{"id":"https://openalex.org/W7204196497","doi":"https://doi.org/10.5281/zenodo.22090849","title":"Gumbel Distribution: Extreme Value Theory's Type I Rare Event Statistics \u2014 E8 Intelligence Research","display_name":"Gumbel Distribution: Extreme Value Theory's Type I Rare Event Statistics \u2014 E8 Intelligence Research","publication_year":2026,"publication_date":"2026-08-25","ids":{"openalex":"https://openalex.org/W7204196497","doi":"https://doi.org/10.5281/zenodo.22090849"},"language":"en","primary_location":{"id":"doi:10.5281/zenodo.22090849","doi":"https://doi.org/10.5281/zenodo.22090849","is_oa":true,"landing_page_url":"https://doi.org/10.5281/zenodo.22090849","pdf_url":null,"source":{"id":"https://openalex.org/S4306400562","display_name":"Zenodo (CERN European Organization for Nuclear Research)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I67311998","host_organization_name":"European Organization for Nuclear Research","host_organization_lineage":["https://openalex.org/I67311998"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Preprint"},"volume":null,"type":"preprint","indexed_in":["datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://doi.org/10.5281/zenodo.22090849","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5136862907","display_name":"Andrew Stewart Caldin","orcid":null,"observed_orcids":[]},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Caldin, Andrew Stewart","raw_affiliation_strings":["Independent Researcher, United Kingdom"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Independent Researcher, United Kingdom","institution_ids":[]}]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":["https://openalex.org/A5136862907"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":false,"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/T10968","display_name":"Statistical Distribution Estimation and Applications","score":0.40059998631477356,"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/T10968","display_name":"Statistical Distribution Estimation and Applications","score":0.40059998631477356,"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/T13500","display_name":"Probability and Statistical Research","score":0.34450000524520874,"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/T11720","display_name":"Probability and Risk Models","score":0.1509999930858612,"subfield":{"id":"https://openalex.org/subfields/1803","display_name":"Management Science and Operations Research"},"field":{"id":"https://openalex.org/fields/18","display_name":"Decision Sciences"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/gumbel-distribution","display_name":"Gumbel distribution","score":1.0},{"id":"https://openalex.org/keywords/extreme-value-theory","display_name":"extreme value theory","score":0.9589999914169312},{"id":"https://openalex.org/keywords/rare-events","display_name":"rare events","score":0.7850000262260437},{"id":"https://openalex.org/keywords/frechet-distribution","display_name":"Fr\u00e9chet distribution","score":0.7870000004768372},{"id":"https://openalex.org/keywords/weibull-distribution","display_name":"Weibull distribution","score":1.0},{"id":"https://openalex.org/keywords/shape-parameter","display_name":"shape parameter","score":0.7919999957084656},{"id":"https://openalex.org/keywords/euler-mascheroni-constant","display_name":"Euler-Mascheroni constant","score":0.9319999814033508},{"id":"https://openalex.org/keywords/basel-problem","display_name":"Basel problem","score":0.9160000085830688},{"id":"https://openalex.org/keywords/eisenstein-series","display_name":"Eisenstein series","score":0.8849999904632568},{"id":"https://openalex.org/keywords/hexagonal-lattice","display_name":"hexagonal lattice","score":0.8809999823570251},{"id":"https://openalex.org/keywords/close-packing","display_name":"close packing","score":0.5590000152587891},{"id":"https://openalex.org/keywords/logarithmic-spiral","display_name":"logarithmic spiral","score":0.7789999842643738},{"id":"https://openalex.org/keywords/regular-tilings","display_name":"regular tilings","score":0.6959999799728394},{"id":"https://openalex.org/keywords/e8-lattice","display_name":"E8 lattice","score":0.5049999952316284}],"concepts":[{"id":"https://openalex.org/C137610916","wikidata":"https://www.wikidata.org/wiki/Q1096862","display_name":"Gumbel distribution","level":3,"score":0.972100019454956},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7734000086784363},{"id":"https://openalex.org/C147581598","wikidata":"https://www.wikidata.org/wiki/Q729429","display_name":"Extreme