Fractional generalized cumulative entropy and its dynamic version
•A fractional version of the generalized cumulative entropy is introduced.•The proposed notion is a variability measure connected with fractional integrals.•This is suitable for distributions satisfying the proportional reversed hazard model.•The related dynamic measure is an extension of the mean i...
Uloženo v:
| Vydáno v: | Communications in nonlinear science & numerical simulation Ročník 102; s. 105899 |
|---|---|
| Hlavní autoři: | , , |
| Médium: | Journal Article |
| Jazyk: | angličtina |
| Vydáno: |
Amsterdam
Elsevier B.V
01.11.2021
Elsevier Science Ltd |
| Témata: | |
| ISSN: | 1007-5704, 1878-7274 |
| On-line přístup: | Získat plný text |
| Tagy: |
Přidat tag
Žádné tagy, Buďte první, kdo vytvoří štítek k tomuto záznamu!
|
| Abstract | •A fractional version of the generalized cumulative entropy is introduced.•The proposed notion is a variability measure connected with fractional integrals.•This is suitable for distributions satisfying the proportional reversed hazard model.•The related dynamic measure is an extension of the mean inactivity time.•We discuss properties of the empirical measure and apply it to real data.
Following the theory of information measures based on the cumulative distribution function, we propose the fractional generalized cumulative entropy, and its dynamic version. These entropies are particularly suitable to deal with distributions satisfying the proportional reversed hazard model. We study the connection with fractional integrals, and some bounds and comparisons based on stochastic orderings, that allow to show that the proposed measure is actually a variability measure. The investigation also involves various notions of reliability theory, since the considered dynamic measure is a suitable extension of the mean inactivity time. We also introduce the empirical generalized fractional cumulative entropy as a non-parametric estimator of the new measure. It is shown that the empirical measure converges to the proposed notion almost surely. Then, we address the stability of the empirical measure and provide an example of application to real data. Finally, a central limit theorem is established under the exponential distribution. |
|---|---|
| AbstractList | Following the theory of information measures based on the cumulative distribution function, we propose the fractional generalized cumulative entropy, and its dynamic version. These entropies are particularly suitable to deal with distributions satisfying the proportional reversed hazard model. We study the connection with fractional integrals, and some bounds and comparisons based on stochastic orderings, that allow to show that the proposed measure is actually a variability measure. The investigation also involves various notions of reliability theory, since the considered dynamic measure is a suitable extension of the mean inactivity time. We also introduce the empirical generalized fractional cumulative entropy as a non-parametric estimator of the new measure. It is shown that the empirical measure converges to the proposed notion almost surely. Then, we address the stability of the empirical measure and provide an example of application to real data. Finally, a central limit theorem is established under the exponential distribution. •A fractional version of the generalized cumulative entropy is introduced.•The proposed notion is a variability measure connected with fractional integrals.•This is suitable for distributions satisfying the proportional reversed hazard model.•The related dynamic measure is an extension of the mean inactivity time.