{"id":"https://openalex.org/W4360846767","doi":"https://doi.org/10.3390/sym15040794","title":"Confidence Interval Estimation for the Ratio of the Percentiles of Two Delta-Lognormal Distributions with Application to Rainfall Data","display_name":"Confidence Interval Estimation for the Ratio of the Percentiles of Two Delta-Lognormal Distributions with Application to Rainfall Data","publication_year":2023,"publication_date":"2023-03-24","ids":{"openalex":"https://openalex.org/W4360846767","doi":"https://doi.org/10.3390/sym15040794"},"language":"en","primary_location":{"id":"doi:10.3390/sym15040794","is_oa":true,"landing_page_url":"https://doi.org/10.3390/sym15040794","pdf_url":"https://www.mdpi.com/2073-8994/15/4/794/pdf?version=1679654850","source":{"id":"https://openalex.org/S190787756","display_name":"Symmetry","issn_l":"2073-8994","issn":["2073-8994"],"is_oa":true,"is_in_doaj":false,"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":"Symmetry","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://www.mdpi.com/2073-8994/15/4/794/pdf?version=1679654850","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5047790709","display_name":"Warisa Thangjai","orcid":"https://orcid.org/0000-0002-9306-3742"},"institutions":[{"id":"https://openalex.org/I58196637","display_name":"Ramkhamhaeng University","ror":"https://ror.org/00mrw8k38","country_code":"TH","type":"education","lineage":["https://openalex.org/I58196637"]}],"countries":["TH"],"is_corresponding":false,"raw_author_name":"Warisa Thangjai","raw_affiliation_strings":["Department of Statistics, Faculty of Science, Ramkhamhaeng University, Bangkok 10240, Thailand"],"raw_orcid":"https://orcid.org/0000-0002-9306-3742","affiliations":[{"raw_affiliation_string":"Department of Statistics, Faculty of Science, Ramkhamhaeng University, Bangkok 10240, Thailand","institution_ids":["https://openalex.org/I58196637"]}]},{"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":false,"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":"middle","author":{"id":null,"display_name":"Sa-Aat 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":"middle","author":{"id":"https://openalex.org/A5013080807","display_name":"Suparat Niwitpong","orcid":"https://orcid.org/0000-0003-3059-1131"},"institutions":[{"id":"https://openalex.org/I4210118263","display_name":"Rajamangala University of Technology Phra Nakhon","ror":"https://ror.org/02mg36m74","country_code":"TH","type":"education","lineage":["https://openalex.org/I10245363","https://openalex.org/I4210118263"]},{"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":"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 Mathematics and Statistics, Faculty of Science and Technology, Rajamangala University of Technology Phra Nakhon, 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 Mathematics and Statistics, Faculty of Science and Technology, Rajamangala University of Technology Phra Nakhon, Bangkok 10800, Thailand","institution_ids":["https://openalex.org/I4210118263"]}]},{"author_position":"middle","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"],"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"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5013672337","display_name":"Narudee Smithpreecha","orcid":null},"institutions":[{"id":"https://openalex.org/I4210118263","display_name":"Rajamangala University of Technology Phra Nakhon","ror":"https://ror.org/02mg36m74","country_code":"TH","type":"education","lineage":["https://openalex.org/I10245363","https://openalex.org/I4210118263"]}],"countries":["TH"],"is_corresponding":false,"raw_author_name":"Narudee Smithpreecha","raw_affiliation_strings":["Department of Mathematics and Statistics, Faculty of Science and Technology, Rajamangala University of Technology Phra Nakhon, Bangkok 10800, Thailand"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics and Statistics, Faculty of Science and Technology, Rajamangala University of Technology Phra Nakhon, Bangkok 