{"65532":{"#nid":"65532","#data":{"type":"event","title":"Peakedness and Peakedness Ordering","body":[{"value":"\u003Cp\u003E\u003Cstrong\u003ETITLE:\u0026nbsp; \u003C\/strong\u003EPeakedness and Peakedness Ordering\u003C\/p\u003E\u003Cp\u003E\u003Cstrong\u003ESPEAKER:\u003C\/strong\u003E\u0026nbsp; Hammou El Barmi\u003C\/p\u003E\u003Cp\u003E\u003Cstrong\u003EABSTRACT:\u003C\/strong\u003E\u003C\/p\u003E\u003Ctable border=\u00220\u0022 cellspacing=\u00220\u0022 cellpadding=\u00220\u0022 width=\u0022576\u0022\u003E\n \u003Ctbody\u003E\u003Ctr\u003E\n  \u003Ctd align=\u0022left\u0022 valign=\u0022top\u0022\u003E\n  \u003Cp\u003EThe peakedness of a random variable (RV) X about a point a\n  is de\ufb01ned by Pa(x)= P (|X \u2212 a|\u2264 x),x \u2265 0. A RV X is said to be less peaked about a than a RV Y about b, denoted\n  by X \u2264pkd(a,b) Y , if P (|X \u2212 a|\u2264 x) \u2264 P (|Y \u2212 b|\u2264 x) for all x \u2265 0, i.e., |X \u2212 a| is stochastically larger than |Y \u2212 b|. These generalize the original de\ufb01nitions of\n  Birnbaum (1948) who considered the cases where X\n  and Y were symmetric about a and b,\n  respectively. Statistical inferences about the distribution functions of\n  continuous X and Y under peakedness ordering in the symmetric\n  case have been treated in the literature. Rojo et al. (2007) provided\n  estimators of the distributions in the general case and analyzed their\n  properties. We show that these estimators could have poor asymptotic\n  properties relative to those of the empiricals. We provide improved\n  estimators of the DFs, show that they are consistent, derive the weak\n  convergence of the estimators, compare them with the empirical estimators,\n  and provide formulas for statistical inferences. \u003C\/p\u003E\n  \u003C\/td\u003E\n \u003C\/tr\u003E\n\u003C\/tbody\u003E\u003C\/table\u003E","summary":null,"format":"limited_html"}],"field_subtitle":"","field_summary":"","field_summary_sentence":[{"value":"Peakedness and Peakedness Ordering"}],"uid":"27187","created_gmt":"2011-04-12 13:38:44","changed_gmt":"2016-10-08 01:54:46","author":"Anita Race","boilerplate_text":"","field_publication":"","field_article_url":"","field_event_time":{"event_time_start":"2011-04-21T13:00:00-04:00","event_time_end":"2011-04-21T14:00:00-04:00","event_time_end_last":"2011-04-21T14:00:00-04:00","gmt_time_start":"2011-04-21 17:00:00","gmt_time_end":"2011-04-21 18:00:00","gmt_time_end_last":"2011-04-21 18:00:00","rrule":null,"timezone":"America\/New_York"},"extras":[],"groups":[{"id":"1242","name":"School of Industrial and Systems Engineering (ISYE)"}],"categories":[],"keywords":[],"core_research_areas":[],"news_room_topics":[],"event_categories":[],"invited_audience":[],"affiliations":[],"classification":[],"areas_of_expertise":[],"news_and_recent_appearances":[],"phone":[],"contact":[],"email":[],"slides":[],"orientation":[],"userdata":""}}}