•We discuss properties of the empirical measure and apply it to real data. Following the theory of information measures based on the cumulative distribution function, we propose the fractional generalized cumulative entropy, and its dynamic version. These entropies are particularly suitable to deal with distributions satisfying the proportional reversed hazard model. We study the connection with fractional integrals, and some bounds and comparisons based on stochastic orderings, that allow to show that the proposed measure is actually a variability measure. The investigation also involves various notions of reliability theory, since the considered dynamic measure is a suitable extension of the mean inactivity time. We also introduce the empirical generalized fractional cumulative entropy as a non-parametric estimator of the new measure. It is shown that the empirical measure converges to the proposed notion almost surely. Then, we address the stability of the empirical measure and provide an example of application to real data. Finally, a central limit theorem is established under the exponential distribution. |
| ArticleNumber | 105899 |
| Author | Meoli, Alessandra Di Crescenzo, Antonio Kayal, Suchandan |
| Author_xml | – sequence: 1 givenname: Antonio orcidid: 0000-0003-4751-7341 surname: Di Crescenzo fullname: Di Crescenzo, Antonio email: adicrescenzo@unisa.it organization: Dipartimento di Matematica, Università degli Studi di Salerno, Via Giovanni Paolo II, 132, Fisciano (SA) 84084, Italy – sequence: 2 givenname: Suchandan surname: Kayal fullname: Kayal, Suchandan email: kayals@nitrkl.ac.in, suchandan.kayal@gmail.com organization: Department of Mathematics, National Institute of Technology Rourkela, Rourkela 769008, India – sequence: 3 givenname: Alessandra surname: Meoli fullname: Meoli, Alessandra email: ameoli@unisa.it organization: Dipartimento di Matematica, Università degli Studi di Salerno, Via Giovanni Paolo II, 132, Fisciano (SA) 84084, Italy |
| BookMark | eNqFkMtOwzAQRS1UJNrCF7CJxDrFzzhZsKgqXlIlNrC2HD-Qo9QptlOpfD0uYcUCNjOj0T2juXcBZn7wBoBrBFcIouq2WykffVxhiFHesLppzsAc1bwuOeZ0lmcIeck4pBdgEWMHM9UwOgfrhyBVcoOXffFuvAmyd59GF2rcjb1M7mAK41MY9sdCel24FAt99HLnVHEwIWbwEpxb2Udz9dOX4O3h_nXzVG5fHp83622pCEGprClDBDHLlWraFiJLFGpp27RVLtZahigjGmFd6YpbWWNUQW0rS7Fu25oQsgQ30919GD5GE5PohjHkv6PAjBOICa1gVjWTSoUhxmCsUC7Jk8EUpOsFguKUmOjEd2LilJiYEsss-cXug9vJcPyHupsok80fnAkiKme8MtoFo5LQg_uT_wIzYYi0 |
| CitedBy_id | crossref_primary_10_1080_03610918_2024_2411362 crossref_primary_10_1080_03610926_2024_2447825 crossref_primary_10_1017_S0269964824000068 crossref_primary_10_1080_00949655_2025_2458718 crossref_primary_10_3390_fractalfract7030241 crossref_primary_10_3390_e24091275 crossref_primary_10_1007_s13171_023_00316_8 crossref_primary_10_3390_e24040444 crossref_primary_10_1016_j_cnsns_2025_109106 crossref_primary_10_3390_fractalfract9060388 crossref_primary_10_3390_e25111525 crossref_primary_10_1016_j_ejor_2024_09_047 crossref_primary_10_1007_s00184_021_00849_8 crossref_primary_10_1016_j_physa_2023_128552 crossref_primary_10_1007_s11009_023_10035_0 crossref_primary_10_3390_sym13101964 crossref_primary_10_1007_s00184_023_00931_3 crossref_primary_10_3390_e24081037 crossref_primary_10_1080_03610926_2022_2044493 crossref_primary_10_3390_fractalfract8100568 crossref_primary_10_3390_e24081041 crossref_primary_10_3390_fractalfract6070400 crossref_primary_10_3390_math10162828 crossref_primary_10_1016_j_jmva_2024_105394 crossref_primary_10_1016_j_physd_2025_134545 crossref_primary_10_1007_s11009_025_10176_4 crossref_primary_10_1515_phys_2022_0234 crossref_primary_10_3390_sym13112001 |
