{"id":"https://openalex.org/W4361282917","doi":"https://doi.org/10.1155/2023/8767200","title":"E-Bayesian Estimation of Hierarchical Poisson-Gamma Model on the Basis of Restricted and Unrestricted Parameter Spaces","display_name":"E-Bayesian Estimation of Hierarchical Poisson-Gamma Model on the Basis of Restricted and Unrestricted Parameter Spaces","publication_year":2023,"publication_date":"2023-03-29","ids":{"openalex":"https://openalex.org/W4361282917","doi":"https://doi.org/10.1155/2023/8767200"},"language":"en","primary_location":{"id":"doi:10.1155/2023/8767200","is_oa":true,"landing_page_url":"https://doi.org/10.1155/2023/8767200","pdf_url":"https://downloads.hindawi.com/journals/complexity/2023/8767200.pdf","source":{"id":"https://openalex.org/S207319443","display_name":"Complexity","issn_l":"1076-2787","issn":["1076-2787","1099-0526"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310319869","host_organization_name":"Hindawi Publishing Corporation","host_organization_lineage":["https://openalex.org/P4310319869"],"host_organization_lineage_names":["Hindawi Publishing Corporation"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Complexity","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://downloads.hindawi.com/journals/complexity/2023/8767200.pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5080298650","display_name":"Azeem Iqbal","orcid":"https://orcid.org/0000-0003-2329-1675"},"institutions":[{"id":"https://openalex.org/I12469534","display_name":"Quaid-i-Azam University","ror":"https://ror.org/04s9hft57","country_code":"PK","type":"education","lineage":["https://openalex.org/I12469534"]}],"countries":["PK"],"is_corresponding":true,"raw_author_name":"Azeem Iqbal","raw_affiliation_strings":["Department of Statistics, Quaid-i-Azam University, Islamabad 45320, Pakistan","Higher Education Department, Govt of the Punjab, Lahore 54000, Pakistan"],"raw_orcid":"https://orcid.org/0000-0003-2329-1675","affiliations":[{"raw_affiliation_string":"Department of Statistics, Quaid-i-Azam University, Islamabad 45320, Pakistan","institution_ids":["https://openalex.org/I12469534"]},{"raw_affiliation_string":"Higher Education Department, Govt of the Punjab, Lahore 54000, Pakistan","institution_ids":[]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5042893321","display_name":"Laila A. Al\u2010Essa","orcid":null},"institutions":[{"id":"https://openalex.org/I106778892","display_name":"Princess Nourah bint Abdulrahman University","ror":"https://ror.org/05b0cyh02","country_code":"SA","type":"education","lineage":["https://openalex.org/I106778892"]}],"countries":["SA"],"is_corresponding":false,"raw_author_name":"Laila A. Al-Essa","raw_affiliation_strings":["Department of Mathematical Sciences, College of Science, Princess Nourah bint Abdulrahman University, P.O. Box 84428, Riyadh 11671, Saudi Arabia"],"raw_orcid":"https://orcid.org/0000-0003-2788-8946","affiliations":[{"raw_affiliation_string":"Department of Mathematical Sciences, College of Science, Princess Nourah bint Abdulrahman University, P.O. Box 84428, Riyadh 11671, Saudi Arabia","institution_ids":["https://openalex.org/I106778892"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5057930156","display_name":"Muhammad Yousaf Shad","orcid":"https://orcid.org/0000-0002-3541-6220"},"institutions":[{"id":"https://openalex.org/I12469534","display_name":"Quaid-i-Azam University","ror":"https://ror.org/04s9hft57","country_code":"PK","type":"education","lineage":["https://openalex.org/I12469534"]},{"id":"https://openalex.org/I2802902501","display_name":"Namal University","ror":"https://ror.org/00zcxra43","country_code":"PK","type":"education","lineage":["https://openalex.org/I2802902501"]}],"countries":["PK"],"is_corresponding":false,"raw_author_name":"Muhammad Yousaf Shad","raw_affiliation_strings":["Department of Mathematics, Namal University, Talagang Road, Mianwali 42250, Pakistan","Department of Statistics, Quaid-i-Azam University, Islamabad 45320, Pakistan"],"raw_orcid":"https://orcid.org/0000-0002-3541-6220","affiliations":[{"raw_affiliation_string":"Department of Mathematics, Namal University, Talagang Road, Mianwali 