{"id":"https://openalex.org/W4311374460","doi":"https://doi.org/10.3390/axioms11120689","title":"Confidence Intervals for the Ratio of Variances of Delta-Gamma Distributions with Applications","display_name":"Confidence Intervals for the Ratio of Variances of Delta-Gamma Distributions with Applications","publication_year":2022,"publication_date":"2022-11-30","ids":{"openalex":"https://openalex.org/W4311374460","doi":"https://doi.org/10.3390/axioms11120689"},"language":"en","primary_location":{"id":"doi:10.3390/axioms11120689","is_oa":true,"landing_page_url":"https://doi.org/10.3390/axioms11120689","pdf_url":"https://www.mdpi.com/2075-1680/11/12/689/pdf?version=1671115506","source":{"id":"https://openalex.org/S4210173132","display_name":"Axioms","issn_l":"2075-1680","issn":["2075-1680"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Axioms","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://www.mdpi.com/2075-1680/11/12/689/pdf?version=1671115506","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5042867371","display_name":"Wansiri Khooriphan","orcid":null},"institutions":[{"id":"https://openalex.org/I82828225","display_name":"King Mongkut's University of Technology North Bangkok","ror":"https://ror.org/04fy6jb97","country_code":"TH","type":"education","lineage":["https://openalex.org/I82828225"]}],"countries":["TH"],"is_corresponding":false,"raw_author_name":"Wansiri Khooriphan","raw_affiliation_strings":["Department of Applied Statistics, Faculty of Applied Science, King Mongkut\u2019s University of Technology North Bangkok, Bangkok 10800, Thailand","Department of Applied Statistics, Faculty of Applied Science, King Mongkut's University of Technology North Bangkok, Bangkok 10800, Thailand"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Applied Statistics, Faculty of Applied Science, King Mongkut\u2019s University of Technology North Bangkok, Bangkok 10800, Thailand","institution_ids":["https://openalex.org/I82828225"]},{"raw_affiliation_string":"Department of Applied Statistics, Faculty of Applied Science, King Mongkut's University of Technology North Bangkok, Bangkok 10800, Thailand","institution_ids":["https://openalex.org/I82828225"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5030283463","display_name":"Sa\u2010Aat Niwitpong","orcid":"https://orcid.org/0000-0001-8269-3397"},"institutions":[{"id":"https://openalex.org/I82828225","display_name":"King Mongkut's University of Technology North Bangkok","ror":"https://ror.org/04fy6jb97","country_code":"TH","type":"education","lineage":["https://openalex.org/I82828225"]}],"countries":["TH"],"is_corresponding":true,"raw_author_name":"Sa-Aat Niwitpong","raw_affiliation_strings":["Department of Applied Statistics, Faculty of Applied Science, King Mongkut\u2019s University of Technology North Bangkok, Bangkok 10800, Thailand","Department of Applied Statistics, Faculty of Applied Science, King Mongkut's University of Technology North Bangkok, Bangkok 10800, Thailand"],"raw_orcid":"https://orcid.org/0000-0001-8269-3397","affiliations":[{"raw_affiliation_string":"Department of Applied Statistics, Faculty of Applied Science, King Mongkut\u2019s University of Technology North Bangkok, Bangkok 10800, Thailand","institution_ids":["https://openalex.org/I82828225"]},{"raw_affiliation_string":"Department of Applied Statistics, Faculty of Applied Science, King Mongkut's University of Technology North Bangkok, Bangkok 10800, Thailand","institution_ids":["https://openalex.org/I82828225"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5013080807","display_name":"Suparat Niwitpong","orcid":"https://orcid.org/0000-0003-3059-1131"},"institutions":[{"id":"https://openalex.org/I82828225","display_name":"King Mongkut's University of Technology North Bangkok","ror":"https://ror.org/04fy6jb97","country_code":"TH","type":"education","lineage":["https://openalex.org/I82828225"]}],"countries":["TH"],"is_corresponding":false,"raw_author_name":"Suparat Niwitpong","raw_affiliation_strings":["Department of Applied Statistics, Faculty of Applied Science, King Mongkut\u2019s University