| Cites_doi | 10.1017/S0269964816000218 10.1016/j.jspi.2007.03.029 10.1080/03610918.2015.1011331 10.1140/epjp/i2019-12554-9 10.1002/j.1538-7305.1948.tb01338.x 10.1109/TIT.2004.828057 10.1142/S0219477520500388 10.1016/j.physa.2019.122582 10.1016/j.jspi.2006.06.035 10.1017/jpr.2020.40 10.1016/S0167-7152(00)00127-9 10.1063/1.5091545 10.1080/03610928608829189 10.3390/e22060709 10.1007/s11009-018-9649-9 10.1016/j.insmatheco.2019.03.005 10.1016/j.ipl.2012.08.019 10.1007/s00184-012-0408-6 10.1016/j.cnsns.2019.104879 10.1016/j.jspi.2009.07.015 10.3390/e16042350 10.1002/asmb.434 10.1239/jap/1032374628 10.1016/j.physleta.2009.05.026 10.1016/j.jspi.2009.05.038 |
| ContentType | Journal Article |
| Copyright | 2021 Elsevier B.V. Copyright Elsevier Science Ltd. Nov 2021 |
| Copyright_xml | – notice: 2021 Elsevier B.V. – notice: Copyright Elsevier Science Ltd. Nov 2021 |
| DBID | AAYXX CITATION |
| DOI | 10.1016/j.cnsns.2021.105899 |
| DatabaseName | CrossRef |
| DatabaseTitle | CrossRef |
| DatabaseTitleList | |
| DeliveryMethod | fulltext_linktorsrc |
| Discipline | Applied Sciences |
| EISSN | 1878-7274 |
| ExternalDocumentID | 10_1016_j_cnsns_2021_105899 S1007570421002112 |
| GroupedDBID | --K --M -01 -0A -0I -0Y -SA -S~ .~1 0R~ 1B1 1RT 1~. 1~5 29F 4.4 457 4G. 5GY 5VR 5VS 7-5 71M 8P~ 92M 9D9 9DA AACTN AAEDT AAEDW AAIAV AAIKJ AAKOC AALRI AAOAW AAQFI AAQXK AAXUO ABAOU ABFNM ABJNI ABMAC ABNEU ABXDB ABYKQ ACAZW ACDAQ ACFVG ACGFS ACNNM ACRLP ADBBV ADEZE ADGUI ADMUD ADTZH AEBSH AECPX AEKER AENEX AFKWA AFTJW AFUIB AGHFR AGUBO AGYEJ AHJVU AIEXJ AIGVJ AIKHN AITUG AIVDX AJBFU AJOXV ALMA_UNASSIGNED_HOLDINGS AMFUW AMRAJ ARUGR ASPBG AVWKF AXJTR AZFZN BJAXD BKOJK BLXMC CAJEA CAJUS CCEZO CCVFK CHBEP CS3 CUBFJ DU5 EBS EFJIC EFLBG EJD EO8 EO9 EP2 EP3 FA0 FDB FEDTE FGOYB FIRID FNPLU FYGXN G-Q GBLVA HVGLF HZ~ IHE J1W JJJVA JUIAU KOM M41 MHUIS MO0 N9A O-L O9- OAUVE OGIMB OZT P-8 P-9 P2P PC. Q-- Q-0 Q38 R-A R-I R2- RIG ROL RPZ RT1 RT9 S.. SDF SDG SES SEW SPC SPCBC SPD SSQ SST SSW SSZ T5K T8Q T8Y U1F U1G U5A U5I U5K UHS ~G- ~LA 9DU AATTM AAXKI AAYWO AAYXX ABWVN ACLOT ACRPL ACVFH ADCNI ADNMO AEIPS AEUPX AFJKZ AFPUW AGQPQ AIGII AIIUN AKBMS AKRWK AKYEP ANKPU APXCP CITATION EFKBS ~HD AFXIZ AGCQF AGRNS BNPGV SSH |
| ID | FETCH-LOGICAL-c331t-8451315f7cc9bb01f3c1b4b9b64b9fff51453d12d6d67fa82160df6f42dbb8333 |
| ISICitedReferencesCount | 32 |
| ISICitedReferencesURI | http://www.webofscience.com/api/gateway?GWVersion=2&SrcApp=Summon&SrcAuth=ProQuest&DestLinkType=CitingArticles&DestApp=WOS_CPL&KeyUT=000684932600014&url=https%3A%2F%2Fcvtisr.summon.serialssolutions.com%2F%23%21%2Fsearch%3Fho%3Df%26include.ft.matches%3Dt%26l%3Dnull%26q%3D |
| ISSN | 1007-5704 |
| IngestDate | Fri Jul 25 06:13:27 EDT 2025 Sat Nov 29 07:07:29 EST 2025 Tue Nov 18 22:24:22 EST 2025 Fri Feb 23 02:43:13 EST 2024 |
| IsPeerReviewed | true |
| IsScholarly | true |
| Keywords | Stochastic orderings Cumulative entropy Estimation Fractional calculus |
| Language | English |
| LinkModel | OpenURL |
| MergedId | FETCHMERGED-LOGICAL-c331t-8451315f7cc9bb01f3c1b4b9b64b9fff51453d12d6d67fa82160df6f42dbb8333 |
| Notes | ObjectType-Article-1 SourceType-Scholarly Journals-1 ObjectType-Feature-2 content type line 14 |
| ORCID | 0000-0003-4751-7341 |
| PQID | 2573023460 |
| PQPubID | 2047477 |
| ParticipantIDs | proquest_journals_2573023460 crossref_citationtrail_10_1016_j_cnsns_2021_105899 crossref_primary_10_1016_j_cnsns_2021_105899 elsevier_sciencedirect_doi_10_1016_j_cnsns_2021_105899 |
| PublicationCentury | 2000 |
| PublicationDate | November 2021 2021-11-00 20211101 |
| PublicationDateYYYYMMDD | 2021-11-01 |
| PublicationDate_xml | – month: 11 year: 2021 text: November 2021 |
| PublicationDecade | 2020 |
| PublicationPlace | Amsterdam |
| PublicationPlace_xml | – name: Amsterdam |
| PublicationTitle | Communications in nonlinear science & numerical simulation |
| PublicationYear | 2021 |
| Publisher | Elsevier B.V Elsevier Science Ltd |
| Publisher_xml | – name: Elsevier B.V – name: Elsevier Science Ltd |
