Probabilistic mean value theorems for conditioned random variables with applications

Di Crescenzo Antonio; Psarrakos Georgios

摘要

Abstract > In this paper, we propose a probabilistic analogue of the mean value theorem for conditional nonnegative random variables ordered in the hazard rate and reversed hazard rate order, upon conditioning on intervals of the form ( <fi>t</fi> , <fi>∞</fi> ) and [0, <fi>t</fi> ]. This result is then specialized within the proportional hazards model and the proportional reversed hazards model with applications to series systems in reliability theory and to absorption random times of linear birth‐death processes. We also study the comparison of residual entropies and discuss some connections to Wasserstein and stop‐loss distances of random variables. A treatment for the additive hazard rate model is finally provided, with an application to life annuities. </abstract> </span> <span class="z_kbtn z_kbtnclass hoverxs" style="display: none;">展开▼</span> </div> <div class="translation abstracttxt"> <span class="zhankaihshouqi fivelineshidden" id="abstract"> <span>机译：</span><Abstract Type =“Main”XML：Lang =“en”XML：ID =“ASMB2427-ABS-ABS-0001”> <标题类型=“main”>抽象</ title> > 在本文中，我们提出了在危险率下订购的条件非负随机变量的平均值定理的概率模拟，并在调节表格间隔时（ <fi> t </ fi> 那 <fi>∞</ fi> [0， <fi> t </ fi> ]。然后在比例危险模型和比例逆转危险模型中专门从中采用应用于可靠性理论的串联系统的比例逆转危险模型以及吸收线性出生死亡过程的随机性危险模型。我们还研究了残留熵的比较，并讨论了与随机变量的瓦斯斯坦和止损距离的一些联系。最终提供对添加剂危险率模型的治疗，并应用于生命年份。 </ p> </摘要> </span> <span class="z_kbtn z_kbtnclass hoverxs" style="display: none;">展开▼</span> </div> </div> <div class="record"> <h2 class="all_title" id="enpatent33" >著录项</h2> <ul> <li> <span class="lefttit">来源</span> <div style="width: 86%;vertical-align: text-top;display: inline-block;"> <a href='/journal-foreign-19344/'>《Applied stochastic models in business and industry》</a> <b style="margin: 0 2px;">|</b><span>2019年第4期</span><b style="margin: 0 2px;">|</b><span>共16页</span> </div> </li> <li> <div class="author"> <span class="lefttit">作者</span> <p id="fAuthorthree" class="threelineshidden zhankaihshouqi"> <a href="/search.html?doctypes=4_5_6_1-0_4-0_1_2_3_7_9&sertext=Di Crescenzo Antonio&option=202" target="_blank" rel="nofollow">Di Crescenzo Antonio;</a> <a href="/search.html?doctypes=4_5_6_1-0_4-0_1_2_3_7_9&sertext=Psarrakos Georgios&option=202" target="_blank" rel="nofollow">Psarrakos Georgios;</a> </p> <span class="z_kbtnclass z_kbtnclassall hoverxs" id="zkzz" style="display: none;">展开▼</span> </div> </li> <li> <div style="display: flex;"> <span class="lefttit">作者单位</span> <div style="position: relative;margin-left: 3px;max-width: 639px;"> <div class="threelineshidden zhankaihshouqi" id="fOrgthree"> <p>Dipartimento di MatematicaUniversità degli Studi di SalernoFisciano Italy;</p> <p>Department of Statistics and Insurance ScienceUniversity of PiraeusPiraeus Greece;</p> </div> <span class="z_kbtnclass z_kbtnclassall hoverxs" id="zhdw" style="display: none;">展开▼</span> </div> </div> </li> <li > <span class="lefttit">收录信息</span> <span style="width: 86%;vertical-align: text-top;display: inline-block;"></span> </li> <li> <span class="lefttit">原文格式</span> <span>PDF</span> </li> <li> <span class="lefttit">正文语种</span> <span>eng</span> </li> <li> <span class="lefttit">中图分类</span> <span><a href="https://www.zhangqiaokeyan.com/clc/1147.html" title="应用数学">应用数学;</a></span> </li> <li class="antistop"> <span class="lefttit">关键词</span> <p style="width: 86%;vertical-align: text-top;"> <a style="color: #3E7FEB;" href="/search.html?doctypes=4_5_6_1-0_4-0_1_2_3_7_9&sertext=additive hazard model&option=203" rel="nofollow">additive hazard model;</a> <a style="color: #3E7FEB;" href="/search.html?doctypes=4_5_6_1-0_4-0_1_2_3_7_9&sertext=equilibrium distribution&option=203" rel="nofollow">equilibrium distribution;</a> <a style="color: #3E7FEB;" href="/search.html?doctypes=4_5_6_1-0_4-0_1_2_3_7_9&sertext=hazard