of Technology North Bangkok, Bangkok 10800, Thailand","Department of Applied Statistics, Faculty of Applied Science, King Mongkut's University of Technology North Bangkok, Bangkok 10800, Thailand"],"raw_orcid":"https://orcid.org/0000-0003-3059-1131","affiliations":[{"raw_affiliation_string":"Department of Applied Statistics, Faculty of Applied Science, King Mongkut\u2019s University of Technology North Bangkok, Bangkok 10800, Thailand","institution_ids":["https://openalex.org/I82828225"]},{"raw_affiliation_string":"Department of Applied Statistics, Faculty of Applied Science, King Mongkut's University of Technology North Bangkok, Bangkok 10800, Thailand","institution_ids":["https://openalex.org/I82828225"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5030283463"],"corresponding_institution_ids":["https://openalex.org/I82828225"],"apc_list":{"value":1600,"currency":"CHF","value_usd":1782},"apc_paid":{"value":1600,"currency":"CHF","value_usd":1782},"fwci":0.8778,"has_fulltext":false,"cited_by_count":4,"citation_normalized_percentile":{"value":0.74885044,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":96},"biblio":{"volume":"11","issue":"12","first_page":"689","last_page":"689"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10968","display_name":"Statistical Distribution Estimation and Applications","score":0.9973000288009644,"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":0.9973000288009644,"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/T11186","display_name":"Hydrology and Drought Analysis","score":0.9957000017166138,"subfield":{"id":"https://openalex.org/subfields/2306","display_name":"Global and Planetary Change"},"field":{"id":"https://openalex.org/fields/23","display_name":"Environmental Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10243","display_name":"Statistical Methods and Bayesian Inference","score":0.9861999750137329,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/confidence-interval","display_name":"Confidence interval","score":0.7671326994895935},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.7095015048980713},{"id":"https://openalex.org/keywords/gamma-distribution","display_name":"Gamma distribution","score":0.7046831846237183},{"id":"https://openalex.org/keywords/prior-probability","display_name":"Prior probability","score":0.6627860069274902},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6494125127792358},{"id":"https://openalex.org/keywords/credible-interval","display_name":"Credible interval","score":0.5640963315963745},{"id":"https://openalex.org/keywords/bayesian-probability","display_name":"Bayesian probability","score":0.5557451248168945},{"id":"https://openalex.org/keywords/coverage-probability","display_name":"Coverage probability","score":0.5012269020080566},{"id":"https://openalex.org/keywords/inverse-gamma-distribution","display_name":"Inverse-gamma distribution","score":0.48431268334388733},{"id":"https://openalex.org/keywords/dispersion","display_name":"Dispersion (optics)","score":0.4748121500015259},{"id":"https://openalex.org/keywords/log-normal-distribution","display_name":"Log-normal distribution","score":0.4582471251487732},{"id":"https://openalex.org/keywords/beta-distribution","display_name":"Beta distribution","score":0.42510920763015747},{"id":"https://openalex.org/keywords/monte-carlo-method","display_name":"Monte Carlo method","score":0.42273151874542236},{"id":"https://openalex.org/keywords/interval","display_name":"Interval (graph theory)","score":0.41933536529541016},{"id":"https://openalex.org/keywords/probability-distribution","display_name":"Probability distribution","score":0.32880258560180664},{"id":"https://openalex.org/keywords/inverse-chi-squared-distribution","display_name":"Inverse-chi-squared distribution","score":0.16517320275306702},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.13850125670433044},{"id":"https://openalex.org/keywords/distribution-fitting","display_name":"Distribution fitting","score":0.13685902953147888},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.11141669750213623}],"concepts":[{"id":"https://openalex.org/C44249647","wikidata":"https://www.wikidata.org/wiki/Q208498","display_name":"Confidence