Moments of the Forward Recurrence Time in a Renewal Process
The forward recurrence time (also known as residual or excess lifetime) is one of the key quantities in renewal theory. The study of the variability of the forward recurrence time (as measured by the variance or the standard deviation) is important especially when we want to predict when the next ev...
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| Veröffentlicht in: | Methodology and computing in applied probability 2020-12, Vol.22 (4), p.1591-1600 |
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| creator | Losidis, Sotirios Politis, Konstadinos |
| description | The forward recurrence time (also known as residual or excess lifetime) is one of the key quantities in renewal theory. The study of the variability of the forward recurrence time (as measured by the variance or the standard deviation) is important especially when we want to predict when the next event will occur. In this paper we study the moments of the forward recurrence time in a renewal process. In particular, we discuss the monotonicity of the variance for these recurrence times and study the covariance between the forward recurrence time at
t
and the number of renewals over [0,
t
]. The forward recurrence time practically applies in a number of cases. For example, in preventive replacement within any production process the forward recurrence time is the remaining time of the component. In medicine, for a chronic disease observed from one point onwards, the forward recurrence time is defined as the time in disease state until healing. |
| doi_str_mv | 10.1007/s11009-018-9681-9 |
| format | Article |
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t
and the number of renewals over [0,
t
]. The forward recurrence time practically applies in a number of cases. For example, in preventive replacement within any production process the forward recurrence time is the remaining time of the component. In medicine, for a chronic disease observed from one point onwards, the forward recurrence time is defined as the time in disease state until healing.</description><identifier>ISSN: 1387-5841</identifier><identifier>EISSN: 1573-7713</identifier><identifier>DOI: 10.1007/s11009-018-9681-9</identifier><language>eng</language><publisher>New York: Springer US</publisher><subject>Business and Management ; Covariance ; Economics ; Electrical Engineering ; Life Sciences ; Mathematics and Statistics ; Predictions ; Probability ; Statistics ; Time measurement ; Variance</subject><ispartof>Methodology and computing in applied probability, 2020-12, Vol.22 (4), p.1591-1600</ispartof><rights>Springer Science+Business Media, LLC, part of Springer Nature 2018</rights><rights>Methodology and Computing in Applied Probability is a copyright of Springer, (2018). All Rights Reserved.</rights><rights>Springer Science+Business Media, LLC, part of Springer Nature 2018.</rights><lds50>peer_reviewed</lds50><woscitedreferencessubscribed>false</woscitedreferencessubscribed><citedby>FETCH-LOGICAL-c344t-e1d79d7256aac6fd193308acb65ae3b2246a3b00e1e3048beaf82d41eec716443</citedby><cites>FETCH-LOGICAL-c344t-e1d79d7256aac6fd193308acb65ae3b2246a3b00e1e3048beaf82d41eec716443</cites><orcidid>0000-0002-1067-2594</orcidid></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><linktopdf>$$Uhttps://link.springer.com/content/pdf/10.1007/s11009-018-9681-9$$EPDF$$P50$$Gspringer$$H</linktopdf><linktohtml>$$Uhttps://link.springer.com/10.1007/s11009-018-9681-9$$EHTML$$P50$$Gspringer$$H</linktohtml><link.rule.ids>314,780,784,27924,27925,41488,42557,51319</link.rule.ids></links><search><creatorcontrib>Losidis, Sotirios</creatorcontrib><creatorcontrib>Politis, Konstadinos</creatorcontrib><title>Moments of the Forward Recurrence Time in a Renewal Process</title><title>Methodology and computing in applied probability</title><addtitle>Methodol Comput Appl Probab</addtitle><description>The forward recurrence time (also known as residual or excess lifetime) is one of the key quantities in renewal theory. The study of the variability of the forward recurrence time (as measured by the variance or the standard deviation) is important especially when we want to predict when the next event will occur. In this paper we study the moments of the forward recurrence time in a renewal process. In particular, we discuss the monotonicity of the variance for these recurrence times and study the covariance between the forward recurrence time at