rate and reversed hazard rate&option=203" rel="nofollow">hazard rate and reversed hazard rate;</a> <a style="color: #3E7FEB;" href="/search.html?doctypes=4_5_6_1-0_4-0_1_2_3_7_9&sertext=mean residual lifetime&option=203" rel="nofollow">mean residual lifetime;</a> <a style="color: #3E7FEB;" href="/search.html?doctypes=4_5_6_1-0_4-0_1_2_3_7_9&sertext=residual entropy&option=203" rel="nofollow">residual entropy;</a> <a style="color: #3E7FEB;" href="/search.html?doctypes=4_5_6_1-0_4-0_1_2_3_7_9&sertext=stop‐loss distance&option=203" rel="nofollow">stop‐loss distance;</a> <a style="color: #3E7FEB;" href="/search.html?doctypes=4_5_6_1-0_4-0_1_2_3_7_9&sertext=Wasserstein distance&option=203" rel="nofollow">Wasserstein distance;</a> </p> <div class="translation"> 机译：添加剂危险模型;平衡分布;危险率和逆转危险率;平均剩余寿命;剩余熵;止损距离;Wasserstein距离; </div> </li> </ul> </div> </div> <div class="literature cardcommon" id="literaturereference" style="display:none"> <div class="similarity "> <h3 class="all_title" id="enpatent111">引文网络</h3> <div class="referencetab clearfix"> <ul id="referencedaohang"> <li dataid="referenceul">参考文献</li> <li dataid="citationul">引证文献</li> <li dataid="commonreferenceul">共引文献</li> <li dataid="commoncitationul">同被引文献</li> <li dataid="tworeferenceul">二级参考文献</li> <li dataid="twocitationul">二级引证文献</li> </ul> </div> <div class="reference_details" id="referenceList"> <ul id="referenceul"></ul> <ul id="citationul"></ul> <ul id="commonreferenceul"></ul> <ul id="commoncitationul"></ul> <ul id="tworeferenceul"></ul> <ul id="twocitationul"></ul> </div> </div> </div> <div class="literature cardcommon"> <div class="similarity "> <h3 class="all_title" id="enpatent66">相似文献</h3> <div class="similaritytab clearfix"> <ul> <li class="active" >外文文献</li> <li >中文文献</li> <li >专利</li> </ul> </div> <div class="similarity_details"> <ul > <li> <div> <b>1. </b><a class="enjiyixqcontent" href="/journal-foreign-detail/0704022680080.html">Probabilistic mean value theorems for conditioned random variables with applications</a> <b>[J]</b> . <span> <a href="/search.html?doctypes=4_5_6_1-0_4-0_1_2_3_7_9&sertext=Di Crescenzo Antonio&option=202" target="_blank" rel="nofollow" class="tuijian_auth tuijian_authcolor">Di Crescenzo Antonio,</a> <a href="/search.html?doctypes=4_5_6_1-0_4-0_1_2_3_7_9&sertext=Psarrakos Georgios&option=202" target="_blank" rel="nofollow" class="tuijian_auth tuijian_authcolor">Psarrakos Georgios </a> <a href="/journal-foreign-19344/" target="_blank" rel="nofollow" class="tuijian_authcolor">Applied stochastic models in business and industry .</a> <span>2019</span><span>,第4期</span> </span> </div> <p class="zwjiyix translation" style="max-width: initial;height: auto;word-break: break-all;white-space: initial;text-overflow: initial;overflow: initial;"> <span>机译：应用程序的条件随机变量的概率平均值定理</span> </p> </li> <li> <div> <b>2. </b><a class="enjiyixqcontent" href="/journal-foreign-detail/070409312860.html">CENTRAL LIMIT THEOREMS FOR DIRECTIONAL AND LINEAR RANDOM VARIABLES WITH APPLICATIONS</a> <b>[J]</b> . <span> <a href="/search.html?doctypes=4_5_6_1-0_4-0_1_2_3_7_9&sertext=Garcia-Portugues Eduardo&option=202" target="_blank" rel="nofollow" class="tuijian_auth tuijian_authcolor">Garcia-Portugues Eduardo,</a> <a href="/search.html?doctypes=4_5_6_1-0_4-0_1_2_3_7_9&sertext=Crujeiras Rosa M.&option=202" target="_blank" rel="nofollow" class="tuijian_auth tuijian_authcolor">Crujeiras Rosa M.,</a> <a href="/search.html?doctypes=4_5_6_1-0_4-0_1_2_3_7_9&sertext=Gonzalez-Manteiga Wenceslao&option=202" target="_blank" rel="nofollow" class="tuijian_auth tuijian_authcolor">Gonzalez-Manteiga Wenceslao </a> <a href="/journal-foreign-28611/" target="_blank" rel="nofollow" class="tuijian_authcolor">Statistica Sinica .