{"id":{"repo_id":"greece","oai_identifier":"oai:10442/1462"},"canonical_url":"https://search.dev.ndltd.org/etd/greece/oai:10442/1462","repository":{"repo_id":"greece","name":"Greek National Archive of PhD Theses","base_url":"https://phdtheses.ekt.gr/eadd_oai/request"},"display":{"title":"ΠΟΛΥΔΙΑΣΤΑΤΕΣ ΚΑΤΑΝΟΜΕΣ Κ-ΤΑΞΗΣ","abstract":"WE DERIVE A MULTIVARIATE NEGATIVE BINOMIAL DISTRIBUTION OF ORDER K BY MEANS OF AN URN SCHEME AND WE OBTAIN TWO LIMITING CASES OF IT WHICH PROVIDE A MULTIVARIATE POISSON DISTRIBUTION OF ORDER K AND A MULTIVARIATE LOGARITHMIC SERIES DISTRIBUTION OF THE SAME ORDER. WE DEFINE THE GENERALIZED SEQUENCE OF ORDER K, AS AN EXTENSION OF INDEPENDENT TRIALS WITH MULTIPLE OUTCOMES, AND BY EMPLOYING THIS SEQUENCE WE DERIVE ANALOGUES MULTIVARIATE EXTENDED DISTRIBUTIONS OF ORDER K. SPECIAL CASES OF THE MULTIVARIATE DISTRIBUTIONS OF ORDER K ARE THE MULTIVARIATE DISTRIBUTIONS OF THE SAME ORDER TYPE-I AND TYPE-II, WHICH ARE ALSO DEFINED. PROBABILITY GENERATING FUNCTIONS, MEANS VARIANCES, COVARIANCES, FURTHER GENESIS SCHEMES, INTERRELATIONSHIPS AND RECURRENCE RELATIONS AND BINOMIAL EXPRESSIONS FOR CALCULATING THE PROBABILITIES OF THE ABOVE DISTRIBUTIONS ARE ALSO GIVEN.","abstract_html":"WE DERIVE A MULTIVARIATE NEGATIVE BINOMIAL DISTRIBUTION OF ORDER K BY MEANS OF AN URN SCHEME AND WE OBTAIN TWO LIMITING CASES OF IT WHICH PROVIDE A MULTIVARIATE POISSON DISTRIBUTION OF ORDER K AND A MULTIVARIATE LOGARITHMIC SERIES DISTRIBUTION OF THE SAME ORDER. WE DEFINE THE GENERALIZED SEQUENCE OF ORDER K, AS AN EXTENSION OF INDEPENDENT TRIALS WITH MULTIPLE OUTCOMES, AND BY EMPLOYING THIS SEQUENCE WE DERIVE ANALOGUES MULTIVARIATE EXTENDED DISTRIBUTIONS OF ORDER K. SPECIAL CASES OF THE