Statistical inference for a stochastic generalized logistic differential equation
In this research we aim to estimate three parameters in a stochastic generalized logistic differential equation. We assume the intrinsic growth rate and shape parameters are constant but unknown. To estimate these two parameters, we use the maximum likelihood method and establish that the estimators...
Uložené v:
| Vydané v: | Communications in nonlinear science & numerical simulation Ročník 139; s. 108261 |
|---|---|
| Hlavní autori: | , , , |
| Médium: | Journal Article |
| Jazyk: | English |
| Vydavateľské údaje: |
Elsevier B.V
01.12.2024
|
| Predmet: | |
| ISSN: | 1007-5704 |
| On-line prístup: | Získať plný text |
| Tagy: |
Pridať tag
Žiadne tagy, Buďte prvý, kto otaguje tento záznam!
|
| Abstract | In this research we aim to estimate three parameters in a stochastic generalized logistic differential equation. We assume the intrinsic growth rate and shape parameters are constant but unknown. To estimate these two parameters, we use the maximum likelihood method and establish that the estimators for these two parameters are strongly consistent. We estimate the diffusion parameter by using the quadratic variation processes. To test our results, we evaluate two data scenarios, complete and incomplete, with fixed values assigned to the three parameters. In the incomplete data scenario, we apply an Expectation Maximization algorithm.
•MLE for three parameters in a stochastic generalized logistic differential equation.•The growth rate and shape are estimated using ML and they are shown to be consistent.•The ML estimator proposed exhibits a high level of efficiency and robustness. |
|---|---|
| AbstractList | In this research we aim to estimate three parameters in a stochastic generalized logistic differential equation. We assume the intrinsic growth rate and shape parameters are constant but unknown. To estimate these two parameters, we use the maximum likelihood method and establish that the estimators for these two parameters are strongly consistent. We estimate the diffusion parameter by using the quadratic variation processes. To test our results, we evaluate two data scenarios, complete and incomplete, with fixed values assigned to the three parameters. In the incomplete data scenario, we apply an Expectation Maximization algorithm.
•MLE for three parameters in a stochastic generalized logistic differential equation.•The growth rate and shape are estimated using ML and they are shown to be consistent.•The ML estimator proposed exhibits a high level of efficiency and robustness. |
| ArticleNumber | 108261 |
| Author | Diaz-Infante, Saul Gomez, Eduardo Lince Delgado-Vences, Francisco Baltazar-Larios, Fernando |
| Author_xml | – sequence: 1 givenname: Fernando surname: Baltazar-Larios fullname: Baltazar-Larios, Fernando organization: Facultad de Ciencias - Universidad Nacional Autónoma de Mexico, Ciudad Universitaria, Ciudad de Mexico, Mexico – sequence: 2 givenname: Francisco orcidid: 0000-0002-0880-720X surname: Delgado-Vences fullname: Delgado-Vences, Francisco email: delgado@im.unam.mx organization: Conahcyt Research Fellow - Universidad Nacional Autónoma de México. Instituto de Matemáticas, Oaxaca de Juarez, Mexico – sequence: 3 givenname: Saul orcidid: 0000-0001-9559-1293 surname: Diaz-Infante fullname: Diaz-Infante, Saul organization: Conahcyt Research Fellow - Universidad de Sonora, Blvd. Luis Encinas y Rosales S/N, Hermosillo, 83000, Sonora, Mexico – sequence: 4 givenname: Eduardo Lince surname: Gomez fullname: Gomez, Eduardo Lince organization: Facultad de Ciencias - Universidad Nacional Autónoma de Mexico, Ciudad Universitaria, Ciudad de Mexico, Mexico |
