{"id":"https://openalex.org/W4297988709","doi":"https://doi.org/10.3390/axioms11100516","title":"Mixture of Akash Distributions: Estimation, Simulation and Application","display_name":"Mixture of Akash Distributions: Estimation, Simulation and Application","publication_year":2022,"publication_date":"2022-09-29","ids":{"openalex":"https://openalex.org/W4297988709","doi":"https://doi.org/10.3390/axioms11100516"},"language":"en","primary_location":{"id":"doi:10.3390/axioms11100516","is_oa":true,"landing_page_url":"https://doi.org/10.3390/axioms11100516","pdf_url":"https://www.mdpi.com/2075-1680/11/10/516/pdf?version=1666600848","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/2075-1680/11/10/516/pdf?version=1666600848","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5070937697","display_name":"Anum Shafiq","orcid":"https://orcid.org/0000-0001-7186-7216"},"institutions":[{"id":"https://openalex.org/I200845125","display_name":"Nanjing University of Information Science and Technology","ror":"https://ror.org/02y0rxk19","country_code":"CN","type":"education","lineage":["https://openalex.org/I200845125"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Anum Shafiq","raw_affiliation_strings":["School of Mathematics and Statistics, Nanjing University of Information Science and Technology, Nanjing 210044, China"],"raw_orcid":"https://orcid.org/0000-0001-7186-7216","affiliations":[{"raw_affiliation_string":"School of Mathematics and Statistics, Nanjing University of Information Science and Technology, Nanjing 210044, China","institution_ids":["https://openalex.org/I200845125"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5010255093","display_name":"Tabassum Naz Sindhu","orcid":"https://orcid.org/0000-0001-9433-4981"},"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":false,"raw_author_name":"Tabassum Naz Sindhu","raw_affiliation_strings":["Department of Statistics, Quaid-i-Azam University, Islamabad 44000, Pakistan"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Statistics, Quaid-i-Azam University, Islamabad 44000, Pakistan","institution_ids":["https://openalex.org/I12469534"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5071973429","display_name":"Showkat Ahmad Lone","orcid":"https://orcid.org/0000-0001-7149-3314"},"institutions":[{"id":"https://openalex.org/I120238654","display_name":"Saudi Electronic University","ror":"https://ror.org/05ndh7v49","country_code":"SA","type":"education","lineage":["https://openalex.org/I120238654"]}],"countries":["SA"],"is_corresponding":false,"raw_author_name":"Showkat Ahmad Lone","raw_affiliation_strings":["Department of Basic Sciences College of Science and Theoretical Studies, Saudi Electronic University, Riyadh 11673, Saudi Arabia"],"raw_orcid":"https://orcid.org/0000-0001-7149-3314","affiliations":[{"raw_affiliation_string":"Department of Basic Sciences College of Science and Theoretical Studies, Saudi Electronic University, Riyadh 11673, Saudi Arabia","institution_ids":["https://openalex.org/I120238654"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5053192579","display_name":"Marwa K. H. Hassan","orcid":"https://orcid.org/0000-0003-3730-7869"},"institutions":[{"id":"https://openalex.org/I107720978","display_name":"Ain Shams University","ror":"https://ror.org/00cb9w016","country_code":"EG","type":"education","lineage":["https://openalex.org/I107720978"]}],"countries":["EG"],"is_corresponding":false,"raw_author_name":"Marwa K. H. Hassan","raw_affiliation_strings":["Department of Mathematics, Faculty of Education, Ain Shams University, Cairo 11566, Egypt"],"raw_orcid":"https://orcid.org/0000-0003-3730-7869","affiliations":[{"raw_affiliation_string":"Department of Mathematics, Faculty of Education, Ain Shams University, Cairo 11566, Egypt","institution_ids":["https://openalex.org/I107720978"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5089496116","display_name":"Kamsing Nonlaopon","orcid":"https://orcid.org/0000-0002-7469-5402"},"institutions":[{"id":"https://openalex.org/I179193067","display_name":"Khon Kaen University","ror":"https://ror.org/03cq4gr50","country_code":"TH","type":"education","lineage":["https://openalex.org/I179193067"]}],"countries":["TH"],"is_corresponding":true,"raw_author_name":"Kamsing Nonlaopon","raw_affiliation_strings":["Department of Mathematics, Faculty of Science, Khon Kaen University, Khon Kaen 40002, Thailand"],"raw_orcid":"https://orcid.org/0000-0002-7469-5402","affiliations":[{"raw_affiliation_string":"Department of Mathematics, Faculty of Science, Khon Kaen University, Khon Kaen 