interval","level":2,"score":0.7671326994895935},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.7095015048980713},{"id":"https://openalex.org/C149717495","wikidata":"https://www.wikidata.org/wiki/Q117806","display_name":"Gamma distribution","level":2,"score":0.7046831846237183},{"id":"https://openalex.org/C177769412","wikidata":"https://www.wikidata.org/wiki/Q278090","display_name":"Prior probability","level":3,"score":0.6627860069274902},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6494125127792358},{"id":"https://openalex.org/C121117317","wikidata":"https://www.wikidata.org/wiki/Q4439221","display_name":"Credible interval","level":3,"score":0.5640963315963745},{"id":"https://openalex.org/C107673813","wikidata":"https://www.wikidata.org/wiki/Q812534","display_name":"Bayesian probability","level":2,"score":0.5557451248168945},{"id":"https://openalex.org/C2776292839","wikidata":"https://www.wikidata.org/wiki/Q5179217","display_name":"Coverage probability","level":3,"score":0.5012269020080566},{"id":"https://openalex.org/C4646027","wikidata":"https://www.wikidata.org/wiki/Q3258521","display_name":"Inverse-gamma distribution","level":5,"score":0.48431268334388733},{"id":"https://openalex.org/C177562468","wikidata":"https://www.wikidata.org/wiki/Q182893","display_name":"Dispersion (optics)","level":2,"score":0.4748121500015259},{"id":"https://openalex.org/C151620405","wikidata":"https://www.wikidata.org/wiki/Q826116","display_name":"Log-normal distribution","level":2,"score":0.4582471251487732},{"id":"https://openalex.org/C21621910","wikidata":"https://www.wikidata.org/wiki/Q756254","display_name":"Beta distribution","level":2,"score":0.42510920763015747},{"id":"https://openalex.org/C19499675","wikidata":"https://www.wikidata.org/wiki/Q232207","display_name":"Monte Carlo method","level":2,"score":0.42273151874542236},{"id":"https://openalex.org/C2778067643","wikidata":"https://www.wikidata.org/wiki/Q166507","display_name":"Interval (graph theory)","level":2,"score":0.41933536529541016},{"id":"https://openalex.org/C149441793","wikidata":"https://www.wikidata.org/wiki/Q200726","display_name":"Probability distribution","level":2,"score":0.32880258560180664},{"id":"https://openalex.org/C57205106","wikidata":"https://www.wikidata.org/wiki/Q3258519","display_name":"Inverse-chi-squared distribution","level":4,"score":0.16517320275306702},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.13850125670433044},{"id":"https://openalex.org/C160947583","wikidata":"https://www.wikidata.org/wiki/Q2083147","display_name":"Distribution fitting","level":3,"score":0.13685902953147888},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.11141669750213623},{"id":"https://openalex.org/C120665830","wikidata":"https://www.wikidata.org/wiki/Q14620","display_name":"Optics","level":1,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.3390/axioms11120689","is_oa":true,"landing_page_url":"https://doi.org/10.3390/axioms11120689","pdf_url":"https://www.mdpi.com/2075-1680/11/12/689/pdf?version=1671115506","source":{"id":"https://openalex.org/S4210173132","display_name":"Axioms","issn_l":"2075-1680","issn":["2075-1680"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Axioms","raw_type":"journal-article"},{"id":"pmh:oai:doaj.org/article:27c2b4c24aa64c47ba79a8735962db6e","is_oa":true,"landing_page_url":"https://doaj.org/article/27c2b4c24aa64c47ba79a8735962db6e","pdf_url":null,"source":{"id":"https://openalex.org/S4306401280","display_name":"DOAJ (DOAJ: Directory of Open Access Journals)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by-sa","license_id":"https://openalex.org/licenses/cc-by-sa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Axioms, Vol 11, Iss 12, p 689 (2022)","raw_type":"article"},{"id":"pmh:oai:mdpi.com:/2075-1680/11/12/689/","is_oa":true,"landing_page_url":"https://dx.doi.org/10.3390/axioms11120689","pdf_url":null,"source":{"id":"https://openalex.org/S4306400947","display_name":"MDPI (MDPI