| BookMark | eNp9kE1PAyEQhjnUxLb6C7zwB7YCu-yyBw-m8aNJE2PUM6EwVDYrKKCJ_nr3w7OnSWbmeTPzrNDCBw8IXVCyoYTWl91G--TThhFWDR3BarpAS0pIU_CGVKdolVJHhs2WV0v0-JRVdik7rXrsvIUIXgO2IWKFUw76VY1DfAQPUfXuBwzuw3EisHF2ArIbYPj4HJKCP0MnVvUJzv_qGr3c3jxv74v9w91ue70vNKMlLRpmOCtNSy0FTuxBGVOCMUJoAZSTtmoJaF6VQkMNB6YNaWtlueEgKhBClWtUzrk6hpQiWPke3ZuK35ISOZqQnZxMyNGEnE0M1NVMwXDal4Mok3bjy8ZF0Fma4P7lfwEhTm5a |
| Cites_doi | 10.1007/s00477-022-02170-w 10.3847/1538-4357/aaec08 10.1002/wics.1585 10.1016/j.camwa.2008.01.006 10.1007/BF02309004 10.1093/jxb/10.2.290 10.1016/j.cnsns.2018.12.013 10.1016/j.aml.2012.12.015 10.1016/j.cnsns.2022.106832 10.3150/12-BEJ501 |
| ContentType | Journal Article |
| Copyright | 2024 The Author(s) |
| Copyright_xml | – notice: 2024 The Author(s) |
| DBID | 6I. AAFTH AAYXX CITATION |
| DOI | 10.1016/j.cnsns.2024.108261 |
| DatabaseName | ScienceDirect Open Access Titles Elsevier:ScienceDirect:Open Access CrossRef |
| DatabaseTitle | CrossRef |
| DatabaseTitleList | |
| DeliveryMethod | fulltext_linktorsrc |
| Discipline | Applied Sciences |
| ExternalDocumentID | 10_1016_j_cnsns_2024_108261 S1007570424004465 |
| GroupedDBID | --K --M -01 -0A -0I -0Y -SA -S~ .~1 0R~ 1B1 1RT 1~. 1~5 29F 4.4 457 4G. 5GY 5VR 5VS 6I. 7-5 71M 8P~ 92M 9D9 9DA AACTN AAEDT AAEDW AAFTH AAIKJ AAKOC AALRI AAOAW AAQFI AAQXK AAXDM AAXKI AAXUO ABAOU ABFNM ABJNI ABMAC ABNEU ABWVN ABXDB ACDAQ ACFVG ACGFS ACNNM ACRLP ACRPL ADBBV ADEZE ADGUI ADMUD ADNMO ADTZH AEBSH AECPX AEIPS AEKER AENEX AFJKZ AFKWA AFTJW AFUIB AGHFR AGUBO AGYEJ AHJVU AIEXJ AIGVJ AIKHN AITUG AIVDX AJOXV AKRWK ALMA_UNASSIGNED_HOLDINGS AMFUW AMRAJ ANKPU ARUGR ASPBG AVWKF AXJTR AZFZN BJAXD BKOJK BLXMC CAJEA CCEZO CCVFK CHBEP CS3 CUBFJ DU5 EBS EFJIC 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 AAYWO AAYXX ACLOT ACVFH ADCNI AEUPX AFPUW AGQPQ AIGII AIIUN AKBMS AKYEP APXCP CITATION EFKBS EFLBG ~HD |
| ID | FETCH-LOGICAL-c2131-72d523d91f1e50fbadd3edd88c8e1509490ec5438ce6eb2cd096af5d5e84e88a3 |
| ISSN | 1007-5704 |
| IngestDate | Sat Nov 29 02:23:15 EST 2025 Sat Feb 08 15:51:10 EST 2025 |
| IsDoiOpenAccess | true |
| IsOpenAccess | true |
| IsPeerReviewed | true |
| IsScholarly | true |
| Keywords | Maximum likelihood estimation 60H10 Stochastic generalized logistic differential equation Expectation maximization algorithm Biological growth 62F10 Diffusion bridges 60H35 |
| Language | English |
| License | This is an open access article under the CC BY-NC license. |
| LinkModel | OpenURL |
| MergedId | FETCHMERGED-LOGICAL-c2131-72d523d91f1e50fbadd3edd88c8e1509490ec5438ce6eb2cd096af5d5e84e88a3 |
| ORCID | 0000-0001-9559-1293 0000-0002-0880-720X |
| OpenAccessLink | https://dx.doi.org/10.1016/j.cnsns.2024.108261 |
| ParticipantIDs | crossref_primary_10_1016_j_cnsns_2024_108261 elsevier_sciencedirect_doi_10_1016_j_cnsns_2024_108261 |
| PublicationCentury | 2000 |
| PublicationDate | December 2024 2024-12-00 |
| PublicationDateYYYYMMDD | 2024-12-01 |
| PublicationDate_xml | – month: 12 year: 2024 text: December 2024 |
| PublicationDecade | 2020 |
| PublicationTitle | Communications in nonlinear science & numerical simulation |
| PublicationYear | 2024 |
| Publisher | Elsevier B.V |
| Publisher_xml | – name: Elsevier B.V |