40002, Thailand","institution_ids":["https://openalex.org/I179193067"]}]}],"institutions":[],"countries_distinct_count":5,"institutions_distinct_count":5,"corresponding_author_ids":["https://openalex.org/A5089496116"],"corresponding_institution_ids":["https://openalex.org/I179193067"],"apc_list":{"value":1600,"currency":"CHF","value_usd":1782},"apc_paid":{"value":1600,"currency":"CHF","value_usd":1782},"fwci":0.8778,"has_fulltext":true,"cited_by_count":4,"citation_normalized_percentile":{"value":0.74201355,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":96},"biblio":{"volume":"11","issue":"10","first_page":"516","last_page":"516"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10968","display_name":"Statistical Distribution Estimation and Applications","score":0.9998999834060669,"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":0.9998999834060669,"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/T11901","display_name":"Bayesian Methods and Mixture Models","score":0.9930999875068665,"subfield":{"id":"https://openalex.org/subfields/1702","display_name":"Artificial Intelligence"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer 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":0.9872000217437744,"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/kurtosis","display_name":"Kurtosis","score":0.8259904980659485},{"id":"https://openalex.org/keywords/skewness","display_name":"Skewness","score":0.6859276294708252},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6421312093734741},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.5886185169219971},{"id":"https://openalex.org/keywords/moment","display_name":"Moment (physics)","score":0.5525444149971008},{"id":"https://openalex.org/keywords/exponential-function","display_name":"Exponential function","score":0.5233518481254578},{"id":"https://openalex.org/keywords/mixture-model","display_name":"Mixture model","score":0.5163851976394653},{"id":"https://openalex.org/keywords/cumulant","display_name":"Cumulant","score":0.4925561547279358},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.4884013533592224},{"id":"https://openalex.org/keywords/exponential-distribution","display_name":"Exponential distribution","score":0.4834047853946686},{"id":"https://openalex.org/keywords/index-of-dispersion","display_name":"Index of dispersion","score":0.4508509337902069},{"id":"https://openalex.org/keywords/function","display_name":"Function (biology)","score":0.4490000009536743},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.11445620656013489}],"concepts":[{"id":"https://openalex.org/C166963901","wikidata":"https://www.wikidata.org/wiki/Q287251","display_name":"Kurtosis","level":2,"score":0.8259904980659485},{"id":"https://openalex.org/C122342681","wikidata":"https://www.wikidata.org/wiki/Q330828","display_name":"Skewness","level":2,"score":0.6859276294708252},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6421312093734741},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.5886185169219971},{"id":"https://openalex.org/C179254644","wikidata":"https://www.wikidata.org/wiki/Q13222844","display_name":"Moment (physics)","level":2,"score":0.5525444149971008},{"id":"https://openalex.org/C151376022","wikidata":"https://www.wikidata.org/wiki/Q168698","display_name":"Exponential function","level":2,"score":0.5233518481254578},{"id":"https://openalex.org/C61224824","wikidata":"https://www.wikidata.org/wiki/Q2260434","display_name":"Mixture model","level":2,"score":0.5163851976394653},{"id":"https://openalex.org/C172686274","wikidata":"https://www.wikidata.org/wiki/Q746007","display_name":"Cumulant","level":2,"score":0.4925561547279358},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.4884013533592224},{"id":"https://openalex.org/C55350006","wikidata":"https://www.wikidata.org/wiki/Q237193","display_name":"Exponential distribution","level":2,"score":0.4834047853946686},{"id":"https://openalex.org/C41093919","wikidata":"https://www.wikidata.org/wiki/Q2158178","display_name":"Index of dispersion","level":4,"score":0.4508509337902069},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.4490000009536743},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.11445620656013489},{"id":"https://openalex.org/C149923435","wikidata":"https://www.wikidata.org/wiki/Q37732","display_name":"Demography","level":1,"score":0.0},{"id":"https://openalex.org/C144024400","wikidata":"https://www.wikidata.org/wiki/Q21201","display_name":"Sociology","level":0,"score":0.0},{"id":"https://openalex.org/C2908647359","wikidata":"https://www.wikidata.org/wiki/Q2625603","display_name":"Population","level":2,"score":0.0},{"id":"https://openalex.org/C78458016","wikidata":"https://www.wikidata.org/wiki/Q840400","display_name":"Evolutionary biology","level":1,"score":0.0},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0},{"id":"https://openalex.org/C74650414","wikidata":"https://www.wikidata.org/wiki/Q11397","display_name":"Classical