42250, Pakistan","institution_ids":["https://openalex.org/I2802902501"]},{"raw_affiliation_string":"Department of Statistics, Quaid-i-Azam University, Islamabad 45320, Pakistan","institution_ids":["https://openalex.org/I12469534"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5009704579","display_name":"Fuad S. Alduais","orcid":"https://orcid.org/0000-0002-2255-1167"},"institutions":[{"id":"https://openalex.org/I142608572","display_name":"Prince Sattam Bin Abdulaziz University","ror":"https://ror.org/04jt46d36","country_code":"SA","type":"education","lineage":["https://openalex.org/I142608572"]}],"countries":["SA"],"is_corresponding":false,"raw_author_name":"Fuad S. Alduais","raw_affiliation_strings":["Department of Mathematics, College of Science and Humanities in Al-Aflaj, Prince Sattam Bin Abdulaziz University, Al-Kharj 11912, Saudi Arabia"],"raw_orcid":"https://orcid.org/0000-0002-2255-1167","affiliations":[{"raw_affiliation_string":"Department of Mathematics, College of Science and Humanities in Al-Aflaj, Prince Sattam Bin Abdulaziz University, Al-Kharj 11912, Saudi Arabia","institution_ids":["https://openalex.org/I142608572"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5004639274","display_name":"Mansour F. Yassen","orcid":"https://orcid.org/0000-0002-3952-4341"},"institutions":[{"id":"https://openalex.org/I126427551","display_name":"Damietta University","ror":"https://ror.org/035h3r191","country_code":"EG","type":"education","lineage":["https://openalex.org/I126427551"]},{"id":"https://openalex.org/I142608572","display_name":"Prince Sattam Bin Abdulaziz University","ror":"https://ror.org/04jt46d36","country_code":"SA","type":"education","lineage":["https://openalex.org/I142608572"]}],"countries":["EG","SA"],"is_corresponding":false,"raw_author_name":"Mansour F. Yassen","raw_affiliation_strings":["Department of Mathematics, College of Science and Humanities in Al-Aflaj, Prince Sattam Bin Abdulaziz University, Al-Kharj 11912, Saudi Arabia","Department of Mathematics, Faculty of Science, Damietta University, New Damietta 34517, Damietta, Egypt"],"raw_orcid":"https://orcid.org/0000-0002-3952-4341","affiliations":[{"raw_affiliation_string":"Department of Mathematics, College of Science and Humanities in Al-Aflaj, Prince Sattam Bin Abdulaziz University, Al-Kharj 11912, Saudi Arabia","institution_ids":["https://openalex.org/I142608572"]},{"raw_affiliation_string":"Department of Mathematics, Faculty of Science, Damietta University, New Damietta 34517, Damietta, Egypt","institution_ids":["https://openalex.org/I126427551"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5101807101","display_name":"Ahmad Raza","orcid":"https://orcid.org/0000-0002-5944-5544"},"institutions":[{"id":"https://openalex.org/I40597779","display_name":"Federal Urdu University","ror":"https://ror.org/02b52th27","country_code":"PK","type":"education","lineage":["https://openalex.org/I40597779"]}],"countries":["PK"],"is_corresponding":false,"raw_author_name":"Muhammad Ahmad Raza","raw_affiliation_strings":["Federal Urdu University of Arts Science and Technology, Islamabad, Pakistan"],"raw_orcid":"https://orcid.org/0000-0002-5944-5544","affiliations":[{"raw_affiliation_string":"Federal Urdu University of Arts Science and Technology, Islamabad, Pakistan","institution_ids":["https://openalex.org/I40597779"]}]}],"institutions":[],"countries_distinct_count":3,"institutions_distinct_count":6,"corresponding_author_ids":["https://openalex.org/A5080298650"],"corresponding_institution_ids":["https://openalex.org/I12469534"],"apc_list":{"value":2300,"currency":"USD","value_usd":2300},"apc_paid":{"value":2300,"currency":"USD","value_usd":2300},"fwci":0.0,"has_fulltext":true,"cited_by_count":0,"citation_normalized_percentile":{"value":0.03439167,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"2023","issue":null,"first_page":"1","last_page":"19"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10243","display_name":"Statistical Methods and Bayesian Inference","score":0.9987000226974487,"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/T10243","display_name":"Statistical Methods and Bayesian