{"id":"https://openalex.org/W4409906274","doi":"https://doi.org/10.3390/axioms14050330","title":"Parameter Estimation of the Lomax Lifetime Distribution Based on Middle-Censored Data: Methodology, Applications, and Comparative Analysis","display_name":"Parameter Estimation of the Lomax Lifetime Distribution Based on Middle-Censored Data: Methodology, Applications, and Comparative Analysis","publication_year":2025,"publication_date":"2025-04-26","ids":{"openalex":"https://openalex.org/W4409906274","doi":"https://doi.org/10.3390/axioms14050330"},"language":"en","primary_location":{"id":"doi:10.3390/axioms14050330","is_oa":true,"landing_page_url":"https://doi.org/10.3390/axioms14050330","pdf_url":"https://www.mdpi.com/2075-1680/14/5/330/pdf?version=1745638317","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/2075-1680/14/5/330/pdf?version=1745638317","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5113833158","display_name":"Peter Ren","orcid":null},"institutions":[{"id":"https://openalex.org/I21193070","display_name":"Beijing Jiaotong University","ror":"https://ror.org/01yj56c84","country_code":"CN","type":"education","lineage":["https://openalex.org/I21193070"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Peiyao Ren","raw_affiliation_strings":["School of Mathematics and Statistics, Beijing Jiaotong University, Beijing 100044, China"],"affiliations":[{"raw_affiliation_string":"School of Mathematics and Statistics, Beijing Jiaotong University, Beijing 100044, China","institution_ids":["https://openalex.org/I21193070"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5053074333","display_name":"Wenhao Gui","orcid":"https://orcid.org/0000-0003-4318-1780"},"institutions":[{"id":"https://openalex.org/I21193070","display_name":"Beijing Jiaotong University","ror":"https://ror.org/01yj56c84","country_code":"CN","type":"education","lineage":["https://openalex.org/I21193070"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Wenhao Gui","raw_affiliation_strings":["School of Mathematics and Statistics, Beijing Jiaotong University, Beijing 100044, China"],"affiliations":[{"raw_affiliation_string":"School of Mathematics and Statistics, Beijing Jiaotong University, Beijing 100044, China","institution_ids":["https://openalex.org/I21193070"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5027369782","display_name":"Liang Shan","orcid":"https://orcid.org/0000-0002-8833-2514"},"institutions":[{"id":"https://openalex.org/I21193070","display_name":"Beijing Jiaotong University","ror":"https://ror.org/01yj56c84","country_code":"CN","type":"education","lineage":["https://openalex.org/I21193070"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Shan Liang","raw_affiliation_strings":["School of Mathematics and Statistics, Beijing Jiaotong University, Beijing 100044, China"],"affiliations":[{"raw_affiliation_string":"School of Mathematics and Statistics, Beijing Jiaotong University, Beijing 100044, China","institution_ids":["https://openalex.org/I21193070"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5053074333"],"corresponding_institution_ids":["https://openalex.org/I21193070"],"apc_list":{"value":1400,"currency":"CHF","value_usd":1515},"apc_paid":{"value":1400,"currency":"CHF","value_usd":1515},"fwci":0.0,"has_fulltext":true,"cited_by_count":0,"citation_normalized_percentile":{"value":0.11082449,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"14","issue":"5","first_page":"330","last_page":"330"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11186","display_name":"Hydrology and Drought Analysis","score":0.9962000250816345,"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":0.9962000250816345,"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":0.9941999912261963,"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":0.9898999929428101,"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/lomax-distribution","display_name":"Lomax distribution","score":0.8326192498207092},{"id":"https://openalex.org/keywords/estimation","display_name":"Estimation","score":0.5741121768951416},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.5668862462043762},{"id":"https://openalex.org/keywords/econometrics","display_name":"Econometrics","score":0.46457821130752563},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.39418524503707886},{"id":"https://openalex.org/keywords/pareto-distribution","display_name":"Pareto distribution","score":0.38228848576545715},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.37735894322395325},{"id":"https://openalex.org/keywords/economics","display_name":"Economics","score":0.18650230765342712}],"concepts":[{"id":"https://openalex.org/C18249693","wikidata":"https://www.wikidata.org/wiki/Q2517984","display_name":"Lomax distribution","level":3,"score":0.8326192498207092},{"id":"https://openalex.org/C96250715","wikidata":"https://www.wikidata.org/wiki/Q965330","display_name":"Estimation","level":2,"score":0.5741121768951416},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.5668862462043762},{"id":"https://openalex.org/C149782125","wikidata":"https://www.wikidata.org/wiki/Q160039","display_name":"Econometrics","level":1,"score":0.46457821130752563},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.39418524503707886},{"id":"https://openalex.org/C190373308","wikidata":"https://www.wikidata.org/wiki/Q837683","display_name":"Pareto