MULTIVARIATE DISTRIBUTIONS OF ORDER K ARE THE MULTIVARIATE DISTRIBUTIONS OF THE SAME ORDER TYPE-I AND TYPE-II, WHICH ARE ALSO DEFINED. PROBABILITY GENERATING FUNCTIONS, MEANS VARIANCES, COVARIANCES, FURTHER GENESIS SCHEMES, INTERRELATIONSHIPS AND RECURRENCE RELATIONS AND BINOMIAL EXPRESSIONS FOR CALCULATING THE PROBABILITIES OF THE ABOVE DISTRIBUTIONS ARE ALSO GIVEN.","abstract_has_math":false,"creators":["Antzoulakos, Demetrios","Αντζουλάκος, Δημήτριος"],"institution":"Πανεπιστήμιο Πατρών","degree_name":null,"degree_level":null,"degree_discipline":null,"degree_department":null,"school":null,"contributors":[],"advisors":[],"committee_chairs":[],"committee_members":[],"year":1990,"date_issued":"1990","date_published":"1990","updated_at":"2026-07-24T02:24:56Z","subjects":["CONVOLUTIONS","DISTRIBUTIONS TYPE II","DISTRIBUTIONS TYPEI","EXTENDED DISTRIBUTIONS","MULTIPARAMETER DISTRIBUTIONS","Multivariate distributions of order k","MULTIVARIATE FIBONACCI POLYNOMIAS OF ORDER K","PROPERTIES","ΕΚΤΕΤΑΜΕΝΕΣ ΚΑΤΑΝΟΜΕΣ","ΙΔΙΟΤΗΤΕΣ","ΚΑΤΑΝΟΜΕΣ ΤΥΠΟΥ Ι","ΚΑΤΑΝΟΜΕΣ ΤΥΠΟΥ ΙΙ","Πολυδιάστατες κατανομές τάξεως k","ΠΟΛΥΜΕΤΑΒΛΗΤΑ ΠΟΛΥΩΝΥΜΑ FIBONACCI Κ-ΤΑΞΗΣ","ΠΟΛΥΠΑΡΑΜΕΤΡΙΚΕΣ ΚΑΤΑΝΟΜΕΣ","ΣΥΝΕΛΙΞΕΙΣ","Φυσικές Επιστήμες","Natural Sciences","Μαθηματικά","Mathematics"],"languages":["gre"],"rights":[],"rights_urls":[],"identifier_entries":[{"key":"dc:identifier","label":"Identifier","values":["10.12681/eadd/1462"],"render_values":[{"text":"10.12681/eadd/1462","href":"https://doi.org/10.12681/eadd/1462","code":true}]}]},"links":{"outbound_url":"http://hdl.handle.net/10442/hedi/1462","outbound_label":"Handle","outbound_source":"dc:identifier"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:creator","label":"Author","values":["Antzoulakos, Demetrios","Αντζουλάκος, Δημήτριος"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date","label":"Dc