| References | Li, Wu, Mao (bib0022) 2020; 57 Bickel, Lehmann, Rojo (bib0026) 2012 Yu, Huang, Liu, Chen (bib0015) 2012; 112 Shaked, Shanthikumar (bib0025) 2007 Machado, Lopes (bib0005) 2019; 134 Psarrakos, Navarro (bib0010) 2013; 27 Di Crescenzo, Longobardi (bib0007) 2009; 139 Asadi, Zohrevand (bib0018) 2007; 137 Bagai, Kochar (bib0027) 1986; 15 Dong, Zhang (bib0014) 2020 Abramowitz, Stegun (bib0019) 1994 Samko, Kilbas, Marichev (bib0023) 1993 Di Crescenzo, Toomaj (bib0017) 2017; 53 Di Crescenzo, Ricciardi (bib0029) 2001; 17 Rao, Chen, Vemuri, Wang (bib0006) 2004; 50 Navarro, del Aguila, Asadi (bib0008) 2010; 140 Chowdhury, Mukherjee, Nanda (bib0032) 2017; 46 Shannon (bib0001) 1948; 27 Di Crescenzo (bib0028) 1999; 36 Ubriaco (bib0003) 2009; 373 Kilbas, Srivastava, Trujillo (bib0024) 2006; vol. 204 Gupta, Gupta (bib0021) 2007; 137 Kayal (bib0016) 2016; 30 Cover, Thomas (bib0002) 1991 Machado (bib0004) 2014; 16 Zhang, Shang (bib0012) 2019; 29 . Di Crescenzo, Pellerey (bib0030) 2019; 21 Di Crescenzo, Longobardi (bib0031) 2009; vol. 5601 Psarrakos, Sordo (bib0034) 2019; 86 Toomaj, Di Crescenzo (bib0011) 2020; 22 Wang, Shang (bib0013) 2020; 537 Xiong, Shang, Zhang (bib0009) 2019; 78 Di Crescenzo (bib0020) 2000; 50 Psarrakos (10.1016/j.cnsns.2021.105899_bib0034) 2019; 86 Shannon (10.1016/j.cnsns.2021.105899_bib0001) 1948; 27 Machado (10.1016/j.cnsns.2021.105899_bib0004) 2014; 16 Abramowitz (10.1016/j.cnsns.2021.105899_bib0019) 1994 Di Crescenzo (10.1016/j.cnsns.2021.105899_bib0028) 1999; 36 Psarrakos (10.1016/j.cnsns.2021.105899_bib0010) 2013; 27 Samko (10.1016/j.cnsns.2021.105899_bib0023) 1993 Cover (10.1016/j.cnsns.2021.105899_bib0002) 1991 Asadi (10.1016/j.cnsns.2021.105899_bib0018) 2007; 137 Wang (10.1016/j.cnsns.2021.105899_bib0013) 2020; 537 Chowdhury (10.1016/j.cnsns.2021.105899_bib0032) 2017; 46 Machado (10.1016/j.cnsns.2021.105899_bib0005) 2019; 134 Yu (10.1016/j.cnsns.2021.105899_bib0015) 2012; 112 Rao (10.1016/j.cnsns.2021.105899_bib0006) 2004; 50 Kayal (10.1016/j.cnsns.2021.105899_bib0016) 2016; 30 Zhang (10.1016/j.cnsns.2021.105899_bib0012) 2019; 29 Di Crescenzo (10.1016/j.cnsns.2021.105899_bib0030) 2019; 21 Bickel (10.1016/j.cnsns.2021.105899_bib0026) 2012 Kilbas (10.1016/j.cnsns.2021.105899_bib0024) 2006; vol. 204 Dong (10.1016/j.cnsns.2021.105899_sbref0014) 2020 Shaked (10.1016/j.cnsns.2021.105899_bib0025) 2007 10.1016/j.cnsns.2021.105899_bib0033 Di Crescenzo (10.1016/j.cnsns.2021.105899_bib0020) 2000; 50 Toomaj (10.1016/j.cnsns.2021.105899_bib0011) 2020; 22 Di Crescenzo (10.1016/j.cnsns.2021.105899_bib0029) 2001; 17 Ubriaco (10.1016/j.cnsns.2021.105899_bib0003) 2009; 373 Di Crescenzo (10.1016/j.cnsns.2021.105899_bib0031) 2009; vol. 5601 Di Crescenzo (10.1016/j.cnsns.2021.105899_bib0007) 2009; 139 Xiong (10.1016/j.cnsns.2021.105899_bib0009) 2019; 78 Bagai (10.1016/j.cnsns.2021.105899_bib0027) 1986; 15 Navarro (10.1016/j.cnsns.2021.105899_bib0008) 2010; 140 Gupta (10.1016/j.cnsns.2021.105899_bib0021) 2007; 137 Di Crescenzo (10.1016/j.cnsns.2021.105899_bib0017) 2017; 53 Li (10.1016/j.cnsns.2021.105899_bib0022) 2020; 57 |
| References_xml | – volume: 137 start-page: 3525 year: 2007 end-page: 3536 ident: bib0021 article-title: Proportional reversed hazard rate model and its applications publication-title: J Statist Plann Inference – volume: 16 start-page: 2350 year: 2014 end-page: 2361 ident: bib0004 article-title: Fractional order generalized information publication-title: Entropy – volume: 57 start-page: 832 year: 2020 end-page: 852 ident: bib0022 article-title: Stochastic comparisons of largest-order statistics for proportional reversed hazard rate model and applications publication-title: J Appl Prob – volume: 373 start-page: 2516 year: 2009 end-page: 2519 ident: bib0003 article-title: Entropies based on fractional calculus publication-title: Phys Lett A – volume: 50 start-page: 