{"id":"https://openalex.org/W3029978934","doi":"https://doi.org/10.3390/e22060603","title":"A New Discrete Analog of the Continuous Lindley Distribution, with Reliability Applications","display_name":"A New Discrete Analog of the Continuous Lindley Distribution, with Reliability Applications","publication_year":2020,"publication_date":"2020-05-28","ids":{"openalex":"https://openalex.org/W3029978934","doi":"https://doi.org/10.3390/e22060603","mag":"3029978934","pmid":"https://pubmed.ncbi.nlm.nih.gov/33286375"},"language":"en","primary_location":{"id":"doi:10.3390/e22060603","is_oa":true,"landing_page_url":"https://doi.org/10.3390/e22060603","pdf_url":"https://www.mdpi.com/1099-4300/22/6/603/pdf?version=1593493825","source":{"id":"https://openalex.org/S195231649","display_name":"Entropy","issn_l":"1099-4300","issn":["1099-4300"],"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":"Entropy","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","doaj","pubmed"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://www.mdpi.com/1099-4300/22/6/603/pdf?version=1593493825","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5037266448","display_name":"Abdulhakim A. Al-Babtain","orcid":"https://orcid.org/0000-0003-2189-2629"},"institutions":[{"id":"https://openalex.org/I28022161","display_name":"King Saud University","ror":"https://ror.org/02f81g417","country_code":"SA","type":"education","lineage":["https://openalex.org/I28022161"]}],"countries":["SA"],"is_corresponding":false,"raw_author_name":"Abdulhakim A. Al-Babtain","raw_affiliation_strings":["Department of Statistics and Operations Research, King Saud University, Riyadh 11362, Saudi Arabia"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Statistics and Operations Research, King Saud University, Riyadh 11362, Saudi Arabia","institution_ids":["https://openalex.org/I28022161"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5047266467","display_name":"Abdul Hadi N. Ahmed","orcid":null},"institutions":[{"id":"https://openalex.org/I145487455","display_name":"Cairo University","ror":"https://ror.org/03q21mh05","country_code":"EG","type":"education","lineage":["https://openalex.org/I145487455"]}],"countries":["EG"],"is_corresponding":false,"raw_author_name":"Abdul Hadi N. Ahmed","raw_affiliation_strings":["Department of Mathematical Statistics, Faculty of Graduate Studies for Statistical Research, Cairo University, Giza 12631, Egypt"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematical Statistics, Faculty of Graduate Studies for Statistical Research, Cairo University, Giza 12631, Egypt","institution_ids":["https://openalex.org/I145487455"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5090850000","display_name":"Ahmed Z. Afify","orcid":"https://orcid.org/0000-0002-6723-6785"},"institutions":[{"id":"https://openalex.org/I207547235","display_name":"Benha University","ror":"https://ror.org/03tn5ee41","country_code":"EG","type":"education","lineage":["https://openalex.org/I207547235"]}],"countries":["EG"],"is_corresponding":true,"raw_author_name":"Ahmed Z. Afify","raw_affiliation_strings":["Department of Statistics, Mathematics and Insurance, Benha University, Benha 13511, Egypt"],"raw_orcid":"https://orcid.org/0000-0002-6723-6785","affiliations":[{"raw_affiliation_string":"Department of Statistics, Mathematics and Insurance, Benha University, Benha 13511, Egypt","institution_ids":["https://openalex.org/I207547235"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5090850000"],"corresponding_institution_ids":["https://openalex.org/I207547235"],"apc_list":{"value":2000,"currency":"CHF","value_usd":2227},"apc_paid":{"value":2000,"currency":"CHF","value_usd":2227},"fwci":6.9545,"has_fulltext":true,"cited_by_count":46,"citation_normalized_percentile":{"value":0.97934945,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":94,"max":99},"biblio":{"volume":"22","issue":"6","first_page":"603","last_page":"603"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10968","display_name":"Statistical Distribution Estimation and Applications","score":1.0,"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":1.0,"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":0.989300012588501,"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":0.9889000058174133,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6378989219665527},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.6093759536743164},{"id":"https://openalex.org/keywords/geometric-distribution","display_name":"Geometric distribution","score":0.5724211931228638},{"id":"https://openalex.org/keywords/principle-of-maximum-entropy","display_name":"Principle of maximum entropy","score":0.5575260519981384},{"id":"https://openalex.org/keywords/estimator","display_name":"Estimator","score":0.5198969841003418},{"id":"https://openalex.org/keywords/probability-distribution","display_name":"Probability distribution","score":0.5038709044456482},{"id":"https://openalex.org/keywords/moment","display_name":"Moment (physics)","score":0.4825298488140106},{"id":"https://openalex.org/keywords/entropy","display_name":"Entropy (arrow of time)","score":0.4603841304779053},{"id":"https://openalex.org/keywords/lomax-distribution","display_name":"Lomax distribution","score":0.45433953404426575},{"id":"https://openalex.org/keywords/moment-generating-function","display_name":"Moment-generating function","score":0.4439389407634735},{"id":"https://openalex.org/keywords/beta-binomial-distribution","display_name":"Beta-binomial distribution","score":0.4427882730960846},{"id":"https://openalex.org/keywords/negative-binomial-distribution","display_name":"Negative binomial distribution","score":0.43435797095298767},{"id":"https://openalex.org/keywords/probability-mass-function","display_name":"Probability mass function","score":0.4315023124217987},{"id":"https://openalex.org/keywords/statistical-physics","display_name":"Statistical physics","score":0.4312010109424591},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.3641027510166168},{"id":"https://openalex.org/keywords/poisson-distribution","display_name":"Poisson distribution","score":0.3171558678150177},{"id":"https://openalex.org/keywords/maximum-likelihood","display_name":"Maximum likelihood","score":0.23220130801200867}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6378989219665527},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.6093759536743164},{"id":"https://openalex.org/C39947850","wikidata":"https://www.wikidata.org/wiki/Q729523","display_name":"Geometric distribution","level":3,"score":0.5724211931228638},{"id":"https://openalex.org/C9679016","wikidata":"https://www.wikidata.org/wiki/Q1417473","display_name":"Principle of maximum entropy","level":2,"score":0.5575260519981384},{"id":"https://openalex.org/C185429906","wikidata":"https://www.wikidata.org/wiki/Q1130160","display_name":"Estimator","level":2,"score":0.5198969841003418},{"id":"https://openalex.org/C149441793","wikidata":"https://www.wikidata.org/wiki/Q200726","display_name":"Probability distribution","level":2,"score":0.5038709044456482},{"id":"https://openalex.org/C179254644","wikidata":"https://www.wikidata.org/wiki/Q13222844","display_name":"Moment (physics)","level":2,"score":0.4825298488140106},{"id":"https://openalex.org/C106301342","wikidata":"https://www.wikidata.org/wiki/Q4117933","display_name":"Entropy (arrow of time)","level":2,"score":0.4603841304779053},{"id":"https://openalex.org/C18249693","wikidata":"https://www.wikidata.org/wiki/Q2517984","display_name":"Lomax distribution","level":3,"score":0.45433953404426575},{"id":"https://openalex.org/C101796028","wikidata":"https://www.wikidata.org/wiki/Q535587","display_name":"Moment-generating function","level":3,"score":0.4439389407634735},{"id":"https://openalex.org/C165480597","wikidata":"https://www.wikidata.org/wiki/Q307557","display_name":"Beta-binomial distribution","level":4,"score":0.4427882730960846},{"id":"https://openalex.org/C199335787","wikidata":"https://www.wikidata.org/wiki/Q743364","display_name":"Negative binomial distribution","level":3,"score":0.43435797095298767},{"id":"https://openalex.org/C197096303","wikidata":"https://www.wikidata.org/wiki/Q869887","display_name":"Probability mass function","level":3,"score":0.4315023124217987},{"id":"https://openalex.org/C121864883","wikidata":"https://www.wikidata.org/wiki/Q677916","display_name":"Statistical physics","level":1,"score":0.4312010109424591},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.3641027510166168},{"id":"https://openalex.org/C100906024","wikidata":"https://www.wikidata.org/wiki/Q205692","display_name":"Poisson distribution","level":2,"score":0.3171558678150177},{"id":"https://openalex.org/C49781872","wikidata":"https://www.wikidata.org/wiki/Q1045555","display_name":"Maximum likelihood","level":2,"score":0.23220130801200867},{"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/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}],"mesh":[],"locations_count":5,"locations":[{"id":"doi:10.3390/e22060603","is_oa":true,"landing_page_url":"https://doi.org/10.3390/e22060603","pdf_url":"https://www.mdpi.com/1099-4300/22/6/603/pdf?version=1593493825","source":{"id":"https://openalex.org/S195231649","display_name":"Entropy","issn_l":"1099-4300","issn":["1099-4300"],"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":"Entropy","raw_type":"journal-article"},{"id":"pmid:33286375","is_oa":false,"landing_page_url":"https://pubmed.ncbi.nlm.nih.gov/33286375","pdf_url":null,"source":{"id":"https://openalex.org/S4306525036","display_name":"PubMed","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1299303238","host_organization_name":"National Institutes of Health","host_organization_lineage":["https://openalex.org/I1299303238"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Entropy (Basel, Switzerland)","raw_type":null},{"id":"pmh:oai:pubmedcentral.nih.gov:7517138","is_oa":true,"landing_page_url":"https://www.ncbi.nlm.nih.gov/pmc/articles/7517138","pdf_url":null,"source":{"id":"https://openalex.org/S2764455111","display_name":"PubMed Central","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1299303238","host_organization_name":"National