{"id":25225,"date":"2026-04-01T17:08:27","date_gmt":"2026-04-01T17:08:27","guid":{"rendered":"https:\/\/scientificassociation.org\/?post_type=journal-paper&#038;p=25225"},"modified":"2026-04-01T17:08:27","modified_gmt":"2026-04-01T17:08:27","slug":"introducing-kth-order-equilibrium-lindley-distribution-theory-and-application","status":"publish","type":"journal-paper","link":"https:\/\/scientificassociation.org\/ar\/journal-paper\/introducing-kth-order-equilibrium-lindley-distribution-theory-and-application\/","title":{"rendered":"Introducing Kth-order equilibrium Lindley distribution: Theory and application"},"content":{"rendered":"<div class=\"padding_abstract justify ltr\">This paper introduces the K<sup>th<\/sup>-order Equilibrium Lindley Distribution (KELD), a new two-parameter probability model developed by applying the $K<sup>th<\/sup>-order equilibrium transformation to the Lindley distribution. The motivation for proposing this model arises from the need for more flexible lifetime distributions capable of representing various hazard rate behaviors such as increasing, decreasing, and bathtub shaped (initially decreasing then increasing) patterns commonly observed in reliability and survival studies. Several important statistical properties of KELD are derived and explored, including moments, the moment generating function, entropy measures, stochastic ordering, mean residual and past life functions, and ageing characteristics. A detailed analysis of order statistics, including the sample range and median, is also provided, along with the introduction of a bivariate extension of KELD. Parameters are estimated using the maximum likelihood method, and their asymptotic properties such as bias, mean square error, and normality are evaluated through extensive simulation studies using the Anderson\u2013Darling test. Finally, two real-life datasets are analyzed to demonstrate the applicability of the proposed model. Model performance is assessed using AIC, BIC, HQIC, CAIC, and the K\u2013S test, confirming that KELD provides a better fit compared to other recent extensions of the Lindley distribution.<\/div>\n","protected":false},"featured_media":25196,"template":"","meta":{"_acf_changed":false},"journal-name":[218],"paper-tag":[233,269],"class_list":["post-25225","journal-paper","type-journal-paper","status-publish","has-post-thumbnail","hentry","journal-name-cjmss","paper-tag-issue-1","paper-tag-volume-5"],"acf":[],"_links":{"self":[{"href":"https:\/\/scientificassociation.org\/ar\/wp-json\/wp\/v2\/journal-paper\/25225","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/scientificassociation.org\/ar\/wp-json\/wp\/v2\/journal-paper"}],"about":[{"href":"https:\/\/scientificassociation.org\/ar\/wp-json\/wp\/v2\/types\/journal-paper"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/scientificassociation.org\/ar\/wp-json\/wp\/v2\/media\/25196"}],"wp:attachment":[{"href":"https:\/\/scientificassociation.org\/ar\/wp-json\/wp\/v2\/media?parent=25225"}],"wp:term":[{"taxonomy":"journal-name","embeddable":true,"href":"https:\/\/scientificassociation.org\/ar\/wp-json\/wp\/v2\/journal-name?post=25225"},{"taxonomy":"paper-tag","embeddable":true,"href":"https:\/\/scientificassociation.org\/ar\/wp-json\/wp\/v2\/paper-tag?post=25225"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}