{"paper":{"title":"Ordering Properties of Order Statistics from Heterogeneous Generalized Exponential and Gamma Populations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.ST","stat.TH"],"primary_cat":"stat.AP","authors_text":"Amarjit Kundu, Asok K. Nanda, Nil Kamal Hazra, Shovan Chowdhury","submitted_at":"2014-10-17T13:55:51Z","abstract_excerpt":"Let $X_1, X_2,\\ldots, X_n$ (resp. $Y_1, Y_2,\\ldots, Y_n$) be independent random variables such that $X_i$ (resp. $Y_i$) follows generalized exponential distribution with shape parameter $\\theta_i$ and scale parameter $\\lambda_i$ (resp. $\\delta_i$), $i=1,2,\\ldots, n$. Here it is shown that if $\\left(\\lambda_1, \\lambda_2,\\ldots,\\lambda_n\\right)$ is $p$-larger than (resp. weakly supermajorizes) $\\left(\\delta_1,\\delta_2,\\ldots,\\delta_n\\right)$, then $X_{n:n}$ will be greater than $Y_{n:n}$ in usual stochastic order (resp. reversed hazard rate order). That no relation exists between $X_{n:n}$ and $"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1410.4724","kind":"arxiv","version":3},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}