{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,15]],"date-time":"2026-02-15T08:59:28Z","timestamp":1771145968382,"version":"3.50.1"},"reference-count":44,"publisher":"Wiley","issue":"1","license":[{"start":{"date-parts":[[2021,12,18]],"date-time":"2021-12-18T00:00:00Z","timestamp":1639785600000},"content-version":"vor","delay-in-days":351,"URL":"http:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100007446","name":"King Khalid University","doi-asserted-by":"publisher","award":["RGP. 1\/26\/42"],"award-info":[{"award-number":["RGP. 1\/26\/42"]}],"id":[{"id":"10.13039\/501100007446","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/100009392","name":"Prince Sattam bin Abdulaziz University","doi-asserted-by":"publisher","id":[{"id":"10.13039\/100009392","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["onlinelibrary.wiley.com"],"crossmark-restriction":true},"short-container-title":["Complexity"],"published-print":{"date-parts":[[2021,1]]},"abstract":"<jats:p>In the absence of a correct distribution theory for complex data, neutrosophic algebra can be very useful in quantifying uncertainty. In applied data analysis, implementation of existing gamma distribution becomes inadequate for some applications when dealing with an imprecise, uncertain, or vague dataset. Most existing works have explored distributional properties of the gamma distribution under the assumption that data do not have any kind of indeterminacy. Yet, analytical properties of the gamma model for the more realistic setting when data involved uncertainties remain largely underdeveloped. This paper fills such a gap and develops the notion of neutrosophic gamma distribution (NGD). The proposed distribution represents a generalized structure of the existing gamma distribution. The basic distributional properties, including moments, shape coefficients, and moment generating function (MGF), are established. Several examples are considered to emphasize the relevance of the proposed NGD for dealing with circumstances with inadequate or ambiguous knowledge about the distributional characteristics. The estimation framework for treating vague parameters of the NGD is developed. The Monte Carlo simulation is implemented to examine the performance of the proposed model. The proposed model is applied to a real dataset for the purpose of dealing with inaccurate and vague statistical data. Results show that the NGD has better flexibility in handling real data over the conventional gamma distribution.<\/jats:p>","DOI":"10.1155\/2021\/3701236","type":"journal-article","created":{"date-parts":[[2021,12,18]],"date-time":"2021-12-18T18:35:09Z","timestamp":1639852509000},"update-policy":"https:\/\/doi.org\/10.1002\/crossmark_policy","source":"Crossref","is-referenced-by-count":18,"title":["On Statistical Development of Neutrosophic Gamma Distribution with Applications to Complex Data Analysis"],"prefix":"10.1155","volume":"2021","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-5568-4302","authenticated-orcid":false,"given":"Zahid","family":"Khan","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Afrah","family":"Al-Bossly","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-8427-8760","authenticated-orcid":false,"given":"Mohammed M. A.","family":"Almazah","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-2255-1167","authenticated-orcid":false,"given":"Fuad