1220 year: 2004 end-page: 1228 ident: bib0006 article-title: Cumulative residual entropy: a new measure of information publication-title: IEEE Trans Inf Theory – year: 2012 ident: bib0026 article-title: Descriptive statistics for nonparametric models IV. spread publication-title: Selected Works of E. L. Lehmann. Selected Works in Probability and Statistics. – volume: 29 start-page: 103104 year: 2019 ident: bib0012 article-title: Uncertainty of financial time series based on discrete fractional cumulative residual entropy publication-title: Chaos – year: 1994 ident: bib0019 article-title: Handbook of mathematical functions with formulas, graph, and mathematical tables – year: 1993 ident: bib0023 article-title: Fractional integrals and derivatives publication-title: Theory and Applications – volume: 112 start-page: 916 year: 2012 end-page: 921 ident: bib0015 article-title: Information measures based on fractional calculus publication-title: Inf Proc Lett – volume: 36 start-page: 706 year: 1999 end-page: 719 ident: bib0028 article-title: A probabilistic analogue of the mean value theorem and its applications to reliability theory publication-title: J Appl Prob – year: 2007 ident: bib0025 article-title: Stochastic orders and their applications – volume: 86 start-page: 232 year: 2019 end-page: 240 ident: bib0034 article-title: On a family of risk measures based on proportional hazards models and tail probabilities publication-title: Insurance Math Econ – volume: 140 start-page: 310 year: 2010 end-page: 322 ident: bib0008 article-title: Some new results on the cumulative residual entropy publication-title: J Statist Plann Inference – volume: 21 start-page: 203 year: 2019 end-page: 233 ident: bib0030 article-title: Some results and applications of geometric counting processes publication-title: Methodol Comput Appl Probab – volume: 53 start-page: 959 year: 2017 end-page: 982 ident: bib0017 article-title: Further results on the generalized cumulative entropy publication-title: Kybernetika – volume: 46 start-page: 1715 year: 2017 end-page: 1734 ident: bib0032 article-title: On compounded geometric distributions and their applications publication-title: Comm Stat Simul Comput – volume: 27 start-page: 379 year: 1948 end-page: 423 ident: bib0001 article-title: A note on the concept of entropy publication-title: Bell System Tech J – volume: 537 start-page: 122582 year: 2020 ident: bib0013 article-title: Complexity analysis of time series based on generalized fractional order cumulative residual distribution entropy publication-title: Phys A: Stat Mech Appl – volume: 139 start-page: 4072 year: 2009 end-page: 4087 ident: bib0007 article-title: On cumulative entropies publication-title: J Statist Plann Inference – volume: 30 start-page: 640 year: 2016 end-page: 662 ident: bib0016 article-title: On generalized cumulative entropies publication-title: Prob Engin Inform Sciences – start-page: 2050038 year: 2020 ident: bib0014 article-title: Multiscale fractional cumulative residual entropy of higher-order moments for estimating uncertainty publication-title: Fluct Noise Lett – volume: 17 start-page: 205 year: 2001 end-page: 219 ident: bib0029 article-title: On a discrimination problem for a class of stochastic processes with ordered first-passage times publication-title: Appl Stochastic Models Bus Ind – volume: 78 start-page: 104879 year: 2019 ident: bib0009 article-title: Fractional cumulative residual entropy publication-title: Comm Nonlinear Sci Num Simul – reference: . – volume: 137 start-page: 1931 year: 2007 end-page: 1941 ident: bib0018 article-title: On the dynamic cumulative residual entropy publication-title: J Statist Plann Inference – volume: 50 start-page: 313 year: 2000 end-page: 321 ident: bib0020 article-title: Some results