mechanics","level":1,"score":0.0},{"id":"https://openalex.org/C73269764","wikidata":"https://www.wikidata.org/wiki/Q954529","display_name":"Poisson regression","level":3,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.3390/axioms11100516","is_oa":true,"landing_page_url":"https://doi.org/10.3390/axioms11100516","pdf_url":"https://www.mdpi.com/2075-1680/11/10/516/pdf?version=1666600848","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:233e2e8231cb413dba55ca77ff2787d4","is_oa":true,"landing_page_url":"https://doaj.org/article/233e2e8231cb413dba55ca77ff2787d4","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 10, p 516 (2022)","raw_type":"article"},{"id":"pmh:oai:mdpi.com:/2075-1680/11/10/516/","is_oa":true,"landing_page_url":"https://dx.doi.org/10.3390/axioms11100516","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 10; Pages: 516","raw_type":"Text"}],"best_oa_location":{"id":"doi:10.3390/axioms11100516","is_oa":true,"landing_page_url":"https://doi.org/10.3390/axioms11100516","pdf_url":"https://www.mdpi.com/2075-1680/11/10/516/pdf?version=1666600848","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/W4297988709.pdf","grobid_xml":"https://content.openalex.org/works/W4297988709.grobid-xml"},"referenced_works_count":30,"referenced_works":["https://openalex.org/W306662213","https://openalex.org/W1963792675","https://openalex.org/W1998757538","https://openalex.org/W2046262695","https://openalex.org/W2082576445","https://openalex.org/W2101288603","https://openalex.org/W2112345887","https://openalex.org/W2125671368","https://openalex.org/W2204504220","https://openalex.org/W2340981286","https://openalex.org/W2460232234","https://openalex.org/W2488678869","https://openalex.org/W2562020924","https://openalex.org/W2565157236","https://openalex.org/W2598694153","https://openalex.org/W2599071407","https://openalex.org/W2772313183","https://openalex.org/W2885580044","https://openalex.org/W2975332181","https://openalex.org/W3100086973","https://openalex.org/W3113721704","https://openalex.org/W4200531113","https://openalex.org/W4220995663","https://openalex.org/W4226432920","https://openalex.org/W4280636474","https://openalex.org/W6687646187","https://openalex.org/W6718717955","https://openalex.org/W6746514379","https://openalex.org/W6753734578","https://openalex.org/W6768310140"],"related_works":["https://openalex.org/W4225568567","https://openalex.org/W4286378979","https://openalex.org/W1496883226","https://openalex.org/W4297337052","https://openalex.org/W2028605949","https://openalex.org/W2282665605","https://openalex.org/W3216026256","https://openalex.org/W2093055004","https://openalex.org/W3129919015","https://openalex.org/W4390742338"],"abstract_inverted_index":{"In":[0],"this":[1],"paper,":[2],"we":[3,70,73],"propose":[4],"a":[5,113],"two-component":[6],"mixture":[7,81,149],"of":[8,14,26,31,65,79,100,106,115,134,145,150],"Akash":[9],"model":[10,68,82,141],"(TC-MAM).":[11],"The":[12,43],"behavior":[13,105],"TC-MAM":[15],"distribution":[16,147],"has":[17],"been":[18,34],"presented":[19,41],"graphically.":[20,42],"Moment-based":[21],"measures,":[22],"including":[23],"skewness,":[24],"index":[25],"dispersion,":[27],"kurtosis,":[28],"and":[29,36,56,95,142,153],"coefficient":[30],"variation,":[32],"have":[33],"determined":[35],"hazard":[37],"rate":[38],"functions":[39],"are":[40,61,109],"probability":[44],"generating":[45,59],"function,":[46,50],"Mills":[47],"ratio,":[48],"characteristic":[49],"cumulants,":[51],"mean":[52],"time":[53],"to":[54,103,126],"failure,":[55],"factorial":[57],"moment":[58],"function":[60],"all":[62],"statistical":[63],"aspects":[64],"the":[66,76,80,84,119,128,135,139,143],"mixed":[67],"that":[69],"explore.":[71],"Furthermore,":[72],"figure":[74],"out":[75],"relevant":[77],"parameters":[78],"using":[83],"most":[85],"suitable":[86],"methods,":[87],"such":[88],"as":[89],"least":[90,93],"square,":[91,94],"weighted":[92],"maximum":[96],"likelihood":[97],"mechanisms.":[98],"Findings":[99],"simulation":[101],"experiments":[102],"examine":[104],"these":[107],"estimates":[108],"graphically":[110],"presented.":[111],"Finally,":[112],"set":[114],"data":[116],"taken":[117],"from":[118],"real":[120],"world":[121],"is":[122],"examined":[123],"in":[124],"order":[125],"demonstrate":[127],"new":[129,140],"model\u2019s":[130],"practical":[131],"perspectives.":[132],"All":[133],"metrics":[136],"evaluated":[137],"favor":[138],"superiority":[144],"proposed":[146],"over":[148],"Lindley,":[151],"Shanker,":[152],"exponential":[154],"distributions.":[155]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":2},{"year":2023,"cited_by_count":1}],"updated_date":"2026-07-23T08:03:31.855105","created_date":"2022-10-01T00:00:00"}