S.","family":"Alduais","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"311","published-online":{"date-parts":[[2021,12,18]]},"reference":[{"key":"e_1_2_10_1_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.knosys.2020.106368"},{"key":"e_1_2_10_2_2","doi-asserted-by":"publisher","DOI":"10.1080\/00401706.2017.1328377"},{"key":"e_1_2_10_3_2","doi-asserted-by":"publisher","DOI":"10.1080\/16843703.2021.1953241"},{"key":"e_1_2_10_4_2","doi-asserted-by":"crossref","unstructured":"ZhangY. Martinez-GarciaM. andGordonT. Human response delay estimation and monitoring using gamma distribution analysis Proceedings of the Proc. IEEE Int. Conf. Syst. Man Cybern. SMC 7 October 2018 Miyazaki Japan IEEE 807\u2013812 https:\/\/doi.org\/10.1109\/smc.2018.00145 2-s2.0-85062228203.","DOI":"10.1109\/SMC.2018.00145"},{"key":"e_1_2_10_5_2","doi-asserted-by":"publisher","DOI":"10.1017\/asb.2017.9"},{"key":"e_1_2_10_6_2","doi-asserted-by":"publisher","DOI":"10.1007\/s40745-018-0169-9"},{"key":"e_1_2_10_7_2","doi-asserted-by":"publisher","DOI":"10.1002\/sim.2836"},{"key":"e_1_2_10_8_2","doi-asserted-by":"publisher","DOI":"10.1093\/bioinformatics\/btp687"},{"key":"e_1_2_10_9_2","first-page":"419","article-title":"Use of gamma distribution in hydrological analysis","volume":"24","author":"Aksoy H.","year":"2000","journal-title":"Turkish Journal of Engineering and Environmental Sciences"},{"key":"e_1_2_10_10_2","doi-asserted-by":"publisher","DOI":"10.1198\/tech.2003.s139"},{"key":"e_1_2_10_11_2","doi-asserted-by":"publisher","DOI":"10.1002\/joc.1441"},{"key":"e_1_2_10_12_2","doi-asserted-by":"publisher","DOI":"10.1186\/1471-2105-15-s17-s3"},{"key":"e_1_2_10_13_2","doi-asserted-by":"publisher","DOI":"10.1080\/00949655.2015.1080705"},{"key":"e_1_2_10_14_2","doi-asserted-by":"publisher","DOI":"10.1002\/env.2261"},{"key":"e_1_2_10_15_2","doi-asserted-by":"publisher","DOI":"10.1007\/s11587-019-00471-x"},{"key":"e_1_2_10_16_2","doi-asserted-by":"publisher","DOI":"10.1214\/aoms\/1177704481"},{"key":"e_1_2_10_17_2","volume-title":"A Unifying Field in Logics: Neutrosophic Logic. Neutrosophy, Neutrosophic Set, Neutrosophic Probability","author":"Smarandache F.","year":"1999"},{"key":"e_1_2_10_18_2","volume-title":"New Trends in Neutrosophic Theory and Applications","author":"Smarandache F.","year":"2016"},{"key":"e_1_2_10_19_2","first-page":"287","article-title":"Neutrosophic set a generalization of the intuitionistic fuzzy sets","volume":"24","author":"Smarandache F.","year":"2005","journal-title":"International Journal of Pure and Applied Mathematics"},{"key":"e_1_2_10_20_2","doi-asserted-by":"publisher","DOI":"10.1007\/s40815-017-0380-4"},{"key":"e_1_2_10_21_2","doi-asserted-by":"publisher","DOI":"10.5923\/j.computer.20120207.01"},{"key":"e_1_2_10_22_2","volume-title":"New Trends in Neutrosophic Theory and Applications","author":"Smarandache F.","year":"2018"},{"key":"e_1_2_10_23_2","doi-asserted-by":"publisher","DOI":"10.3233\/jifs-171952"},{"key":"e_1_2_10_24_2","volume-title":"Neutrosophical Statistics","author":"Smarandache F.","year":"2014"},{"key":"e_1_2_10_25_2","unstructured":"SmarandacheF. Neutrosophy and neutrosophic logic Proceedings of the First International Conference on Neutrosophy Neutrosophic Logic Set Probability and Statistics 1 December 2002 Gallup NM 87301 USA University of New Mexico."