on the proportional reversed hazards model publication-title: Stat Prob Lett – year: 1991 ident: bib0002 article-title: Elements of information theory – volume: 27 start-page: 623 year: 2013 end-page: 640 ident: bib0010 article-title: Generalized cumulative residual entropy and record values publication-title: Metrika – volume: vol. 204 year: 2006 ident: bib0024 article-title: Theory and applications of fractional differential equations publication-title: North-Holland Mathematics Studies – volume: 22 start-page: 709 year: 2020 ident: bib0011 article-title: Generalized entropies, variance and applications publication-title: Entropy – volume: vol. 5601 start-page: 132 year: 2009 end-page: 141 ident: bib0031 article-title: On cumulative entropies and lifetime estimations publication-title: Methods and Models in Artificial and Natural Computation. A Homage to Professor Mira’s Scientific Legacy. IWINAC 2009. Lecture Notes in Computer Science – volume: 134 start-page: 217 year: 2019 ident: bib0005 article-title: Fractional rényi entropy publication-title: Eur Phys J Plus – volume: 15 start-page: 1377 year: 1986 end-page: 1388 ident: bib0027 article-title: On tail-ordering and comparison of failure rates publication-title: Comm Stat-Theory and Methods – volume: 30 start-page: 640 issue: 4 year: 2016 ident: 10.1016/j.cnsns.2021.105899_bib0016 article-title: On generalized cumulative entropies publication-title: Prob Engin Inform Sciences doi: 10.1017/S0269964816000218 – volume: vol. 204 year: 2006 ident: 10.1016/j.cnsns.2021.105899_bib0024 article-title: Theory and applications of fractional differential equations – volume: 137 start-page: 3525 issue: 11 year: 2007 ident: 10.1016/j.cnsns.2021.105899_bib0021 article-title: Proportional reversed hazard rate model and its applications publication-title: J Statist Plann Inference doi: 10.1016/j.jspi.2007.03.029 – volume: 46 start-page: 1715 issue: 3 year: 2017 ident: 10.1016/j.cnsns.2021.105899_bib0032 article-title: On compounded geometric distributions and their applications publication-title: Comm Stat Simul Comput doi: 10.1080/03610918.2015.1011331 – volume: 134 start-page: 217 issue: 5 year: 2019 ident: 10.1016/j.cnsns.2021.105899_bib0005 article-title: Fractional rényi entropy publication-title: Eur Phys J Plus doi: 10.1140/epjp/i2019-12554-9 – volume: 27 start-page: 379 issue: 3 year: 1948 ident: 10.1016/j.cnsns.2021.105899_bib0001 article-title: A note on the concept of entropy publication-title: Bell System Tech J doi: 10.1002/j.1538-7305.1948.tb01338.x – volume: 50 start-page: 1220 issue: 6 year: 2004 ident: 10.1016/j.cnsns.2021.105899_bib0006 article-title: Cumulative residual entropy: a new measure of information publication-title: IEEE Trans Inf Theory doi: 10.1109/TIT.2004.828057 – start-page: 2050038 year: 2020 ident: 10.1016/j.cnsns.2021.105899_sbref0014 article-title: Multiscale fractional cumulative residual entropy of higher-order moments for estimating uncertainty publication-title: Fluct Noise Lett doi: 10.1142/S0219477520500388 – volume: vol. 5601 start-page: 132 year: 2009 ident: 10.1016/j.cnsns.2021.105899_bib0031 article-title: On cumulative entropies and lifetime estimations – volume: 537 start-page: 122582 year: 2020 ident: 10.1016/j.cnsns.2021.105899_bib0013 article-title: Complexity analysis of time series based on generalized fractional order cumulative residual distribution entropy publication-title: Phys A: Stat Mech Appl doi: 10.1016/j.physa.2019.122582 – volume: 137 start-page: 1931 year: 2007 ident: 10.1016/j.cnsns.2021.105899_bib0018 article-title: On the dynamic cumulative residual entropy publication-title: J Statist Plann Inference doi: 10.1016/j.jspi.2006.06.035 – volume: 57 start-page: 832 year: 2020 ident: 10.1016/j.cnsns.2021.105899_bib0022 