| References | McLachlan, Krishnan (b6) 1997 Schurz (b13) 2007; 4 Craigmile, Herbei, Liu, Schneider (b14) 2023; 15 Delgado-Vences, Baltazar-Larios, Ornelas Vargas, Morales-Bojórquez, Cruz-Escalona, Salomón Aguilar (b17) 2022; 49 Braun, Golubitsky (b10) 1983 Suryawan (b4) 2018 Liu, Wang (b11) 2013; 26 Bladt, Sørensen (b20) 2014; 20 Küchler, Sørensen (b21) 2006 Baltazar-Larios F, Delgado-Vences F, Diaz-Infante S, Lince-Gomez E. The collection of source code and data for tables and figures for ‘statistical inference for a stochastic generalized logistic differential equation’. GitHub Iacus (b7) 2009 Cortés, Navarro-Quiles, Romero, Roselló (b5) 2019; 72 Grimmett, Stirzaker (b22) 2020 . Panik (b3) 2017 Vogels, Zoeckler, Stasiw, Cerny (b8) 1975; 3 Liptser, Shiryaev (b19) 2001 Wei-Cheng (b18) 2006; 1 Qin, Wu (b9) 2018; 869 Calatayud, Jornet, Mateu (b16) 2022; 36 Richards (b1) 1959; 10 Bevia, Calatayud, Cortés, Jornet (b15) 2023; 116 France, Thornley (b2) 1984 Braumann (b12) 2008; 56 Wei-Cheng (10.1016/j.cnsns.2024.108261_b18) 2006; 1 Braumann (10.1016/j.cnsns.2024.108261_b12) 2008; 56 Bladt (10.1016/j.cnsns.2024.108261_b20) 2014; 20 Craigmile (10.1016/j.cnsns.2024.108261_b14) 2023; 15 Suryawan (10.1016/j.cnsns.2024.108261_b4) 2018 Braun (10.1016/j.cnsns.2024.108261_b10) 1983 Küchler (10.1016/j.cnsns.2024.108261_b21) 2006 Liu (10.1016/j.cnsns.2024.108261_b11) 2013; 26 Bevia (10.1016/j.cnsns.2024.108261_b15) 2023; 116 Calatayud (10.1016/j.cnsns.2024.108261_b16) 2022; 36 Iacus (10.1016/j.cnsns.2024.108261_b7) 2009 Schurz (10.1016/j.cnsns.2024.108261_b13) 2007; 4 Qin (10.1016/j.cnsns.2024.108261_b9) 2018; 869 10.1016/j.cnsns.2024.108261_b23 France (10.1016/j.cnsns.2024.108261_b2) 1984 Delgado-Vences (10.1016/j.cnsns.2024.108261_b17) 2022; 49 Richards (10.1016/j.cnsns.2024.108261_b1) 1959; 10 Vogels (10.1016/j.cnsns.2024.108261_b8) 1975; 3 Grimmett (10.1016/j.cnsns.2024.108261_b22) 2020 Liptser (10.1016/j.cnsns.2024.108261_b19) 2001 McLachlan (10.1016/j.cnsns.2024.108261_b6) 1997 Panik (10.1016/j.cnsns.2024.108261_b3) 2017 Cortés (10.1016/j.cnsns.2024.108261_b5) 2019; 72 |
| References_xml | – volume: 10 start-page: 290 year: 1959 end-page: 300 ident: b1 article-title: A flexible growth function for empirical use publication-title: J Exp Bot – year: 2001 ident: b19 article-title: S of random processes: I. General theory (Vol. 1) – start-page: xi+ year: 1984 end-page: 335 ident: b2 article-title: Mathematical models in agriculture – volume: 3 start-page: 183 year: 1975 end-page: 192 ident: b8 article-title: P. F. Verhulst’s notice sur la loi que la populations suit dans son accroissement from correspondence mathematique et physique. Ghent, vol. X, 1838 publication-title: J Biol Phys – volume: 26 start-page: 601 year: 2013 end-page: 606 ident: b11 article-title: A note on stability of stochastic logistic equation publication-title: Appl Math Lett – volume: 49 start-page: 1 year: 2022 end-page: 24 ident: b17 article-title: Inference for a discretized stochastic logistic differential equation and its application to biological growth publication-title: J Appl Stat – year: 2006 ident: b21 article-title: Exponential families of stochastic processes – volume: 869 start-page: 48 year: 2018 ident: b9 article-title: A model of sunspot number with a modified logistic function publication-title: Astrophys J – volume: 20 start-page: 645 year: 2014 end-page: 675 ident: b20 article-title: Simple simulation of diffusion bridges with application to likelihood inference for diffusions publication-title: Bernoulli – reference: . – volume: 36 start-page: 2907 year: 2022 end-page: 2917 ident: b16 article-title: A stochastic Bayesian bootstrapping model for COVID-19 data publication-title: Stoch Environ Res