{"id":"https://openalex.org/W7211896553","doi":"https://doi.org/10.48550/arxiv.2609.04416","title":"Absolute moments of the binomial distribution folded at its mean","display_name":"Absolute moments of the binomial distribution folded at its mean","publication_year":2026,"publication_date":"2026-09-03","ids":{"openalex":"https://openalex.org/W7211896553","doi":"https://doi.org/10.48550/arxiv.2609.04416"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2609.04416","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.04416","pdf_url":"https://arxiv.org/pdf/2609.04416","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},"volume":null,"type":"preprint","indexed_in":["arxiv","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/2609.04416","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5011731492","display_name":"Neven Elezovi\u0107","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I181343428","display_name":"University of Zagreb","ror":"https://ror.org/00mv6sv71","country_code":"HR","type":"education","lineage":["https://openalex.org/I181343428"]},{"id":"https://openalex.org/I4390039327","display_name":"Faculty of Electrical Engineering and Computing in Zagreb","ror":"https://ror.org/04e90ca47","country_code":"HR","type":"education","lineage":["https://openalex.org/I181343428","https://openalex.org/I4390039327"]}],"countries":["HR"],"is_corresponding":true,"raw_author_name":"Elezovi\u0107, Neven","raw_affiliation_strings":["Department of Applied Mathematics ,","Faculty of Electrical Engineering and Computing , University of Zagreb , 10000 Zagreb , Croatia"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Applied Mathematics ,","institution_ids":[]},{"raw_affiliation_string":"Faculty of Electrical Engineering and Computing , University of Zagreb , 10000 Zagreb , Croatia","institution_ids":["https://openalex.org/I181343428","https://openalex.org/I4390039327"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5011731492"],"corresponding_institution_ids":["https://openalex.org/I181343428","https://openalex.org/I4390039327"],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":true,"cited_by_count":0,"citation_normalized_percentile":null,"cited_by_percentile_year":null,"biblio":{"volume":null,"issue":null,"first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T13500","display_name":"Probability and Statistical Research","score":0.7919999957084656,"subfield":{"id":"https://openalex.org/subfields/2613","display_name":"Statistics and Probability"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T13500","display_name":"Probability and Statistical Research","score":0.7919999957084656,"subfield":{"id":"https://openalex.org/subfields/2613","display_name":"Statistics and Probability"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10968","display_name":"Statistical Distribution Estimation and Applications","score":0.1534000039100647,"subfield":{"id":"https://openalex.org/subfields/2613","display_name":"Statistics and Probability"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11191","display_name":"Mathematical functions and polynomials","score":0.02070000022649765,"subfield":{"id":"https://openalex.org/subfields/2604","display_name":"Applied Mathematics"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/binomial-distribution","display_name":"binomial distribution","score":0.9359999895095825},{"id":"https://openalex.org/keywords/absolute-moments","display_name":"absolute moments","score":0.7929999828338623},{"id":"https://openalex.org/keywords/bernoulli-polynomials","display_name":"Bernoulli polynomials","score":0.8289999961853027},{"id":"https://openalex.org/keywords/large-parameter-asymptotics","display_name":"large parameter asymptotics","score":0.5989999771118164}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7865999937057495},{"id":"https://openalex.org/C34388435","wikidata":"https://www.wikidata.org/wiki/Q2267362","display_name":"Bounded function","level":2,"score":0.5774999856948853},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.47589999437332153},{"id":"https://openalex.org/C34718186","wikidata":"https://www.wikidata.org/wiki/Q209875","display_name":"Binomial coefficient","level":2,"score":0.45339998602867126},{"id":"https://openalex.org/C110121322","wikidata":"https://www.wikidata.org/wiki/Q865811","display_name":"Distribution (mathematics)","level":2,"score":0.45249998569488525},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.43779999017715454},{"id":"https://openalex.org/C180099792","wikidata":"https://www.wikidata.org/wiki/Q26708","display_name":"Binomial theorem","level":2,"score":0.43290001153945923},{"id":"https://openalex.org/C2781204021","wikidata":"https://www.wikidata.org/wiki/Q6497091","display_name":"Lattice (music)","level":2,"score":0.4228000044822693},{"id":"https://openalex.org/C186080144","wikidata":"https://www.wikidata.org/wiki/Q358733","display_name":"Series expansion","level":2,"score":0.4205999970436096},{"id":"https://openalex.org/C179254644","wikidata":"https://www.wikidata.org/wiki/Q13222844","display_name":"Moment (physics)","level":2,"score":0.4097000062465668},{"id":"https://openalex.org/C97137487","wikidata":"https://www.wikidata.org/wiki/Q729138","display_name":"Integer (computer science)","level":2,"score":0.390500009059906},{"id":"https://openalex.org/C143724316","wikidata":"https://www.wikidata.org/wiki/Q312468","display_name":"Series (stratigraphy)","level":2,"score":0.3801000118255615},{"id":"https://openalex.org/C129844170","wikidata":"https://www.wikidata.org/wiki/Q41299","display_name":"Quadratic equation","level":2,"score":0.3723999857902527},{"id":"https://openalex.org/C41054675","wikidata":"https://www.wikidata.org/wiki/Q185547","display_name":"Binomial distribution","level":2,"score":0.35929998755455017},{"id":"https://openalex.org/C199335787","wikidata":"https://www.wikidata.org/wiki/Q743364","display_name":"Negative binomial distribution","level":3,"score":0.351500004529953},{"id":"https://openalex.org/C73905626","wikidata":"https://www.wikidata.org/wiki/Q206925","display_name":"Power series","level":2,"score":0.34630000591278076},{"id":"https://openalex.org/C11683690","wikidata":"https://www.wikidata.org/wiki/Q752726","display_name":"Asymptotic expansion","level":2,"score":0.3434000015258789},{"id":"https://openalex.org/C61062188","wikidata":"https://www.wikidata.org/wiki/Q835065","display_name":"Second moment of area","level":2,"score":0.3325999975204468},{"id":"https://openalex.org/C122123141","wikidata":"https://www.wikidata.org/wiki/Q176623","display_name":"Random variable","level":2,"score":0.3276999890804291},{"id":"https://openalex.org/C120229918","wikidata":"https://www.wikidata.org/wiki/Q1088747","display_name":"Central moment","level":4,"score":0.30000001192092896},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.2962999939918518},{"id":"https://openalex.org/C2781315470","wikidata":"https://www.wikidata.org/wiki/Q193623","display_name":"Binomial (polynomial)","level":2,"score":0.29420000314712524},{"id":"https://openalex.org/C134121241","wikidata":"https://www.wikidata.org/wiki/Q899301","display_name":"Yield (engineering)","level":2,"score":0.26429998874664307},{"id":"https://openalex.org/C118733216","wikidata":"https://www.wikidata.org/wiki/Q332504","display_name":"Absolute continuity","level":2,"score":0.262800008058548}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2609.04416","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.04416","pdf_url":"https://arxiv.org/pdf/2609.04416","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},{"id":"doi:10.48550/arxiv.2609.04416","doi":"https://doi.org/10.48550/arxiv.2609.04416","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2609.04416","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Preprint"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:2609.04416","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.04416","pdf_url":"https://arxiv.org/pdf/2609.04416","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},"sustainable_development_goals":[],"study_designs":[],"awards":[],"funders":[],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W7211896553.pdf","grobid_xml":"https://content.openalex.org/works/W7211896553.grobid-xml"},"referenced_works_count":0,"referenced_works":[],"related_works":["https://openalex.org/W7213516865","https://openalex.org/W2183726438","https://openalex.org/W7097504304","https://openalex.org/W7202005834","https://openalex.org/W7170170891","https://openalex.org/W7170225076","https://openalex.org/W2243058295","https://openalex.org/W7203627371","https://openalex.org/W1990097175","https://openalex.org/W2058723094"],"abstract_inverted_index":{"Let":[0],"$X\\sim":[1],"Bin(N,p)$":[2],"and":[3,24,35],"\\(Y=|X-Np|\\).":[4],"We":[5,53],"derive":[6],"an":[7,76],"exact":[8],"reduction":[9],"for":[10,87,106],"every":[11],"odd":[12,47],"absolute":[13],"moment":[14],"of":[15,71,90,103],"\\(Y\\),":[16],"expressing":[17],"it":[18],"through":[19],"finitely":[20],"many":[21],"central":[22,25],"masses":[23,51],"tail":[26,29,81],"probabilities.":[27],"The":[28],"coefficients":[30,67,82],"satisfy":[31],"a":[32,61,84],"sum":[33],"rule":[34],"are":[36],"divisible":[37],"by":[38],"\\(q-p\\),":[39],"so":[40],"that":[41],"in":[42,68],"the":[43,46,56,72,78,88,91,99,107],"symmetric":[44],"case":[45],"ladder":[48],"collapses":[49],"to":[50],"alone.":[52],"then":[54],"obtain":[55],"complete":[57],"central-tail":[58],"expansion":[59,86,105],"at":[60],"bounded":[62],"lattice":[63],"displacement,":[64],"with":[65],"Bernoulli-polynomial":[66],"integer":[69],"powers":[70],"large":[73],"parameter.":[74],"As":[75],"application,":[77],"first":[79,100],"two":[80,101],"yield":[83],"second-order":[85],"median":[89],"beta":[92],"distribution,":[93],"whose":[94],"formal":[95],"one-parameter":[96],"degeneration":[97],"reproduces":[98],"terms":[102],"Choi's":[104],"gamma":[108],"median.":[109]},"counts_by_year":[],"updated_date":"2026-10-28T10:33:24.094632","created_date":"2026-09-08T00:00:00"}