article-title: Stochastic comparisons of largest-order statistics for proportional reversed hazard rate model and applications publication-title: J Appl Prob doi: 10.1017/jpr.2020.40 – volume: 50 start-page: 313 issue: 4 year: 2000 ident: 10.1016/j.cnsns.2021.105899_bib0020 article-title: Some results on the proportional reversed hazards model publication-title: Stat Prob Lett doi: 10.1016/S0167-7152(00)00127-9 – volume: 29 start-page: 103104 issue: 10 year: 2019 ident: 10.1016/j.cnsns.2021.105899_bib0012 article-title: Uncertainty of financial time series based on discrete fractional cumulative residual entropy publication-title: Chaos doi: 10.1063/1.5091545 – year: 2007 ident: 10.1016/j.cnsns.2021.105899_bib0025 – volume: 15 start-page: 1377 issue: 4 year: 1986 ident: 10.1016/j.cnsns.2021.105899_bib0027 article-title: On tail-ordering and comparison of failure rates publication-title: Comm Stat-Theory and Methods doi: 10.1080/03610928608829189 – volume: 22 start-page: 709 year: 2020 ident: 10.1016/j.cnsns.2021.105899_bib0011 article-title: Generalized entropies, variance and applications publication-title: Entropy doi: 10.3390/e22060709 – volume: 21 start-page: 203 year: 2019 ident: 10.1016/j.cnsns.2021.105899_bib0030 article-title: Some results and applications of geometric counting processes publication-title: Methodol Comput Appl Probab doi: 10.1007/s11009-018-9649-9 – volume: 86 start-page: 232 year: 2019 ident: 10.1016/j.cnsns.2021.105899_bib0034 article-title: On a family of risk measures based on proportional hazards models and tail probabilities publication-title: Insurance Math Econ doi: 10.1016/j.insmatheco.2019.03.005 – volume: 112 start-page: 916 year: 2012 ident: 10.1016/j.cnsns.2021.105899_bib0015 article-title: Information measures based on fractional calculus publication-title: Inf Proc Lett doi: 10.1016/j.ipl.2012.08.019 – volume: 27 start-page: 623 year: 2013 ident: 10.1016/j.cnsns.2021.105899_bib0010 article-title: Generalized cumulative residual entropy and record values publication-title: Metrika doi: 10.1007/s00184-012-0408-6 – volume: 78 start-page: 104879 year: 2019 ident: 10.1016/j.cnsns.2021.105899_bib0009 article-title: Fractional cumulative residual entropy publication-title: Comm Nonlinear Sci Num Simul doi: 10.1016/j.cnsns.2019.104879 – year: 2012 ident: 10.1016/j.cnsns.2021.105899_bib0026 article-title: Descriptive statistics for nonparametric models IV. spread – volume: 140 start-page: 310 year: 2010 ident: 10.1016/j.cnsns.2021.105899_bib0008 article-title: Some new results on the cumulative residual entropy publication-title: J Statist Plann Inference doi: 10.1016/j.jspi.2009.07.015 – volume: 53 start-page: 959 issue: 5 year: 2017 ident: 10.1016/j.cnsns.2021.105899_bib0017 article-title: Further results on the generalized cumulative entropy publication-title: Kybernetika – ident: 10.1016/j.cnsns.2021.105899_bib0033 – volume: 16 start-page: 2350 issue: 4 year: 2014 ident: 10.1016/j.cnsns.2021.105899_bib0004 article-title: Fractional order generalized information publication-title: Entropy doi: 10.3390/e16042350 – volume: 17 start-page: 205 year: 2001 ident: 10.1016/j.cnsns.2021.105899_bib0029 article-title: On a discrimination problem for a class of stochastic processes with ordered first-passage times publication-title: Appl Stochastic Models Bus Ind doi: 10.1002/asmb.434 – year: 1994 ident: 10.1016/j.cnsns.2021.105899_bib0019 – volume: 36 start-page: 706 issue: 3 year: 1999 ident: 10.1016/j.cnsns.2021.105899_bib0028 article-title: A probabilistic analogue of the mean value theorem and its applications to reliability theory publication-title: J Appl Prob doi: 10.1239/jap/1032374628 – volume: 373 start-page: 2516 issue: 30 year: 2009 ident: 10.1016/j.cnsns.2021.105899_bib0003 article-title: Entropies based on fractional calculus publication-title: Phys Lett A doi: 10.1016/j.physleta.2009.05.026 – volume: 139 start-page: 4072 issue: 12 year: 2009 ident: 10.1016/j.cnsns.2021.105899_bib0007 article-title: On cumulative entropies publication-title: J Statist Plann Inference doi: 10.1016/j.jspi.2009.05.038 – year: 1991 ident: 10.1016/j.cnsns.2021.105899_bib0002 – year: 1993 ident: 10.1016/j.cnsns.2021.105899_bib0023 article-title: Fractional integrals and derivatives |