distribution","level":2,"score":0.38228848576545715},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.37735894322395325},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.18650230765342712},{"id":"https://openalex.org/C187736073","wikidata":"https://www.wikidata.org/wiki/Q2920921","display_name":"Management","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.3390/axioms14050330","is_oa":true,"landing_page_url":"https://doi.org/10.3390/axioms14050330","pdf_url":"https://www.mdpi.com/2075-1680/14/5/330/pdf?version=1745638317","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:b694464af93b4d4f94864bf62c8f7968","is_oa":true,"landing_page_url":"https://doaj.org/article/b694464af93b4d4f94864bf62c8f7968","pdf_url":null,"source":{"id":"https://openalex.org/S112646816","display_name":"SHILAP Revista de lepidopterolog\u00eda","issn_l":"0300-5267","issn":["0300-5267","2340-4078"],"is_oa":true,"is_in_doaj":true,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Axioms, Vol 14, Iss 5, p 330 (2025)","raw_type":"article"}],"best_oa_location":{"id":"doi:10.3390/axioms14050330","is_oa":true,"landing_page_url":"https://doi.org/10.3390/axioms14050330","pdf_url":"https://www.mdpi.com/2075-1680/14/5/330/pdf?version=1745638317","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":[],"awards":[],"funders":[],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W4409906274.pdf","grobid_xml":"https://content.openalex.org/works/W4409906274.grobid-xml"},"referenced_works_count":28,"referenced_works":["https://openalex.org/W1527691279","https://openalex.org/W1550022419","https://openalex.org/W1963783234","https://openalex.org/W1965040604","https://openalex.org/W2001222925","https://openalex.org/W2021721740","https://openalex.org/W2021829921","https://openalex.org/W2038941270","https://openalex.org/W2044018331","https://openalex.org/W2049633694","https://openalex.org/W2053742104","https://openalex.org/W2055455082","https://openalex.org/W2077995492","https://openalex.org/W2084696120","https://openalex.org/W2165787955","https://openalex.org/W2806944458","https://openalex.org/W2924177802","https://openalex.org/W3001148940","https://openalex.org/W3009839402","https://openalex.org/W3120803118","https://openalex.org/W3171910361","https://openalex.org/W3203084907","https://openalex.org/W3212023591","https://openalex.org/W4214641344","https://openalex.org/W4224296477","https://openalex.org/W4391597034","https://openalex.org/W4391733905","https://openalex.org/W6788968604"],"related_works":["https://openalex.org/W1982525302","https://openalex.org/W4386194226","https://openalex.org/W2125760495","https://openalex.org/W2318688414","https://openalex.org/W2039455518","https://openalex.org/W84751559","https://openalex.org/W3031119225","https://openalex.org/W2160818730","https://openalex.org/W2515358769","https://openalex.org/W2005148544"],"abstract_inverted_index":{"The":[0,46],"Lomax":[1,40,64],"distribution":[2,41],"has":[3],"important":[4,19],"applications":[5],"in":[6,29],"survival":[7],"analysis,":[8],"reliability":[9],"engineering,":[10],"insurance,":[11],"finance,":[12],"and":[13,22,88,139,153],"other":[14],"fields.":[15],"Middle-censoring":[16],"is":[17,49,132,144],"an":[18],"censoring":[20,28],"scheme,":[21],"data":[23,69,152,155],"with":[24,107],"middle-censoring":[25],"will":[26],"produce":[27],"random":[30],"intervals.":[31],"This":[32],"paper":[33],"studies":[34],"the":[35,39,53,58,63,68,71,75,84,89,93,97,102,108,117,121,125,129,140,147,160,163],"parameter":[36,76,131],"estimation":[37,122,127,165],"of":[38,57,62,101,116,162],"based":[42],"on":[43],"middle-censored":[44],"data.":[45],"expectation\u2013maximization":[47],"algorithm":[48],"employed":[50,145],"to":[51,158],"compute":[52],"maximum":[54],"likelihood":[55],"estimates":[56,77],"two":[59,81,103],"unknown":[60],"parameters":[61,104],"distribution.":[65],"After":[66],"processing":[67],"using":[70,134],"midpoint":[72],"approach":[73],"estimation,":[74],"are":[78,105,156],"obtained":[79],"by":[80],"computational":[82],"methods:":[83],"Newton\u2013Raphson":[85],"iteration":[86],"method":[87,143],"fixed-point":[90],"method.":[91],"Moreover,":[92],"calculation":[94],"methods":[95],"for":[96,119,146],"asymptotic":[98],"confidence":[99,109],"intervals":[100],"provided,":[106],"interval":[110],"coverage":[111],"rate":[112],"serving":[113],"as":[114],"one":[115],"criteria":[118],"evaluating":[120],"performance.":[123],"In":[124],"Bayesian":[126],"aspect,":[128],"shape":[130],"estimated":[133],"a":[135],"Gamma":[136],"prior":[137],"distribution,":[138],"Gibbs":[141],"sampling":[142],"solution.":[148],"Finally,":[149],"both":[150],"simulation":[151],"real":[154],"used":[157],"compare":[159],"accuracy":[161],"various":[164],"methods.":[166]},"counts_by_year":[],"updated_date":"2026-02-27T16:54:17.756197","created_date":"2025-10-10T00:00:00"}