Date","values":["1990"]},{"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":["CONVOLUTIONS","DISTRIBUTIONS TYPE II","DISTRIBUTIONS TYPEI","EXTENDED DISTRIBUTIONS","MULTIPARAMETER DISTRIBUTIONS","Multivariate distributions of order k","MULTIVARIATE FIBONACCI POLYNOMIAS OF ORDER K","PROPERTIES","ΕΚΤΕΤΑΜΕΝΕΣ ΚΑΤΑΝΟΜΕΣ","ΙΔΙΟΤΗΤΕΣ","ΚΑΤΑΝΟΜΕΣ ΤΥΠΟΥ Ι","ΚΑΤΑΝΟΜΕΣ ΤΥΠΟΥ ΙΙ","Πολυδιάστατες κατανομές τάξεως k","ΠΟΛΥΜΕΤΑΒΛΗΤΑ ΠΟΛΥΩΝΥΜΑ FIBONACCI Κ-ΤΑΞΗΣ","ΠΟΛΥΠΑΡΑΜΕΤΡΙΚΕΣ ΚΑΤΑΝΟΜΕΣ","ΣΥΝΕΛΙΞΕΙΣ","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/1462","http://hdl.handle.net/10442/hedi/1462"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description","label":"Description","values":["WE DERIVE A MULTIVARIATE NEGATIVE BINOMIAL DISTRIBUTION OF ORDER K BY MEANS OF AN URN SCHEME AND WE OBTAIN TWO LIMITING CASES OF IT WHICH PROVIDE A MULTIVARIATE POISSON DISTRIBUTION OF ORDER K AND A MULTIVARIATE LOGARITHMIC SERIES DISTRIBUTION OF THE SAME ORDER. WE DEFINE THE GENERALIZED SEQUENCE OF ORDER K, AS AN EXTENSION OF INDEPENDENT TRIALS WITH MULTIPLE OUTCOMES, AND BY EMPLOYING THIS SEQUENCE WE DERIVE ANALOGUES MULTIVARIATE EXTENDED DISTRIBUTIONS OF ORDER K. SPECIAL CASES OF THE MULTIVARIATE DISTRIBUTIONS OF ORDER K ARE THE MULTIVARIATE DISTRIBUTIONS OF THE SAME ORDER TYPE-I AND TYPE-II, WHICH ARE ALSO DEFINED. PROBABILITY GENERATING FUNCTIONS, MEANS VARIANCES, COVARIANCES, FURTHER GENESIS SCHEMES, INTERRELATIONSHIPS AND RECURRENCE RELATIONS AND BINOMIAL EXPRESSIONS FOR CALCULATING THE PROBABILITIES OF THE ABOVE DISTRIBUTIONS ARE ALSO GIVEN.","Η