{"id":"https://openalex.org/W4400469858","doi":"https://doi.org/10.37190/ord240203","title":"On the theory of order statistics of the flexible Lomax distribution","display_name":"On the theory of order statistics of the flexible Lomax distribution","publication_year":2024,"publication_date":"2024-01-01","ids":{"openalex":"https://openalex.org/W4400469858","doi":"https://doi.org/10.37190/ord240203"},"language":"en","primary_location":{"id":"doi:10.37190/ord240203","is_oa":true,"landing_page_url":"http://doi.org/10.37190/ord240203","pdf_url":"https://doi.org/10.37190/ord240203","source":{"id":"https://openalex.org/S2739399646","display_name":"Badania Operacyjne i Decyzje/Operations Research and Decisions","issn_l":"1230-1868","issn":["1230-1868","2081-8858","2391-6060"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310317492","host_organization_name":"Wroc\u0142aw University of Science and Technology","host_organization_lineage":["https://openalex.org/P4310317492"],"host_organization_lineage_names":["Wroc\u0142aw University of Science and Technology"],"type":"journal"},"license":"cc-by-nc-nd","license_id":"https://openalex.org/licenses/cc-by-nc-nd","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Operations Research and Decisions","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"diamond","oa_url":"https://doi.org/10.37190/ord240203","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5010653691","display_name":"Farrukh Jamal","orcid":"https://orcid.org/0000-0001-6192-9890"},"institutions":[{"id":"https://openalex.org/I174731842","display_name":"Islamia University of Bahawalpur","ror":"https://ror.org/002rc4w13","country_code":"PK","type":"education","lineage":["https://openalex.org/I174731842"]}],"countries":["PK"],"is_corresponding":true,"raw_author_name":"Farrukh Jamal","raw_affiliation_strings":["Department of Statistics, The Islamia University of Bahawalpur, Punjab, Pakistan"],"affiliations":[{"raw_affiliation_string":"Department of Statistics, The Islamia University of Bahawalpur, Punjab, Pakistan","institution_ids":["https://openalex.org/I174731842"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5101791108","display_name":"Muhammad Ijaz","orcid":"https://orcid.org/0000-0002-0050-9435"},"institutions":[{"id":"https://openalex.org/I2801349156","display_name":"University of Haripur","ror":"https://ror.org/05vtb1235","country_code":"PK","type":"education","lineage":["https://openalex.org/I2801349156"]}],"countries":["PK"],"is_corresponding":false,"raw_author_name":"Muhammad Ijaz","raw_affiliation_strings":["Department of Mathematics and Statistics, The University of Haripur, KP, Pakistan"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics and Statistics, The University of Haripur, KP, Pakistan","institution_ids":["https://openalex.org/I2801349156"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5100635090","display_name":"Ghulam Mustafa","orcid":"https://orcid.org/0000-0003-1687-5656"},"institutions":[{"id":"https://openalex.org/I206573129","display_name":"Islamia College University","ror":"https://ror.org/02p2c1595","country_code":"PK","type":"education","lineage":["https://openalex.org/I206573129"]}],"countries":["PK"],"is_corresponding":false,"raw_author_name":"Ghulam Mustafa","raw_affiliation_strings":["Department of Statistics, Islamia College University, Peshawar, Pakistan"],"affiliations":[{"raw_affiliation_string":"Department of Statistics, Islamia College University, Peshawar, Pakistan","institution_ids":["https://openalex.org/I206573129"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5055042534","display_name":"Sadaf Khan","orcid":"https://orcid.org/0000-0002-0258-5124"},"institutions":[{"id":"https://openalex.org/I79839403","display_name":"University of Veterinary and Animal Sciences","ror":"https://ror.org/00g325k81","country_code":"PK","type":"education","lineage":["https://openalex.org/I79839403"]},{"id":"https://openalex.org/I174731842","display_name":"Islamia University of Bahawalpur","ror":"https://ror.org/002rc4w13","country_code":"PK","type":"education","lineage":["https://openalex.org/I174731842"]}],"countries":["PK"],"is_corresponding":false,"raw_author_name":"Sadaf Khan","raw_affiliation_strings":["Department of Statistics, The Islamia University of Bahawalpur, Punjab, Pakistan","Department of Social and Allied Sciences, Cholistan