑΝΑΣΤΡΟΦΗ POLYA, BOSE-EINSTEIN. ΣΤΗ ΣΥΝΕΧΕΙΑ ΓΙΝΕΤΑΙ ΑΝΤΙΣΤΟΙΧΗ ΜΕΛΕΤΗ ΤΩΝ ΚΑΤΑΝΟΜΩΝ ΑΥΤΩΝ. ΤΕΛΟΣ ΕΙΣΑΓΕΤΑΙ ΜΙΑ ΕΝΟΠΟΙΗΜΕΝΗ ΠΟΛΥΔΙΑΣΤΑΤΗ ΚΑΤΑΝΟΜΗ ΤΑΞΕΩΣ Κ, ΕΙΔΙΚΕΣ ΠΕΡΙΠΤΩΣΕΙΣ ΤΗΣ ΟΠΟΙΑΣ ΑΠΟΤΕΛΟΥΝ ΟΛΕΣ ΟΙ ΚΑΤΑΝΟΜΕΣ ΠΟΥ ΑΝΑΦΕΡΘΗΚΑΝ ΠΙΟ ΠΑΝΩ."],"dc:identifier":["10.12681/eadd/1601","http://hdl.handle.net/10442/hedi/1601"],"dc:language":["gre"],"dc:publisher":["Πανεπιστήμιο Πατρών","University of Patras"],"dc:subject":["HYPERGEOMETRIC","INVERSE HYPERGEOMETRIC","INVERSE POLYA","NEGATIVE HYPERGEOMETRIC","NEGATIVE INVERSE HYPERGEOMETRIC","POLYA","UNIFIED HYPERGEOMETRIC DISTRIBUTION OF ORDER K","UNIFORM DISTRIBUTION ON THE INTEGERS 1,...,K","ΑΝΑΣΤΡΟΦΗ POLYA","ΑΝΑΣΤΡΟΦΗ ΥΠΕΡΓΕΩΜΕΤΡΙΚΗ","ΑΡΝΗΤΙΚΗ ΑΝΑΣΤΡΟΦΗ ΥΠΕΡΓΕΩΜΕΤΡΙΚΗ","ΑΡΝΗΤΙΚΗ ΥΠΕΡΓΕΩΜΕΤΡΙΚΗ","ΕΝΟΠΟΙΗΜΕΝΗ ΥΠΕΡΓΕΩΜΕΤΡΙΚΗ ΚΑΤΑΝΟΜΗ ΤΑΞΕΩΣ Κ","ΚΑΤΑΝΟΜΕΣ ΤΑΞΕΩΣ Κ-ΜΟΝΟΔΙΑΣΤΑΤΕΣ & ΠΟΛΥΔΙΑΣΤΑΤΕΣ ΥΠΕΡΓΕΩΜΕΤΡΙΚΗ","ΟΜΟΙΟΜΟΡΦΗ ΚΑΤΑΝΟΜΗ ΕΠΙ ΤΩΝ ΑΚΕΡΑΙΩΝ 1,...,Κ","Φυσικές Επιστήμες","Natural Sciences","Μαθηματικά","Mathematics"],"dc:title":["ΜΟΝΟΔΙΑΣΤΑΤΕΣ ΚΑΙ ΠΟΛΥΔΙΑΣΤΑΤΕΣ ΚΑΤΑΝΟΜΕΣ POLYA ΚΑΙ ΑΝΑΣΤΡΟΦΗ POLYA ΤΑΞΕΩΣ Κ","UNIVARIATE AND MULTIVARIATE POLYA AND INVERSE POLYA DISTRIBUTIONS OF ORDER K"],"dc:type":["PhD Thesis"]},"updated_at":"2026-07-24T02:25:02Z"}