Inference","score":0.9987000226974487,"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":0.9954000115394592,"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/T12011","display_name":"Insurance, Mortality, Demography, Risk Management","score":0.9901999831199646,"subfield":{"id":"https://openalex.org/subfields/3317","display_name":"Demography"},"field":{"id":"https://openalex.org/fields/33","display_name":"Social Sciences"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/estimator","display_name":"Estimator","score":0.7809790968894958},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7325716614723206},{"id":"https://openalex.org/keywords/poisson-distribution","display_name":"Poisson distribution","score":0.7246341705322266},{"id":"https://openalex.org/keywords/gamma-distribution","display_name":"Gamma distribution","score":0.6573551893234253},{"id":"https://openalex.org/keywords/conjugate-prior","display_name":"Conjugate prior","score":0.630168080329895},{"id":"https://openalex.org/keywords/bayesian-probability","display_name":"Bayesian probability","score":0.5826644897460938},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.5578829050064087},{"id":"https://openalex.org/keywords/hierarchical-database-model","display_name":"Hierarchical database model","score":0.5419794321060181},{"id":"https://openalex.org/keywords/bayes-estimator","display_name":"Bayes estimator","score":0.538901686668396},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.5293163657188416},{"id":"https://openalex.org/keywords/bayesian-hierarchical-modeling","display_name":"Bayesian hierarchical modeling","score":0.5085078477859497},{"id":"https://openalex.org/keywords/mean-squared-error","display_name":"Mean squared error","score":0.4995417594909668},{"id":"https://openalex.org/keywords/basis","display_name":"Basis (linear algebra)","score":0.4987668991088867},{"id":"https://openalex.org/keywords/parameter-space","display_name":"Parameter space","score":0.48009875416755676},{"id":"https://openalex.org/keywords/inverse-gamma-distribution","display_name":"Inverse-gamma distribution","score":0.4204009175300598},{"id":"https://openalex.org/keywords/prior-probability","display_name":"Prior probability","score":0.4028164744377136},{"id":"https://openalex.org/keywords/bayesian-inference","display_name":"Bayesian inference","score":0.2890668511390686},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.1945478320121765},{"id":"https://openalex.org/keywords/asymptotic-distribution","display_name":"Asymptotic distribution","score":0.11058580875396729}],"concepts":[{"id":"https://openalex.org/C185429906","wikidata":"https://www.wikidata.org/wiki/Q1130160","display_name":"Estimator","level":2,"score":0.7809790968894958},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7325716614723206},{"id":"https://openalex.org/C100906024","wikidata":"https://www.wikidata.org/wiki/Q205692","display_name":"Poisson distribution","level":2,"score":0.7246341705322266},{"id":"https://openalex.org/C149717495","wikidata":"https://www.wikidata.org/wiki/Q117806","display_name":"Gamma distribution","level":2,"score":0.6573551893234253},{"id":"https://openalex.org/C26004113","wikidata":"https://www.wikidata.org/wiki/Q3711784","display_name":"Conjugate prior","level":4,"score":0.630168080329895},{"id":"https://openalex.org/C107673813","wikidata":"https://www.wikidata.org/wiki/Q812534","display_name":"Bayesian probability","level":2,"score":0.5826644897460938},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.5578829050064087},{"id":"https://openalex.org/C144986985","wikidata":"https://www.wikidata.org/wiki/Q871236","display_name":"Hierarchical database model","level":2,"score":0.5419794321060181},{"id":"https://openalex.org/C68022304","wikidata":"https://www.wikidata.org/wiki/Q842217","display_name":"Bayes estimator","level":3,"score":0.538901686668396},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.5293163657188416},{"id":"https://openalex.org/C191413810","wikidata":"https://www.wikidata.org/wiki/Q17100952","display_name":"Bayesian hierarchical modeling","level":4,"score":0.5085078477859497},{"id":"https://openalex.org/C139945424","wikidata":"https://www.wikidata.org/wiki/Q1940696","display_name":"Mean