| SSID | ssj0016954 |
| Score | 2.5033665 |
| Snippet | •A fractional version of the generalized cumulative entropy is introduced.•The proposed notion is a variability measure connected with fractional... Following the theory of information measures based on the cumulative distribution function, we propose the fractional generalized cumulative entropy, and its... |
| SourceID | proquest crossref elsevier |
| SourceType | Aggregation Database Enrichment Source Index Database Publisher |
| StartPage | 105899 |
| SubjectTerms | Cumulative entropy Distribution functions Entropy Estimation Fractional calculus Parameter estimation Probability distribution functions Stochastic models Stochastic orderings |
| Title | Fractional generalized cumulative entropy and its dynamic version |
| URI | https://dx.doi.org/10.1016/j.cnsns.2021.105899 https://www.proquest.com/docview/2573023460 |
| Volume | 102 |
| WOSCitedRecordID | wos000684932600014&url=https%3A%2F%2Fcvtisr.summon.serialssolutions.com%2F%23%21%2Fsearch%3Fho%3Df%26include.ft.matches%3Dt%26l%3Dnull%26q%3D |
| hasFullText | 1 |
| inHoldings | 1 |
| isFullTextHit | |
| isPrint | |
| journalDatabaseRights | – providerCode: PRVESC databaseName: Elsevier SD Freedom Collection Journals 2021 customDbUrl: eissn: 1878-7274 dateEnd: 99991231 omitProxy: false ssIdentifier: ssj0016954 issn: 1007-5704 databaseCode: AIEXJ dateStart: 19960101 isFulltext: true titleUrlDefault: https://www.sciencedirect.com providerName: Elsevier |
| link | http://cvtisr.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwtV1La9wwEBYl6aGXvkvTpkWH3lwHy5Yl-biEhLbQUGgKezN6WGXDxrt4HyT59R097N1kaWgLvYhFu7bMzOfZmZFmPoQ-SK4byRlEqlLSlDaiSRUvTCrBNeGSW5NZ48km-NmZGI-rb3G7YOHpBHjbiqurav5fVQ1zoGxXOvsX6h5uChPwGZQOI6gdxj9S_GkXahVA9j9DT-nJDXiVenXpmbrWTeISurP59bBvYAIrfbIOubNtf_VW_Yg_OtuG3hqyS_qKIAeedhV2fqbJYnIZGcEGH3mSHHe-a9TNLPYrAEMyG0y9vPakA2DDXBWy2cD1azMLxdujqSNqaU0nt5MUOYnVekPmbKd6xhtblyYteaAfPmrCnICoFnwqestC-6LsXWsfEg8XR7pdtK71ek4cbbEIjEt32mh_d6u5xXLXdJY4Yur9nJcVGPP90eeT8Zdh74lVnjtveLq-V5U_Fbiz1O_8mTv_7N5dOX-KHsc4A48CPp6hB037HD2JMQeOFn3xAo02cMFbcMEbuOAIFwwKwAAXHOGCI1xeoh-nJ-fHn9JIq5HqoiDLVNCSFKS0XOtKqYzYQhNFVaUYDNZacKHLwpDcMMO4lSInLDOWWZobpURRFK_QHmCteY1wxbgpZaWEBs8fQl-paSmkEFQRJWmVHaC8F06tY895R30yrfvDhRe1l2jtJFoHiR6gj8NF89By5f6fs17qdQR-8AZrgMn9Fx72Oqrj-wvfl9zRaFGWvfnX-75FjzavwCHaW3ar5h16qNfLyaJ7H9H2C8ubn78 |
| linkProvider | Elsevier |
| openUrl | ctx_ver=Z39.88-2004&ctx_enc=info%3Aofi%2Fenc%3AUTF-8&rfr_id=info%3Asid%2Fsummon.serialssolutions.com&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.atitle=Fractional+generalized+cumulative+entropy+and+its+dynamic+version&rft.jtitle=Communications+in+nonlinear+science+%26+numerical+simulation&rft.au=Di+Crescenzo%2C+Antonio&rft.au=Kayal%2C+Suchandan&rft.au=Meoli%2C+Alessandra&rft.date=2021-11-01&rft.pub=Elsevier+B.V&rft.issn=1007-5704&rft.eissn=1878-7274&rft.volume=102&rft_id=info:doi/10.1016%2Fj.cnsns.2021.105899&rft.externalDocID=S1007570421002112 |
| thumbnail_l | http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/lc.gif&issn=1007-5704&client=summon |
| thumbnail_m | http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/mc.gif&issn=1007-5704&client=summon |
| thumbnail_s | http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/sc.gif&issn=1007-5704&client=summon |