ΠΟΛΥΔΙΑΣΤΑΤΗ ΑΡΝΗΤΙΚΗ ΔΥΝΑΜΙΚΗ ΚΑΤΑΝΟΜΗ Κ-ΤΑΞΗΣ ΕΞΑΓΕΤΑΙ ΧΡΗΣΙΜΟΠΟΙΩΝΤΑΣ ΚΑΤΑΛΛΗΛΟ ΠΕΙΡΑΜΑ ΤΥΧΗΣ ΚΑΙ ΑΠΟ ΑΥΤΗΝ ΟΡΙΑΚΑ ΑΒΡΙΣΚΟΥΜΕ ΤΗΝ ΠΟΛΥΔΙΑΣΤΑΤΗ ΚΑΤΑΝΟΜΗ ΙΔΙΑΣ ΤΑΞΗΣ. ΟΡΙΖΟΥΜΕ ΤΗΝ ΓΕΝΙΚΕΥΜΕΝΗ ΑΚΟΛΟΥΘΙΑ Κ-ΤΑΞΗΣ, ΣΑΝ ΜΙΑ ΠΡΟΕΚΤΑΣΗ ΤΩΝ ΑΝΕΞΑΡΤΗΤΩΝ ΠΡΟΣΠΑΘΕΙΩΝ ΜΕ ΠΟΛΛΑΠΛΑ ΕΝΔΕΧΟΜΕΝΑ, ΚΑΙ ΧΡΗΣΙΜΟΠΟΙΩΝΤΑΣ ΤΗ ΚΑΤΑΛΛΗΛΑΕΞΑΓΟΥΜΕ ΑΝΑΛΟΓΕΣ ΠΟΛΥΔΙΑΣΤΑΤΕΣ ΕΚΤΕΤΑΜΕΝΕΣ ΚΑΤΑΝΟΜΕΣ Κ -ΤΑΞΗΣ. ΕΙΔΙΚΕΣ ΠΕΡΙΠΤΩΣΕΙΣ ΤΩΝ ΠΟΛΥΔΙΑΣΤΑΤΩΝ ΚΑΤΑΝΟΜΩΝ Κ-ΤΑΞΗΣ ΕΙΝΑΙ ΟΙ ΠΟΛΥΔΙΑΣΤΑΤΕΣ ΚΑΤΑΝΟΜΕΣ ΤΗΣ ΙΔΙΑΣ ΤΑΞΕΩΣ ΤΥΠΟΥ-Ι ΚΑΙ ΤΥΠΟΥ-ΙΙ, ΟΙ ΟΠΟΙΕΣ ΟΡΙΖΟΝΤΑΙ. ΕΠΙΣΗΣ, ΠΙΘΑΝΟΓΕΝΝΗΤΡΙΕΣ, ΜΕΣΕΣ ΤΙΜΕΣ, ΔΙΑΣΠΟΡΕΣ, ΣΥΝΔΙΑΣΠΟΡΕΣ, ΑΛΛΟΙ ΤΡΟΠΟΙ ΓΕΝΝΗΣΕΩΣ, ΙΔΙΟΤΗΤΕΣ ΚΑΙ ΑΝΑΔΡΟΜΙΚΕΣ ΣΧΕΣΕΙΣ ΚΑΙ ΔΙΩΝΥΜΙΚΕΣ ΕΚΦΡΑΣΕΙΣ ΓΙΑ ΤΟΝ ΥΠΟΛΟΓΙΣΜΟ ΤΩΝ ΠΙΘΑΝΟΤΗΤΩΝΤΩΝ ΠΑΡΑΠΑΝΩ ΚΑΤΟΝΟΜΩΝ ΔΙΔΟΝΤΑΙ."]},{"key":"dc:title","label":"Title","values":["ΠΟΛΥΔΙΑΣΤΑΤΕΣ ΚΑΤΑΝΟΜΕΣ Κ-ΤΑΞΗΣ","MULTIVARIATE DISTRIBUTIONS OF ORDER K"]}]}],"canonical_facts":{"dc:creator":["Antzoulakos, Demetrios","Αντζουλάκος, Δημήτριος"],"dc:date":["1990"],"dc:description":["WE DERIVE A MULTIVARIATE NEGATIVE BINOMIAL DISTRIBUTION OF ORDER K BY MEANS OF AN URN SCHEME AND WE OBTAIN TWO LIMITING CASES OF IT WHICH PROVIDE A MULTIVARIATE POISSON DISTRIBUTION OF ORDER K AND A MULTIVARIATE LOGARITHMIC SERIES DISTRIBUTION OF THE SAME ORDER. WE DEFINE THE GENERALIZED SEQUENCE OF ORDER K, AS AN EXTENSION OF INDEPENDENT TRIALS WITH MULTIPLE OUTCOMES, AND BY EMPLOYING THIS SEQUENCE WE DERIVE ANALOGUES MULTIVARIATE EXTENDED DISTRIBUTIONS OF ORDER K. SPECIAL CASES OF THE MULTIVARIATE DISTRIBUTIONS OF ORDER K ARE THE MULTIVARIATE DISTRIBUTIONS OF THE SAME ORDER TYPE-I AND TYPE-II, WHICH ARE ALSO DEFINED. PROBABILITY GENERATING FUNCTIONS, MEANS VARIANCES, COVARIANCES, FURTHER GENESIS