squared error","level":2,"score":0.4995417594909668},{"id":"https://openalex.org/C12426560","wikidata":"https://www.wikidata.org/wiki/Q189569","display_name":"Basis (linear algebra)","level":2,"score":0.4987668991088867},{"id":"https://openalex.org/C73586568","wikidata":"https://www.wikidata.org/wiki/Q2600211","display_name":"Parameter space","level":2,"score":0.48009875416755676},{"id":"https://openalex.org/C4646027","wikidata":"https://www.wikidata.org/wiki/Q3258521","display_name":"Inverse-gamma distribution","level":5,"score":0.4204009175300598},{"id":"https://openalex.org/C177769412","wikidata":"https://www.wikidata.org/wiki/Q278090","display_name":"Prior probability","level":3,"score":0.4028164744377136},{"id":"https://openalex.org/C160234255","wikidata":"https://www.wikidata.org/wiki/Q812535","display_name":"Bayesian inference","level":3,"score":0.2890668511390686},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.1945478320121765},{"id":"https://openalex.org/C65778772","wikidata":"https://www.wikidata.org/wiki/Q12345341","display_name":"Asymptotic distribution","level":3,"score":0.11058580875396729},{"id":"https://openalex.org/C124101348","wikidata":"https://www.wikidata.org/wiki/Q172491","display_name":"Data mining","level":1,"score":0.0},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.0},{"id":"https://openalex.org/C91395904","wikidata":"https://www.wikidata.org/wiki/Q7051756","display_name":"Normal-gamma distribution","level":4,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1155/2023/8767200","is_oa":true,"landing_page_url":"https://doi.org/10.1155/2023/8767200","pdf_url":"https://downloads.hindawi.com/journals/complexity/2023/8767200.pdf","source":{"id":"https://openalex.org/S207319443","display_name":"Complexity","issn_l":"1076-2787","issn":["1076-2787","1099-0526"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310319869","host_organization_name":"Hindawi Publishing Corporation","host_organization_lineage":["https://openalex.org/P4310319869"],"host_organization_lineage_names":["Hindawi Publishing Corporation"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Complexity","raw_type":"journal-article"},{"id":"pmh:oai:RePEc:hin:complx:8767200","is_oa":false,"landing_page_url":"http://downloads.hindawi.com/journals/complexity/2023/8767200.xml","pdf_url":null,"source":{"id":"https://openalex.org/S4306401271","display_name":"RePEc: Research Papers in Economics","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I77793887","host_organization_name":"Federal Reserve Bank of St. Louis","host_organization_lineage":["https://openalex.org/I77793887"],"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":"article"},{"id":"pmh:oai:doaj.org/article:4dbc151a9c4e4cbcba8d55db5d54da4c","is_oa":true,"landing_page_url":"https://doaj.org/article/4dbc151a9c4e4cbcba8d55db5d54da4c","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":"Complexity, Vol 2023 (2023)","raw_type":"article"}],"best_oa_location":{"id":"doi:10.1155/2023/8767200","is_oa":true,"landing_page_url":"https://doi.org/10.1155/2023/8767200","pdf_url":"https://downloads.hindawi.com/journals/complexity/2023/8767200.pdf","source":{"id":"https://openalex.org/S207319443","display_name":"Complexity","issn_l":"1076-2787","issn":["1076-2787","1099-0526"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310319869","host_organization_name":"Hindawi Publishing Corporation","host_organization_lineage":["https://openalex.org/P4310319869"],"host_organization_lineage_names":["Hindawi Publishing Corporation"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Complexity","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G1579623012","display_name":null,"funder_award_id":"PNURSP2023R443","funder_id":"https://openalex.org/F4320311227","funder_display_name":"Prince Sattam bin Abdulaziz University"},{"id":"https://openalex.org/G2246833281","display_name":null,"funder_award_id":"PSAU/2023/R/1444","funder_id":"https://openalex.org/F4320311227","funder_display_name":"Prince Sattam bin Abdulaziz