AG)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I4210097602","host_organization_name":"Multidisciplinary Digital Publishing Institute (Switzerland)","host_organization_lineage":["https://openalex.org/I4210097602"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Axioms; Volume 11; Issue 12; Pages: 689","raw_type":"Text"}],"best_oa_location":{"id":"doi:10.3390/axioms11120689","is_oa":true,"landing_page_url":"https://doi.org/10.3390/axioms11120689","pdf_url":"https://www.mdpi.com/2075-1680/11/12/689/pdf?version=1671115506","source":{"id":"https://openalex.org/S4210173132","display_name":"Axioms","issn_l":"2075-1680","issn":["2075-1680"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Axioms","raw_type":"journal-article"},"sustainable_development_goals":[{"display_name":"Climate action","score":0.41999998688697815,"id":"https://metadata.un.org/sdg/13"}],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W4311374460.pdf"},"referenced_works_count":27,"referenced_works":["https://openalex.org/W846737580","https://openalex.org/W1969009767","https://openalex.org/W1978344903","https://openalex.org/W2008319693","https://openalex.org/W2015457120","https://openalex.org/W2081819788","https://openalex.org/W2111799303","https://openalex.org/W2526298724","https://openalex.org/W2527352898","https://openalex.org/W2755639562","https://openalex.org/W2962880433","https://openalex.org/W3006371736","https://openalex.org/W3033395254","https://openalex.org/W3036327336","https://openalex.org/W3122238704","https://openalex.org/W3128415192","https://openalex.org/W3196673788","https://openalex.org/W3204398787","https://openalex.org/W4221078923","https://openalex.org/W4248681815","https://openalex.org/W4280575767","https://openalex.org/W4286433703","https://openalex.org/W4288084970","https://openalex.org/W4296283298","https://openalex.org/W6654437011","https://openalex.org/W6744343454","https://openalex.org/W6778923063"],"related_works":["https://openalex.org/W4229773611","https://openalex.org/W2547792281","https://openalex.org/W41148922","https://openalex.org/W1964921333","https://openalex.org/W2060932764","https://openalex.org/W2980159702","https://openalex.org/W3202358895","https://openalex.org/W2365963962","https://openalex.org/W4296283298","https://openalex.org/W4311374460"],"abstract_inverted_index":{"Since":[0],"rainfall":[1,21,25],"data":[2,130],"often":[3],"contain":[4],"zero":[5],"observations,":[6],"the":[7,10,20,32,36,39,47,56,70,79,103,111,139,142],"ratio":[8,37],"of":[9,12,38,41,78,88,125,141],"variances":[11,40],"delta-gamma":[13,43],"distributions":[14,44],"can":[15],"be":[16],"used":[17,136],"to":[18,137],"compare":[19],"dispersion":[22],"between":[23],"two":[24,42],"datasets.":[26],"To":[27],"this":[28],"end,":[29],"we":[30],"constructed":[31],"confidence":[33,81],"interval":[34,82],"for":[35,117],"by":[45],"using":[46],"fiducial":[48],"quantity":[49],"method,":[50],"Bayesian":[51],"credible":[52],"intervals":[53,67,105],"based":[54,68,106],"on":[55,69,107],"Jeffreys,":[57,71],"uniform,":[58,72],"or":[59,73],"normal-gamma-beta":[60,74,112],"priors,":[61],"and":[62,92,110,122],"highest":[63],"posterior":[64],"density":[65],"(HPD)":[66],"priors.":[75],"The":[76],"performances":[77],"proposed":[80,143],"methods":[83,144],"were":[84],"evaluated":[85],"in":[86],"terms":[87],"their":[89],"coverage":[90],"probabilities":[91],"average":[93],"lengths":[94],"via":[95],"Monte":[96],"Carlo":[97],"simulation.":[98],"Our":[99],"findings":[100],"show":[101],"that":[102],"HPD":[104],"Jeffreys":[108],"prior":[109,113],"are":[114,135],"both":[115],"suitable":[116],"datasets":[118],"with":[119,145],"a":[120],"small":[121],"large":[123],"probability":[124],"containing":[126],"zeros,":[127],"respectively.":[128],"Rainfall":[129],"from":[131],"Phrae":[132],"province,":[133],"Thailand,":[134],"illustrate":[138],"practicability":[140],"real":[146],"data.":[147]},"counts_by_year":[{"year":2024,"cited_by_count":2},{"year":2023,"cited_by_count":1},{"year":2022,"cited_by_count":1}],"updated_date":"2026-07-23T08:03:31.855105","created_date":"2025-10-10T00:00:00"}