10800, Thailand","institution_ids":["https://openalex.org/I4210118263"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5013080807"],"corresponding_institution_ids":["https://openalex.org/I4210118263","https://openalex.org/I82828225"],"apc_list":{"value":2000,"currency":"CHF","value_usd":2227},"apc_paid":{"value":2000,"currency":"CHF","value_usd":2227},"fwci":1.0492,"has_fulltext":false,"cited_by_count":9,"citation_normalized_percentile":{"value":0.72442985,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":94,"max":97},"biblio":{"volume":"15","issue":"4","first_page":"794","last_page":"794"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11186","display_name":"Hydrology and Drought Analysis","score":0.991100013256073,"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"}},"topics":[{"id":"https://openalex.org/T11186","display_name":"Hydrology and Drought Analysis","score":0.991100013256073,"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/T10968","display_name":"Statistical Distribution Estimation and Applications","score":0.9884999990463257,"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/T10243","display_name":"Statistical Methods and Bayesian Inference","score":0.9693999886512756,"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/mathematics","display_name":"Mathematics","score":0.6976956129074097},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.6887479424476624},{"id":"https://openalex.org/keywords/log-normal-distribution","display_name":"Log-normal distribution","score":0.6718630194664001},{"id":"https://openalex.org/keywords/percentile","display_name":"Percentile","score":0.663554847240448},{"id":"https://openalex.org/keywords/confidence-interval","display_name":"Confidence interval","score":0.5391350984573364},{"id":"https://openalex.org/keywords/distribution-fitting","display_name":"Distribution fitting","score":0.4651328921318054},{"id":"https://openalex.org/keywords/coverage-probability","display_name":"Coverage probability","score":0.4255434572696686},{"id":"https://openalex.org/keywords/probability-distribution","display_name":"Probability distribution","score":0.3537728190422058}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6976956129074097},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.6887479424476624},{"id":"https://openalex.org/C151620405","wikidata":"https://www.wikidata.org/wiki/Q826116","display_name":"Log-normal distribution","level":2,"score":0.6718630194664001},{"id":"https://openalex.org/C122048520","wikidata":"https://www.wikidata.org/wiki/Q2913954","display_name":"Percentile","level":2,"score":0.663554847240448},{"id":"https://openalex.org/C44249647","wikidata":"https://www.wikidata.org/wiki/Q208498","display_name":"Confidence interval","level":2,"score":0.5391350984573364},{"id":"https://openalex.org/C160947583","wikidata":"https://www.wikidata.org/wiki/Q2083147","display_name":"Distribution fitting","level":3,"score":0.4651328921318054},{"id":"https://openalex.org/C2776292839","wikidata":"https://www.wikidata.org/wiki/Q5179217","display_name":"Coverage probability","level":3,"score":0.4255434572696686},{"id":"https://openalex.org/C149441793","wikidata":"https://www.wikidata.org/wiki/Q200726","display_name":"Probability distribution","level":2,"score":0.3537728190422058}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.3390/sym15040794","is_oa":true,"landing_page_url":"https://doi.org/10.3390/sym15040794","pdf_url":"https://www.mdpi.com/2073-8994/15/4/794/pdf?version=1679654850","source":{"id":"https://openalex.org/S190787756","display_name":"Symmetry","issn_l":"2073-8994","issn":["2073-8994"],"is_oa":true,"is_in_doaj":false,"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":"Symmetry","raw_type":"journal-article"},{"id":"pmh:oai:doaj.org/article:5358b8bd241b439f8893ce4da8887257","is_oa":false,"landing_page_url":"https://doaj.org/article/5358b8bd241b439f8893ce4da8887257","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":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Symmetry, Vol 15, Iss 4, p 794 (2023)","raw_type":"article"},{"id":"pmh:oai:mdpi.com:/2073-8994/15/4/794/","is_oa":true,"landing_page_url":"https://dx.doi.org/10.3390/sym15040794","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":"Symmetry","raw_type":"Text"}],"best_oa_location":{"id":"doi:10.3390/sym15040794","is_oa":true,"landing_page_url":"https://doi.org/10.3390/sym15040794","pdf_url":"https://www.mdpi.com/2073-8994/15/4/794/pdf?version=1679654850","source":{"id":"https://openalex.org/S190787756","display_name":"Symmetry","issn_l":"2073-8994","issn":["2073-8994"],"is_oa":true,"is_in_doaj":false,"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":"Symmetry","raw_type":"journal-article"},"sustainable_development_goals":[{"score":0.47999998927116394,"display_name":"Life in Land","id":"https://metadata.un.org/sdg/15"}],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W4360846767.pdf"},"referenced_works_count":7,"referenced_works":["https://openalex.org/W2030021611","https://openalex.org/W2052561761","https://openalex.org/W2075934519","https://openalex.org/W2155916505","https://openalex.org/W2567369906","https://openalex.org/W2792718348","https://openalex.org/W4311717163"],"related_works":["https://openalex.org/W2116341137","https://openalex.org/W2394033032","https://openalex.org/W2391465306","https://openalex.org/W2113227311","https://openalex.org/W2106645586","https://openalex.org/W2059487999","https://openalex.org/W4312779177","https://openalex.org/W2340789781","https://openalex.org/W2001724610","https://openalex.org/W1982479288"],"abstract_inverted_index":{"The":[0,53,224,251],"log-normal":[1,39],"distribution":[2,4,40,83,117],"(skewed":[3],"or":[5,124],"asymmetry":[6],"distribution)":[7],"is":[8,19,84,241,256],"used":[9,257],"to":[10,37,87,110,120,232,238,244,258],"describe":[11],"random":[12],"variables":[13],"comprising":[14],"positive":[15,222],"real":[16,249],"values.":[17,223],"It":[18],"well":[20,197],"known":[21],"that":[22],"the":[23,38,45,67,81,90,93,97,100,113,121,132,136,139,155,159,164,168,179,185,189,192,205,212,233,254],"logarithm":[24],"values":[25],"of":[26,47,55,69,92,103,112,138,141,184,211,253],"these":[27],"are":[28,41,145],"normally":[29],"distributed":[30,77],"(symmetry":[31],"distribution).":[32],"Positively":[33],"right-skewed":[34],"data":[35,70,106,217,227,240],"applicable":[36],"frequently":[42],"observed":[43],"in":[44,66,115,182,209],"fields":[46],"environmental":[48],"studies,":[49],"biology,":[50],"and":[51,158,167,188,221],"medicine.":[52],"number":[54],"zero":[56,72,220],"observations":[57,73,122],"follows":[58],"a":[59,104,116],"binomial":[60],"distribution.":[61,235],"However,":[62],"problems":[63],"can":[64,228],"arise":[65],"analysis":[68,91],"containing":[71],"along":[74,203],"with":[75,118,204,248],"log-normally":[76],"data,":[78],"for":[79,88,131,135],"which":[80],"delta-lognormal":[82,143,234],"often":[85],"referred":[86],"using":[89,147,178],"data.":[94,250],"In":[95,127],"statistics,":[96],"percentile":[98],"provides":[99],"relative":[101],"standing":[102],"numerical":[105],"point":[107],"when":[108],"compared":[109],"all":[111,210],"others":[114],"reference":[119],"at":[123],"below":[125],"it.":[126],"this":[128],"study,":[129],"estimates":[130],"confidence":[133,150],"interval":[134,151],"ratio":[137],"percentiles":[140],"two":[142,260],"distributions":[144],"constructed":[146],"fiducial":[148,156,162],"generalized":[149,161],"approaches":[152],"based":[153],"on":[154],"quantity":[157],"optimal":[160],"quantity,":[163],"Bayesian":[165,193],"approach,":[166],"parametric":[169],"bootstrap":[170],"method.":[171],"As":[172],"assessed":[173],"by":[174,198],"Monte":[175],"Carlo":[176],"simulations":[177],"RStudio":[180],"programming":[181],"terms":[183],"coverage":[186,201],"probability":[187],"average":[190,207],"length,":[191],"approach":[194,255],"performed":[195],"quite":[196],"providing":[199],"adequate":[200],"probabilities":[202],"shortest":[206],"lengths":[208],"scenarios":[213],"tested.":[214],"Daily":[215],"rainfall":[216,226,239,261],"contain":[218],"both":[219],"daily":[225],"usually":[229],"be":[230],"fitted":[231],"Their":[236],"application":[237],"also":[242],"provided":[243],"illustrate":[245],"their":[246],"efficacies":[247],"efficacy":[252],"compare":[259],"dispersion":[262],"populations.":[263]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":2},{"year":2024,"cited_by_count":3},{"year":2023,"cited_by_count":3}],"updated_date":"2026-08-16T07:02:28.622633","created_date":"2025-10-10T00:00:00"}