University"},{"id":"https://openalex.org/G3143669702","display_name":null,"funder_award_id":"PNURSP2023R443","funder_id":"https://openalex.org/F4320322484","funder_display_name":"Princess Nourah Bint Abdulrahman University"},{"id":"https://openalex.org/G4293615652","display_name":null,"funder_award_id":"PSAU/2023/R/1444","funder_id":"https://openalex.org/F4320322484","funder_display_name":"Princess Nourah Bint Abdulrahman University"},{"id":"https://openalex.org/G8487744027","display_name":null,"funder_award_id":"PSAU/ 2023/R/1444","funder_id":"https://openalex.org/F4320311227","funder_display_name":"Prince Sattam bin Abdulaziz University"}],"funders":[{"id":"https://openalex.org/F4320311227","display_name":"Prince Sattam bin Abdulaziz University","ror":"https://ror.org/04jt46d36"},{"id":"https://openalex.org/F4320322484","display_name":"Princess Nourah Bint Abdulrahman University","ror":"https://ror.org/05b0cyh02"}],"has_content":{"pdf":true,"grobid_xml":false},"content_urls":{"pdf":"https://content.openalex.org/works/W4361282917.pdf"},"referenced_works_count":24,"referenced_works":["https://openalex.org/W128740895","https://openalex.org/W628329697","https://openalex.org/W1964899747","https://openalex.org/W2027090435","https://openalex.org/W2061974965","https://openalex.org/W2316016756","https://openalex.org/W2484809223","https://openalex.org/W2513296691","https://openalex.org/W2621826118","https://openalex.org/W2766861897","https://openalex.org/W2782855538","https://openalex.org/W2911566046","https://openalex.org/W2963292900","https://openalex.org/W2968170494","https://openalex.org/W2968729735","https://openalex.org/W2991937975","https://openalex.org/W3015595103","https://openalex.org/W3119278052","https://openalex.org/W3158891219","https://openalex.org/W4240458502","https://openalex.org/W4306248581","https://openalex.org/W4319841838","https://openalex.org/W4319878507","https://openalex.org/W4388295403"],"related_works":["https://openalex.org/W2958433599","https://openalex.org/W3201780946","https://openalex.org/W2171321819","https://openalex.org/W2472610123","https://openalex.org/W4302562250","https://openalex.org/W2787783668","https://openalex.org/W2964811814","https://openalex.org/W2033123229","https://openalex.org/W2926633495","https://openalex.org/W4361282917"],"abstract_inverted_index":{"In":[0],"this":[1],"study,":[2],"we":[3],"use":[4],"the":[5,8,18,23,29,37,52,59,63,104,114,124,127,136,148,152],"idea":[6,30],"of":[7,17,31,36,65,106,126,154],"hierarchical":[9,19,32,39,128],"model":[10,21],"(HM)":[11],"to":[12,45,51,102,122,156],"estimate":[13,123],"an":[14],"unknown":[15],"parameter":[16,77,119,125],"Poisson-Gamma":[20,129],"using":[22,79,92],"E-Bayesian":[24],"(E-B)":[25],"theory.":[26],"We":[27,43],"propose":[28],"probability":[33],"function":[34],"instead":[35],"traditional":[38],"prior":[40,55],"density":[41],"function.":[42],"aim":[44],"infer":[46],"E-B":[47,83,107,137],"estimates":[48],"with":[49,58,87],"respect":[50],"conjugate":[53],"Gamma":[54],"distribution":[56],"along":[57],"E-posterior":[60],"risks":[61],"on":[62],"basis":[64],"different":[66],"symmetric":[67],"and":[68,75,144,166],"asymmetric":[69],"loss":[70],"functions":[71],"(LFs)":[72],"under":[73,116],"restricted":[74,118],"unrestricted":[76],"spaces":[78],"uniform":[80],"hyperprior.":[81],"Whereas,":[82],"estimators":[84,90,108,138],"are":[85,100,139],"compared":[86],"maximum":[88],"likelihood":[89],"(MLEs)":[91],"mean":[93],"squared":[94],"error":[95],"(MSE).":[96],"Monte":[97],"Carlo":[98],"simulations":[99],"prosecuted":[101],"study":[103],"efficiency":[105],"empirically.":[109],"It":[110,131],"is":[111,132],"shown":[112],"that":[113,135],"LFs":[115],"a":[117,157],"space":[120],"dominate":[121],"model.":[130],"also":[133],"found":[134],"more":[140],"precise":[141],"than":[142],"MLEs,":[143],"Stein\u2019s":[145],"LF":[146],"has":[147,160],"least":[149],"E-PR.":[150],"Moreover,":[151],"application":[153],"outcomes":[155],"real-life":[158],"example":[159],"been":[161],"made":[162],"for":[163],"analysis,":[164],"comparison,":[165],"motivation.":[167]},"counts_by_year":[],"updated_date":"2026-05-21T06:26:12.895304","created_date":"2025-10-10T00:00:00"}