value theory","level":2,"score":0.7168999910354614},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.5511999726295471},{"id":"https://openalex.org/C39927690","wikidata":"https://www.wikidata.org/wiki/Q11197","display_name":"Logarithm","level":2,"score":0.5311999917030334},{"id":"https://openalex.org/C173291955","wikidata":"https://www.wikidata.org/wiki/Q732332","display_name":"Weibull distribution","level":2,"score":0.5293999910354614},{"id":"https://openalex.org/C91716921","wikidata":"https://www.wikidata.org/wiki/Q1289366","display_name":"Scale parameter","level":2,"score":0.4440000057220459},{"id":"https://openalex.org/C2778755073","wikidata":"https://www.wikidata.org/wiki/Q10858537","display_name":"Scale (ratio)","level":2,"score":0.43140000104904175},{"id":"https://openalex.org/C95611797","wikidata":"https://www.wikidata.org/wiki/Q17502105","display_name":"Infimum and supremum","level":2,"score":0.42669999599456787},{"id":"https://openalex.org/C91528185","wikidata":"https://www.wikidata.org/wiki/Q520952","display_name":"Maxima","level":3,"score":0.4122999906539917},{"id":"https://openalex.org/C196083921","wikidata":"https://www.wikidata.org/wiki/Q7915758","display_name":"Variance (accounting)","level":2,"score":0.35679998993873596},{"id":"https://openalex.org/C61797465","wikidata":"https://www.wikidata.org/wiki/Q1188986","display_name":"Term (time)","level":2,"score":0.3433000147342682},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.3246999979019165},{"id":"https://openalex.org/C143724316","wikidata":"https://www.wikidata.org/wiki/Q312468","display_name":"Series (stratigraphy)","level":2,"score":0.319599986076355},{"id":"https://openalex.org/C2777027219","wikidata":"https://www.wikidata.org/wiki/Q1284190","display_name":"Constant (computer programming)","level":2,"score":0.3131999969482422},{"id":"https://openalex.org/C169707849","wikidata":"https://www.wikidata.org/wiki/Q1617240","display_name":"Generalized extreme value distribution","level":3,"score":0.3102000057697296},{"id":"https://openalex.org/C199435849","wikidata":"https://www.wikidata.org/wiki/Q3179293","display_name":"Shape parameter","level":2,"score":0.3093999922275543},{"id":"https://openalex.org/C2776291640","wikidata":"https://www.wikidata.org/wiki/Q2912517","display_name":"Value (mathematics)","level":2,"score":0.3082999885082245},{"id":"https://openalex.org/C39847760","wikidata":"https://www.wikidata.org/wiki/Q1385465","display_name":"Extreme point","level":2,"score":0.29649999737739563},{"id":"https://openalex.org/C55350006","wikidata":"https://www.wikidata.org/wiki/Q237193","display_name":"Exponential distribution","level":2,"score":0.2962000072002411},{"id":"https://openalex.org/C139676723","wikidata":"https://www.wikidata.org/wiki/Q1193832","display_name":"Sign (mathematics)","level":2,"score":0.29319998621940613},{"id":"https://openalex.org/C139912040","wikidata":"https://www.wikidata.org/wiki/Q937378","display_name":"Logarithmic scale","level":2,"score":0.29010000824928284},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.289000004529953},{"id":"https://openalex.org/C203858083","wikidata":"https://www.wikidata.org/wiki/Q188347","display_name":"Harmonic mean","level":2,"score":0.2800999879837036},{"id":"https://openalex.org/C113658590","wikidata":"https://www.wikidata.org/wiki/Q3571727","display_name":"Muck","level":2,"score":0.2685000002384186},{"id":"https://openalex.org/C149782125","wikidata":"https://www.wikidata.org/wiki/Q160039","display_name":"Econometrics","level":1,"score":0.2667999863624573},{"id":"https://openalex.org/C122123141","wikidata":"https://www.wikidata.org/wiki/Q176623","display_name":"Random variable","level":2,"score":0.2646999955177307},{"id":"https://openalex.org/C2777317252","wikidata":"https://www.wikidata.org/wiki/Q18393516","display_name":"Rare events","level":2,"score":0.26109999418258667},{"id":"https://openalex.org/C121864883","wikidata":"https://www.wikidata.org/wiki/Q677916","display_name":"Statistical physics","level":1,"score":0.25929999351501465},{"id":"https://openalex.org/C17825722","wikidata":"https://www.wikidata.org/wiki/Q17285","display_name":"Plane (geometry)","level":2,"score":0.2565999925136566},{"id":"https://openalex.org/C2779886137","wikidata":"https://www.wikidata.org/wiki/Q21030012","display_name":"Symmetry (geometry)","level":2,"score":0.25600001215934753},{"id":"https://openalex.org/C188198153","wikidata":"https://www.wikidata.org/wiki/Q1613840","display_name":"Limiting","level":2,"score":0.25060001015663147}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.5281/zenodo.22090849","doi":"https://doi.org/10.5281/zenodo.22090849","is_oa":true,"landing_page_url":"https://doi.org/10.5281/zenodo.22090849","pdf_url":null,"source":{"id":"https://openalex.org/S4306400562","display_name":"Zenodo (CERN European Organization for Nuclear Research)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I67311998","host_organization_name":"European Organization for Nuclear Research","host_organization_lineage":["https://openalex.org/I67311998"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":null,"is_accepted":false,"is_published":null,"raw_source_name":null,"raw_type":"Preprint"},{"id":"doi:10.5281/zenodo.22090850","doi":"https://doi.org/10.5281/zenodo.22090850","is_oa":true,"landing_page_url":"https://doi.org/10.5281/zenodo.22090850","pdf_url":null,"source":{"id":"https://openalex.org/S4306400562","display_name":"Zenodo (CERN European Organization for Nuclear Research)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I67311998","host_organization_name":"European Organization for Nuclear Research","host_organization_lineage":["https://openalex.org/I67311998"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":null,"is_accepted":false,"is_published":null,"raw_source_name":null,"raw_type":"Preprint"}],"best_oa_location":{"id":"doi:10.5281/zenodo.22090849","doi":"https://doi.org/10.5281/zenodo.22090849","is_oa":true,"landing_page_url":"https://doi.org/10.5281/zenodo.22090849","pdf_url":null,"source":{"id":"https://openalex.org/S4306400562","display_name":"Zenodo (CERN European Organization for Nuclear Research)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I67311998","host_organization_name":"European Organization for Nuclear Research","host_organization_lineage":["https://openalex.org/I67311998"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Preprint"},"sustainable_development_goals":[],"sustainable_development_goals_aurora":[{"score":0.40336355566978455,"display_name":"Decent work and economic growth","id":"https://metadata.un.org/sdg/8"}],"study_designs":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":0,"referenced_works":[],"related_works":[],"abstract_inverted_index":{"FINDING:":[0],"Extreme":[1],"Value":[2],"Theory":[3],"(EVT)":[4],"formalizes":[5],"the":[6,12,18,52,55,81,85,91,94,98,108,119,123,131,136,142,160],"statistics":[7],"of":[8,54,135,159],"rare":[9],"events":[10],"via":[11,90,141],"Gumbel":[13,33,120],"distribution":[14],"(Type":[15],"I),":[16],"with":[17],"shape":[19,143],"parameter":[20,41],"\u03be=0":[21],"distinguishing":[22],"it":[23],"from":[24],"Fr\u00e9chet":[25],"(\u03be>0)":[26],"and":[27,84,104],"Weibull":[28],"(\u03be<0)":[29],"families.":[30],"|":[31,69],"MATH:":[32],"CDF:":[34],"\\(":[35,58,66,74],"F(x)":[36],"=":[37,60,76],"\\exp(-\\exp(-(x-\\mu)/\\sigma))":[38],"\\);":[39,64],"scale":[40],"\u03c3;":[42],"location":[43],"\u03bc;":[44],"Euler\u2013Mascheroni":[45,95],"constant":[46],"\u03b3":[47,96],"\u2248":[48],"0.57721":[49],"appears":[50],"as":[51],"mean":[53],"standard":[56],"Gumbel:":[57],"E[X]":[59],"\\mu":[61],"+":[62],"\\gamma\\sigma":[63],"variance":[65,72],"\\sigma^2\\pi^2/6":[67],"\\).":[68],"CONNECTION:":[70],"The":[71],"term":[73],"\\pi^2/6":[75],"\\zeta(2)":[77],"\\)":[78],"links":[79],"to":[80,107,130],"Basel":[82],"problem":[83],"hexagonal":[86],"lattice":[87],"(2D":[88],"close-packing)":[89],"Eisenstein":[92],"series;":[93],"is":[97],"limiting":[99],"difference":[100],"between":[101],"harmonic":[102],"series":[103],"log(n),":[105],"tying":[106],"logarithmic":[109],"spiral's":[110],"growth":[111],"rate.":[112],"No":[113],"direct":[114],"0.382/0.618/0.786/1.618/2.618":[115],"ratios":[116],"appear":[117],"in":[118],"itself,":[121],"but":[122],"extreme":[124],"value":[125],"theorem's":[126],"three":[127,132],"types":[128],"map":[129],"regular":[133],"tilings":[134],"plane":[137],"(triangular,":[138],"square,":[139],"hexagonal)":[140],"parameter's":[144],"sign":[145],"\u2014":[146],"a":[147],"crystallographic":[148],"symmetry":[149],"an":[150],"Author:":[151],"Andrew":[152],"Stewart":[153],"Caldin,":[154],"Independent":[155],"Researcher,":[156],"UK.":[157],"Part":[158],"E8":[161],"Intelligence":[162],"Research":[163],"series.":[164],"Platform:":[165],"e8intelligence.com":[166]},"counts_by_year":[],"updated_date":"2026-10-07T09:51:55.459714","created_date":"2026-08-26T00:00:00"}