t
and the number of renewals over [0,
t
]. The forward recurrence time practically applies in a number of cases. For example, in preventive replacement within any production process the forward recurrence time is the remaining time of the component. In medicine, for a chronic disease observed from one point onwards, the forward recurrence time is defined as the time in disease state until healing.</description><subject>Business and Management</subject><subject>Covariance</subject><subject>Economics</subject><subject>Electrical Engineering</subject><subject>Life Sciences</subject><subject>Mathematics and Statistics</subject><subject>Predictions</subject><subject>Probability</subject><subject>Statistics</subject><subject>Time measurement</subject><subject>Variance</subject><issn>1387-5841</issn><issn>1573-7713</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2020</creationdate><recordtype>article</recordtype><sourceid>ABUWG</sourceid><sourceid>AFKRA</sourceid><sourceid>AZQEC</sourceid><sourceid>BENPR</sourceid><sourceid>CCPQU</sourceid><sourceid>DWQXO</sourceid><sourceid>GNUQQ</sourceid><recordid>eNp9kE1LAzEQhoMoWKs_wFvAczSTj00WT1JsFSqK1HPIZme1pd3UZEvx37tlBU96mmF43nfgIeQS-DVwbm4y9KNkHCwrCwusPCIj0EYyY0Ae97u0hmmr4JSc5bziXICWakRun-IG2y7T2NDuA-k0pr1PNX3FsEsJ24B0sdwgXbbU98cW935NX1IMmPM5OWn8OuPFzxyTt-n9YvLA5s-zx8ndnAWpVMcQalPWRujC-1A0NZRScutDVWiPshJCFV5WnCOg5MpW6BsragWIwUChlByTq6F3m-LnDnPnVnGX2v6lE8qA0tLo4l8KwHAprDhQMFAhxZwTNm6blhufvhxwdzDpBpOuN-kOJl3ZZ8SQyT3bvmP6bf479A0oS3PC</recordid><startdate>20201201</startdate><enddate>20201201</enddate><creator>Losidis, Sotirios</creator><creator>Politis, Konstadinos</creator><general>Springer US</general><general>Springer Nature B.V</general><scope>AAYXX</scope><scope>CITATION</scope><scope>3V.</scope><scope>7WY</scope><scope>7WZ</scope><scope>7XB</scope><scope>87Z</scope><scope>88I</scope><scope>8AO</scope><scope>8FE</scope><scope>8FG</scope><scope>8FK</scope><scope>8FL</scope><scope>ABJCF</scope><scope>ABUWG</scope><scope>AFKRA</scope><scope>ARAPS</scope><scope>AZQEC</scope><scope>BENPR</scope><scope>BEZIV</scope><scope>BGLVJ</scope><scope>CCPQU</scope><scope>DWQXO</scope><scope>FRNLG</scope><scope>F~G</scope><scope>GNUQQ</scope><scope>HCIFZ</scope><scope>JQ2</scope><scope>K60</scope><scope>K6~</scope><scope>K7-</scope><scope>L.-</scope><scope>L6V</scope><scope>M0C</scope><scope>M2P</scope><scope>M7S</scope><scope>P5Z</scope><scope>P62</scope><scope>PQBIZ</scope><scope>PQBZA</scope><scope>PQEST</scope><scope>PQQKQ</scope><scope>PQUKI</scope><scope>PRINS</scope><scope>PTHSS</scope><scope>PYYUZ</scope><scope>Q9U</scope><orcidid>https://orcid.org/0000-0002-1067-2594</orcidid></search><sort><creationdate>20201201</creationdate><title>Moments of the Forward Recurrence Time in a Renewal Process</title><author>Losidis, Sotirios ; 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t
and the number of renewals over [0,
t
]. The forward recurrence time practically applies in a number of cases. For example, in preventive replacement within any production process the forward recurrence time is the remaining time of the component. In medicine, for a chronic disease observed from one point onwards, the forward recurrence time is defined as the time in disease state until healing.</abstract><cop>New York</cop><pub>Springer US</pub><doi>10.1007/s11009-018-9681-9</doi><tpages>10</tpages><orcidid>https://orcid.org/0000-0002-1067-2594</orcidid></addata></record> |
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| source | SpringerNature Journals; EBSCOhost Business Source Complete |
| subjects | Business and Management Covariance Economics Electrical Engineering Life Sciences Mathematics and Statistics Predictions Probability Statistics Time measurement Variance |
| title | Moments of the Forward Recurrence Time in a Renewal Process |
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