University of Veterinary and Animal Sciences, Bahawalpur, Punjab, Pakistan"],"affiliations":[{"raw_affiliation_string":"Department of Statistics, The Islamia University of Bahawalpur, Punjab, Pakistan","institution_ids":["https://openalex.org/I174731842"]},{"raw_affiliation_string":"Department of Social and Allied Sciences, Cholistan University of Veterinary and Animal Sciences, Bahawalpur, Punjab, Pakistan","institution_ids":["https://openalex.org/I79839403"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5023207229","display_name":"Shakaiba Shafiq","orcid":null},"institutions":[{"id":"https://openalex.org/I174731842","display_name":"Islamia University of Bahawalpur","ror":"https://ror.org/002rc4w13","country_code":"PK","type":"education","lineage":["https://openalex.org/I174731842"]}],"countries":["PK"],"is_corresponding":false,"raw_author_name":"Shakaiba Shafiq","raw_affiliation_strings":["Department of Statistics, The Islamia University of Bahawalpur, Punjab, Pakistan"],"affiliations":[{"raw_affiliation_string":"Department of Statistics, The Islamia University of Bahawalpur, Punjab, Pakistan","institution_ids":["https://openalex.org/I174731842"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":5,"corresponding_author_ids":["https://openalex.org/A5010653691"],"corresponding_institution_ids":["https://openalex.org/I174731842"],"apc_list":null,"apc_paid":null,"fwci":0.7552,"has_fulltext":false,"cited_by_count":1,"citation_normalized_percentile":{"value":0.72349997,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":91,"max":95},"biblio":{"volume":"34","issue":"2","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":0.9993000030517578,"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":0.9993000030517578,"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":0.9771000146865845,"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/T11871","display_name":"Advanced Statistical Methods and Models","score":0.9545000195503235,"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/order-statistic","display_name":"Order statistic","score":0.7636688351631165},{"id":"https://openalex.org/keywords/l-moment","display_name":"L-moment","score":0.7518132925033569},{"id":"https://openalex.org/keywords/kurtosis","display_name":"Kurtosis","score":0.7499639987945557},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.7029617428779602},{"id":"https://openalex.org/keywords/skewness","display_name":"Skewness","score":0.6853514909744263},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.651229202747345},{"id":"https://openalex.org/keywords/lomax-distribution","display_name":"Lomax distribution","score":0.5479041934013367},{"id":"https://openalex.org/keywords/entropy","display_name":"Entropy (arrow of time)","score":0.4549604654312134},{"id":"https://openalex.org/keywords/order","display_name":"Order (exchange)","score":0.44135814905166626},{"id":"https://openalex.org/keywords/pareto-distribution","display_name":"Pareto distribution","score":0.2691308557987213}],"concepts":[{"id":"https://openalex.org/C44082924","wikidata":"https://www.wikidata.org/wiki/Q1767128","display_name":"Order statistic","level":2,"score":0.7636688351631165},{"id":"https://openalex.org/C1797436","wikidata":"https://www.wikidata.org/wiki/Q6456145","display_name":"L-moment","level":3,"score":0.7518132925033569},{"id":"https://openalex.org/C166963901","wikidata":"https://www.wikidata.org/wiki/Q287251","display_name":"Kurtosis","level":2,"score":0.7499639987945557},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.7029617428779602},{"id":"https://openalex.org/C122342681","wikidata":"https://www.wikidata.org/wiki/Q330828","display_name":"Skewness","level":2,"score":0.6853514909744263},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.651229202747345},{"id":"https://openalex.org/C18249693","wikidata":"https://www.wikidata.org/wiki/Q2517984","display_name":"Lomax distribution","level":3,"score":0.5479041934013367},{"id":"https://openalex.org/C106301342","wikidata":"https://www.wikidata.org/wiki/Q4117933","display_name":"Entropy (arrow of time)","level":2,"score":0.4549604654312134},{"id":"https://openalex.org/C182306322","wikidata":"https://www.wikidata.org/wiki/Q1779371","display_name":"Order (exchange)","level":2,"score":0.44135814905166626},{"id":"https://openalex.org/C190373308","wikidata":"https://www.wikidata.org/wiki/Q837683","display_name":"Pareto