},{"key":"e_1_2_10_26_2","article-title":"The neutrosophic statistics distribution, more Problems, more solutions","volume":"12","author":"Patro S. K.","year":"2016","journal-title":"Neutrosophic Sets and Systems"},{"key":"e_1_2_10_27_2","volume-title":"Introduction to Neutrosophic Measure, Integral, Probability","author":"Smarandache F.","year":"2015"},{"key":"e_1_2_10_28_2","volume-title":"New Neutrosophic Crisp Topological Concepts","author":"Salama A. A.","year":"2014"},{"key":"e_1_2_10_29_2","doi-asserted-by":"publisher","DOI":"10.1109\/access.2020.2995998"},{"key":"e_1_2_10_30_2","doi-asserted-by":"publisher","DOI":"10.3233\/jifs-191439"},{"key":"e_1_2_10_31_2","doi-asserted-by":"publisher","DOI":"10.1109\/access.2021.3078150"},{"key":"e_1_2_10_32_2","doi-asserted-by":"publisher","DOI":"10.3390\/sym10110562"},{"key":"e_1_2_10_33_2","volume-title":"Neutrosophic Precalculus and Neutrosophic Calculus","author":"Smarandache F.","year":"2018"},{"key":"e_1_2_10_34_2","first-page":"30","article-title":"Some neutrosophic probability distributions","volume":"38","author":"Alhabib R.","year":"2018","journal-title":"Neutrosophic Sets and Systems"},{"key":"e_1_2_10_35_2","doi-asserted-by":"publisher","DOI":"10.1155\/2021\/5970613"},{"key":"e_1_2_10_36_2","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-030-57197-9_8"},{"key":"e_1_2_10_37_2","first-page":"209","article-title":"Neutrosophic beta distribution with properties and applications","volume":"41","author":"Sherwan R. A. K.","year":"2021","journal-title":"Neutrosophic Sets Syst"},{"key":"e_1_2_10_38_2","doi-asserted-by":"publisher","DOI":"10.1155\/2021\/6635846"},{"key":"e_1_2_10_39_2","doi-asserted-by":"publisher","DOI":"10.1371\/journal.pone.0255671"},{"key":"e_1_2_10_40_2","doi-asserted-by":"publisher","DOI":"10.1038\/s41598-021-97344-x"},{"key":"e_1_2_10_41_2","doi-asserted-by":"publisher","DOI":"10.1155\/2021\/9766986"},{"key":"e_1_2_10_42_2","volume-title":"Model Selection","author":"Linhart H.","year":"1986"},{"key":"e_1_2_10_43_2","doi-asserted-by":"publisher","DOI":"10.3390\/sym12050851"},{"key":"e_1_2_10_44_2","doi-asserted-by":"publisher","DOI":"10.5351\/csam.2016.23.2.147"}],"container-title":["Complexity"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/downloads.hindawi.com\/journals\/complexity\/2021\/3701236.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/downloads.hindawi.com\/journals\/complexity\/2021\/3701236.xml","content-type":"application\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/pdf\/10.1155\/2021\/3701236","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2024,8,9]],"date-time":"2024-08-09T22:31:26Z","timestamp":1723242686000},"score":1,"resource":{"primary":{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/10.1155\/2021\/3701236"}},"subtitle":[],"editor":[{"given":"Zeljko","family":"Stevic","sequence":"additional","affiliation":[],"role":[{"role":"editor","vocabulary":"crossref"}]}],"short-title":[],"issued":{"date-parts":[[2021,1]]},"references-count":44,"journal-issue":{"issue":"1","published-print":{"date-parts":[[2021,1]]}},"alternative-id":["10.1155\/2021\/3701236"],"URL":"https:\/\/doi.org\/10.1155\/2021\/3701236","archive":["Portico"],"relation":{},"ISSN":["1076-2787","1099-0526"],"issn-type":[{"value":"1076-2787","type":"print"},{"value":"1099-0526","type":"electronic"}],"subject":[],"published":{"date-parts":[[2021,1]]},"assertion":[{"value":"2021-09-18","order":0,"name":"received","label":"Received","group":{"name":"publication_history","label":"Publication History"}},{"value":"2021-12-03","order":2,"name":"accepted","label":"Accepted","group":{"name":"publication_history","label":"Publication History"}},{"value":"2021-12-18","order":3,"name":"published","label":"Published","group":{"name":"publication_history","label":"Publication History"}}],"article-number":"3701236"}}