</a> <span>2015</span><span>,第3期</span> </span> </div> <p class="zwjiyix translation" style="max-width: initial;height: auto;word-break: break-all;white-space: initial;text-overflow: initial;overflow: initial;"> <span>机译：方向和线性随机变量的中心极限定理及其应用</span> </p> </li> <li> <div> <b>3. </b><a class="enjiyixqcontent" href="/journal-foreign-detail/07040583555.html">Bounds for the covariance of functions of infinite variance stable random variables with applications to central limit theorems and wavelet-based estimation</a> <b>[J]</b> . <span> <a href="/search.html?doctypes=4_5_6_1-0_4-0_1_2_3_7_9&sertext=Pipiras V&option=202" target="_blank" rel="nofollow" class="tuijian_auth tuijian_authcolor">Pipiras V,</a> <a href="/search.html?doctypes=4_5_6_1-0_4-0_1_2_3_7_9&sertext=Taqqu MS&option=202" target="_blank" rel="nofollow" class="tuijian_auth tuijian_authcolor">Taqqu MS,</a> <a href="/search.html?doctypes=4_5_6_1-0_4-0_1_2_3_7_9&sertext=Abry P&option=202" target="_blank" rel="nofollow" class="tuijian_auth tuijian_authcolor">Abry P </a> <a href="/journal-foreign-15566/" target="_blank" rel="nofollow" class="tuijian_authcolor">Bernoulli: official journal of the Bernoulli Society for Mathematical Statistics and Probability .</a> <span>2007</span><span>,第4期</span> </span> </div> <p class="zwjiyix translation" style="max-width: initial;height: auto;word-break: break-all;white-space: initial;text-overflow: initial;overflow: initial;"> <span>机译：无限方差稳定随机变量函数的协方差的界值，适用于中心极限定理和基于小波的估计</span> </p> </li> <li> <div> <b>4. </b><a class="enjiyixqcontent" href="/academic-conference-foreign_meeting-227036_thesis/020515589204.html">Application of non-intrusive polynomial chaos expansion in probabilistic power flow with truncated random variables</a> <b>[C]</b> . <span> <a href="/search.html?doctypes=4_5_6_1-0_4-0_1_2_3_7_9&sertext=F. 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</b><a class="enjiyixqcontent" href="/patent-detail/06130471355712.html">DEVICE FOR DETERMINING PROBABILISTIC CHARACTERISTICS OF RANDOM VARIABLE</a> <b>[P]</b> . <span> 外国专利：  SU1198766A1 </span> <span> . 1985-12-15</span> </div> <p class="zwjiyix translation" style="max-width: initial;height: auto;word-break: break-all;white-space: initial;text-overflow: initial;overflow: initial;"> <span>机译：确定随机变量概率特征的装置 </span> </p> </li> <li> <div> <b>4. </b><a class="enjiyixqcontent" href="/patent-detail/06130439075823.html">Random number generator for cryptographic applications e.g. for chip card, has intermediate condition of pseudo-random number generator stored in memory as initializing information</a> <b>[P]</b> . <span> 外国专利：  DE10357782B3 </span> <span> . 2005-05-04</span> </div> <p class="zwjiyix translation" style="max-width: initial;height: auto;word-break: break-all;white-space: initial;text-overflow: initial;overflow: initial;"> <span>机译：用于密码应用程序的随机数生成器对于芯片卡，将伪随机数生成器的中间条件存储在内存中作为初始化信息 </span> </p> </li> <li> <div> <b>5. </b><a class="enjiyixqcontent" href="/patent-detail/06130436627189.html">Clamping with speed-variable maximum deceleration in the case of application of the random pwm - switching with a variable delay</a> <b>[P]</b> . <span> 外国专利：  DE102005041622A1 </span> <span> . 2006-06-01</span> </div> <p class="zwjiyix translation" style="max-width: initial;height: auto;word-break: break-all;white-space: initial;text-overflow: initial;overflow: initial;"> <span>机译：在应用随机pwm的情况下以最大可变速度夹紧-可变延迟切换 </span> </p> </li> </ul> </div> </div> </div> <div class="theme cardcommon" style="overflow: auto;display:none"> <h3 class="all_title" id="enpatent55">相关主题</h3> <ul id="subject"> </ul> </div> </div> </div> </div> </div> <div id="thesis_get_original1" class="downloadBth" style="bottom: 19px;z-index: 999;" onclick="ywcd('0704022680080','4',7,2,1,'',this,24)" class="delivery" prompt="010401" title="通过人工服务将文献原文发送至邮箱" >获取原文</div> <div class="journalsub-pop-up" style="display: 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