distribution","level":2,"score":0.2691308557987213},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0},{"id":"https://openalex.org/C10138342","wikidata":"https://www.wikidata.org/wiki/Q43015","display_name":"Finance","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.37190/ord240203","is_oa":true,"landing_page_url":"http://doi.org/10.37190/ord240203","pdf_url":"https://doi.org/10.37190/ord240203","source":{"id":"https://openalex.org/S2739399646","display_name":"Badania Operacyjne i Decyzje/Operations Research and Decisions","issn_l":"1230-1868","issn":["1230-1868","2081-8858","2391-6060"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310317492","host_organization_name":"Wroc\u0142aw University of Science and Technology","host_organization_lineage":["https://openalex.org/P4310317492"],"host_organization_lineage_names":["Wroc\u0142aw University of Science and Technology"],"type":"journal"},"license":"cc-by-nc-nd","license_id":"https://openalex.org/licenses/cc-by-nc-nd","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Operations Research and Decisions","raw_type":"journal-article"}],"best_oa_location":{"id":"doi:10.37190/ord240203","is_oa":true,"landing_page_url":"http://doi.org/10.37190/ord240203","pdf_url":"https://doi.org/10.37190/ord240203","source":{"id":"https://openalex.org/S2739399646","display_name":"Badania Operacyjne i Decyzje/Operations Research and Decisions","issn_l":"1230-1868","issn":["1230-1868","2081-8858","2391-6060"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310317492","host_organization_name":"Wroc\u0142aw University of Science and Technology","host_organization_lineage":["https://openalex.org/P4310317492"],"host_organization_lineage_names":["Wroc\u0142aw University of Science and Technology"],"type":"journal"},"license":"cc-by-nc-nd","license_id":"https://openalex.org/licenses/cc-by-nc-nd","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Operations Research and Decisions","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W4400469858.pdf"},"referenced_works_count":14,"referenced_works":["https://openalex.org/W1972045164","https://openalex.org/W2021447134","https://openalex.org/W2038174233","https://openalex.org/W2073438733","https://openalex.org/W2134418049","https://openalex.org/W2142586058","https://openalex.org/W2161572875","https://openalex.org/W2171547964","https://openalex.org/W2551951959","https://openalex.org/W4250212944","https://openalex.org/W4281724040","https://openalex.org/W4298217738","https://openalex.org/W4310831476","https://openalex.org/W4377864126"],"related_works":["https://openalex.org/W4225568567","https://openalex.org/W4286378979","https://openalex.org/W1496883226","https://openalex.org/W4297337052","https://openalex.org/W3122185550","https://openalex.org/W2626476433","https://openalex.org/W3201983651","https://openalex.org/W2341535927","https://openalex.org/W1984005109","https://openalex.org/W2529620828"],"abstract_inverted_index":{"This":[0],"paper":[1],"studies":[2],"the":[3,16,26,35,48,57,77,83],"flexible":[4,102],"Lomax":[5,103],"distribution\u2019s":[6],"order":[7,54,70,88,98],"statistics":[8,41,55,89,99],"with":[9,15],"graphical":[10],"and":[11,28,50,94,112],"numerical":[12],"findings.":[13],"Along":[14],"quantitative":[17],"measurements,":[18],"some":[19,63],"plots":[20],"are":[21,116],"furnished,":[22],"including":[23],"those":[24],"for":[25,66],"skewness":[27],"kurtosis":[29],"measures.":[30,96],"We":[31,46,72],"will":[32],"dwell":[33],"on":[34],"numerous":[36],"results":[37],"that":[38],"relate":[39],"to":[40,75,80,90],"of":[42,44,53,69,85,100,108],"moments":[43,68,84,93],"order.":[45],"consider":[47],"single":[49,67],"product":[51],"moment":[52],"from":[56],"new":[58],"distribution.":[59],"Further,":[60],"we":[61],"establish":[62,91],"recurrence":[64],"relation":[65],"statistics.":[71],"have":[73],"sought":[74],"apply":[76],"derived":[78],"relations":[79],"empirically":[81],"evaluate":[82],"smallest":[86],"(largest)":[87],"well-known":[92],"related":[95],"For":[97],"a":[101],"distribution,":[104],"exact":[105],"analytical":[106],"expressions":[107],"entropy,":[109,111],"residual":[110],"past":[113],"latent":[114],"entropy":[115],"determined.":[117]},"counts_by_year":[{"year":2025,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}