Institutes of Health","host_organization_lineage":["https://openalex.org/I1299303238"],"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":"Entropy (Basel)","raw_type":"Text"},{"id":"pmh:oai:doaj.org/article:9115d556bf7a4014ae29a16324a72fa5","is_oa":true,"landing_page_url":"https://doaj.org/article/9115d556bf7a4014ae29a16324a72fa5","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":"Entropy, Vol 22, Iss 6, p 603 (2020)","raw_type":"article"},{"id":"pmh:oai:mdpi.com:/1099-4300/22/6/603/","is_oa":true,"landing_page_url":"http://dx.doi.org/10.3390/e22060603","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":"Entropy","raw_type":"Text"}],"best_oa_location":{"id":"doi:10.3390/e22060603","is_oa":true,"landing_page_url":"https://doi.org/10.3390/e22060603","pdf_url":"https://www.mdpi.com/1099-4300/22/6/603/pdf?version=1593493825","source":{"id":"https://openalex.org/S195231649","display_name":"Entropy","issn_l":"1099-4300","issn":["1099-4300"],"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":"Entropy","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G6658874159","display_name":null,"funder_award_id":"RSP-2020/156","funder_id":"https://openalex.org/F4320321145","funder_display_name":"King Saud University"}],"funders":[{"id":"https://openalex.org/F4320321145","display_name":"King Saud University","ror":"https://ror.org/02f81g417"}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W3029978934.pdf","grobid_xml":"https://content.openalex.org/works/W3029978934.grobid-xml"},"referenced_works_count":35,"referenced_works":["https://openalex.org/W1496462336","https://openalex.org/W1965481583","https://openalex.org/W1974503901","https://openalex.org/W1979848870","https://openalex.org/W1988976727","https://openalex.org/W1993883527","https://openalex.org/W1998216465","https://openalex.org/W2001990291","https://openalex.org/W2005534927","https://openalex.org/W2043618624","https://openalex.org/W2049082138","https://openalex.org/W2060571012","https://openalex.org/W2063774389","https://openalex.org/W2066134817","https://openalex.org/W2067338535","https://openalex.org/W2082910530","https://openalex.org/W2086988408","https://openalex.org/W2109533003","https://openalex.org/W2110717129","https://openalex.org/W2115478782","https://openalex.org/W2119119860","https://openalex.org/W2125697860","https://openalex.org/W2157007713","https://openalex.org/W2168504156","https://openalex.org/W2188492196","https://openalex.org/W2329088563","https://openalex.org/W2486038092","https://openalex.org/W2514070233","https://openalex.org/W2518223548","https://openalex.org/W2904579171","https://openalex.org/W3016399469","https://openalex.org/W3125216635","https://openalex.org/W4243608702","https://openalex.org/W4245777296","https://openalex.org/W6661278794"],"related_works":["https://openalex.org/W2911419698","https://openalex.org/W3030640343","https://openalex.org/W3009110069","https://openalex.org/W2045441198","https://openalex.org/W3083528821","https://openalex.org/W2366236262","https://openalex.org/W2971627378","https://openalex.org/W1526257359","https://openalex.org/W3033482967","https://openalex.org/W4250996952"],"abstract_inverted_index":{"In":[0],"this":[1],"paper,":[2],"we":[3],"propose":[4],"and":[5,28,66,95,112],"study":[6],"a":[7,14,24],"new":[8,33],"probability":[9],"mass":[10],"function":[11],"by":[12,78],"creating":[13],"natural":[15],"discrete":[16,46,116],"analog":[17],"to":[18,43,89],"the":[19,58,76,79,90,101,106],"continuous":[20],"Lindley":[21],"distribution":[22,34,60,108],"as":[23],"mixture":[25],"of":[26,57,75,100,103,105],"geometric":[27],"negative":[29],"binomial":[30],"distributions.":[31],"The":[32],"has":[35],"many":[36,44],"interesting":[37],"properties":[38,56],"that":[39],"make":[40],"it":[41],"superior":[42],"other":[45,115],"distributions,":[47],"particularly":[48],"in":[49],"analyzing":[50],"over-dispersed":[51],"count":[52],"data.":[53],"Several":[54],"statistical":[55],"introduced":[59],"have":[61,109],"been":[62,110],"established":[63],"including":[64],"moments":[65],"moment":[67],"generating":[68],"function,":[69],"residual":[70],"moments,":[71],"characterization,":[72],"entropy,":[73],"estimation":[74],"parameter":[77],"maximum":[80],"likelihood":[81],"method.":[82],"A":[83],"bias":[84],"reduction":[85],"method":[86],"is":[87],"applied":[88],"derived":[91],"estimator;":[92],"its":[93],"existence":[94],"uniqueness":[96],"are":[97],"discussed.":[98],"Applications":[99],"goodness":[102],"fit":[104],"proposed":[107],"examined":[111],"compared":[113],"with":[114],"distributions":[117],"using":[118],"three":[119],"real":[120],"data":[121],"sets":[122],"from":[123],"biological":[124],"sciences.":[125]},"counts_by_year":[{"year":2026,"cited_by_count":4},{"year":2025,"cited_by_count":2},{"year":2024,"cited_by_count":5},{"year":2023,"cited_by_count":12},{"year":2022,"cited_by_count":6},{"year":2021,"cited_by_count":15},{"year":2020,"cited_by_count":2}],"updated_date":"2026-08-11T07:18:39.950985","created_date":"2025-10-10T00:00:00"}