SCHEMES, INTERRELATIONSHIPS AND RECURRENCE RELATIONS AND BINOMIAL EXPRESSIONS FOR CALCULATING THE PROBABILITIES OF THE ABOVE DISTRIBUTIONS ARE ALSO GIVEN.","Η ΠΟΛΥΔΙΑΣΤΑΤΗ ΑΡΝΗΤΙΚΗ ΔΥΝΑΜΙΚΗ ΚΑΤΑΝΟΜΗ Κ-ΤΑΞΗΣ ΕΞΑΓΕΤΑΙ ΧΡΗΣΙΜΟΠΟΙΩΝΤΑΣ ΚΑΤΑΛΛΗΛΟ ΠΕΙΡΑΜΑ ΤΥΧΗΣ ΚΑΙ ΑΠΟ ΑΥΤΗΝ ΟΡΙΑΚΑ ΑΒΡΙΣΚΟΥΜΕ ΤΗΝ ΠΟΛΥΔΙΑΣΤΑΤΗ ΚΑΤΑΝΟΜΗ ΙΔΙΑΣ ΤΑΞΗΣ. ΟΡΙΖΟΥΜΕ ΤΗΝ ΓΕΝΙΚΕΥΜΕΝΗ ΑΚΟΛΟΥΘΙΑ Κ-ΤΑΞΗΣ, ΣΑΝ ΜΙΑ ΠΡΟΕΚΤΑΣΗ ΤΩΝ ΑΝΕΞΑΡΤΗΤΩΝ ΠΡΟΣΠΑΘΕΙΩΝ ΜΕ ΠΟΛΛΑΠΛΑ ΕΝΔΕΧΟΜΕΝΑ, ΚΑΙ ΧΡΗΣΙΜΟΠΟΙΩΝΤΑΣ ΤΗ ΚΑΤΑΛΛΗΛΑΕΞΑΓΟΥΜΕ ΑΝΑΛΟΓΕΣ ΠΟΛΥΔΙΑΣΤΑΤΕΣ ΕΚΤΕΤΑΜΕΝΕΣ ΚΑΤΑΝΟΜΕΣ Κ -ΤΑΞΗΣ. ΕΙΔΙΚΕΣ ΠΕΡΙΠΤΩΣΕΙΣ ΤΩΝ ΠΟΛΥΔΙΑΣΤΑΤΩΝ ΚΑΤΑΝΟΜΩΝ Κ-ΤΑΞΗΣ ΕΙΝΑΙ ΟΙ ΠΟΛΥΔΙΑΣΤΑΤΕΣ ΚΑΤΑΝΟΜΕΣ ΤΗΣ ΙΔΙΑΣ ΤΑΞΕΩΣ ΤΥΠΟΥ-Ι ΚΑΙ ΤΥΠΟΥ-ΙΙ, ΟΙ ΟΠΟΙΕΣ ΟΡΙΖΟΝΤΑΙ. ΕΠΙΣΗΣ, ΠΙΘΑΝΟΓΕΝΝΗΤΡΙΕΣ, ΜΕΣΕΣ ΤΙΜΕΣ, ΔΙΑΣΠΟΡΕΣ, ΣΥΝΔΙΑΣΠΟΡΕΣ, ΑΛΛΟΙ ΤΡΟΠΟΙ ΓΕΝΝΗΣΕΩΣ, ΙΔΙΟΤΗΤΕΣ ΚΑΙ ΑΝΑΔΡΟΜΙΚΕΣ ΣΧΕΣΕΙΣ ΚΑΙ ΔΙΩΝΥΜΙΚΕΣ ΕΚΦΡΑΣΕΙΣ ΓΙΑ ΤΟΝ ΥΠΟΛΟΓΙΣΜΟ ΤΩΝ ΠΙΘΑΝΟΤΗΤΩΝΤΩΝ ΠΑΡΑΠΑΝΩ ΚΑΤΟΝΟΜΩΝ ΔΙΔΟΝΤΑΙ."],"dc:identifier":["10.12681/eadd/1462","http://hdl.handle.net/10442/hedi/1462"],"dc:language":["gre"],"dc:publisher":["Πανεπιστήμιο Πατρών","University of Patras"],"dc:subject":["CONVOLUTIONS","DISTRIBUTIONS TYPE II","DISTRIBUTIONS TYPEI","EXTENDED DISTRIBUTIONS","MULTIPARAMETER DISTRIBUTIONS","Multivariate distributions of order k","MULTIVARIATE FIBONACCI POLYNOMIAS OF ORDER K","PROPERTIES","ΕΚΤΕΤΑΜΕΝΕΣ ΚΑΤΑΝΟΜΕΣ","ΙΔΙΟΤΗΤΕΣ","ΚΑΤΑΝΟΜΕΣ ΤΥΠΟΥ Ι","ΚΑΤΑΝΟΜΕΣ ΤΥΠΟΥ ΙΙ","Πολυδιάστατες κατανομές τάξεως k","ΠΟΛΥΜΕΤΑΒΛΗΤΑ ΠΟΛΥΩΝΥΜΑ FIBONACCI Κ-ΤΑΞΗΣ","ΠΟΛΥΠΑΡΑΜΕΤΡΙΚΕΣ ΚΑΤΑΝΟΜΕΣ","ΣΥΝΕΛΙΞΕΙΣ","Φυσικές Επιστήμες","Natural Sciences","Μαθηματικά","Mathematics"],"dc:title":["ΠΟΛΥΔΙΑΣΤΑΤΕΣ ΚΑΤΑΝΟΜΕΣ Κ-ΤΑΞΗΣ","MULTIVARIATE DISTRIBUTIONS OF ORDER K"],"dc:type":["PhD Thesis"]},"updated_at":"2026-07-24T02:24:56Z"}