Risk Assess – volume: 15 year: 2023 ident: b14 article-title: Statistical inference for stochastic differential equations publication-title: Wiley Interdiscip Rev Comput Stat – year: 1983 ident: b10 article-title: Differential equations and their applications (Vol. 1) – year: 1997 ident: b6 article-title: The EM algorithm and extensions – volume: 1 start-page: 763 year: 2006 end-page: 776 ident: b18 article-title: Estimation of diffusion parameters in diffusion processes and their asymptotic normality publication-title: Int J Contemp Math Sci – reference: Baltazar-Larios F, Delgado-Vences F, Diaz-Infante S, Lince-Gomez E. The collection of source code and data for tables and figures for ‘statistical inference for a stochastic generalized logistic differential equation’. GitHub, – volume: 116 year: 2023 ident: b15 article-title: On the generalized logistic random differential equation: Theoretical analysis and numerical simulations with real-world data publication-title: Commun Nonlinear Sci Numer Simul – year: 2018 ident: b4 article-title: Analytic solution of a stochastic richards equation driven by Brownian motion publication-title: Journal of physics: conference series, Vol. 1097 – volume: 56 start-page: 631 year: 2008 end-page: 644 ident: b12 article-title: Growth and extinction of populations in randomly varying environments publication-title: Comput Math Appl – year: 2017 ident: b3 article-title: Stochastic differential equations: an introduction with applications in population dynamics modeling – volume: 4 start-page: 178 year: 2007 end-page: 197 ident: b13 article-title: Modeling, analysis and discretization of stochastic logistic equations publication-title: Int J Numer Anal Model – year: 2009 ident: b7 article-title: Simulation and inference for stochastic differential equations: with R examples – volume: 72 start-page: 121 year: 2019 end-page: 138 ident: b5 article-title: Analysis of random non-autonomous logistic-type differential equations via the Karhunen–Loève expansion and the random variable transformation technique publication-title: Commun Nonlinear Sci Numer Simul – year: 2020 ident: b22 article-title: Probability and random processes – year: 1983 ident: 10.1016/j.cnsns.2024.108261_b10 – year: 2017 ident: 10.1016/j.cnsns.2024.108261_b3 – volume: 36 start-page: 2907 issue: 9 year: 2022 ident: 10.1016/j.cnsns.2024.108261_b16 article-title: A stochastic Bayesian bootstrapping model for COVID-19 data publication-title: Stoch Environ Res Risk Assess doi: 10.1007/s00477-022-02170-w – year: 2006 ident: 10.1016/j.cnsns.2024.108261_b21 – volume: 869 start-page: 48 year: 2018 ident: 10.1016/j.cnsns.2024.108261_b9 article-title: A model of sunspot number with a modified logistic function publication-title: Astrophys J doi: 10.3847/1538-4357/aaec08 – volume: 15 issue: 2 year: 2023 ident: 10.1016/j.cnsns.2024.108261_b14 article-title: Statistical inference for stochastic differential equations publication-title: Wiley Interdiscip Rev Comput Stat doi: 10.1002/wics.1585 – volume: 56 start-page: 631 issue: 3 year: 2008 ident: 10.1016/j.cnsns.2024.108261_b12 article-title: Growth and extinction of populations in randomly varying environments publication-title: Comput Math Appl doi: 10.1016/j.camwa.2008.01.006 – year: 2020 ident: 10.1016/j.cnsns.2024.108261_b22 – volume: 3 start-page: 183 year: 1975 ident: 10.1016/j.cnsns.2024.108261_b8 article-title: P. F. Verhulst’s notice sur la loi que la populations suit dans son accroissement from correspondence mathematique et physique. Ghent, vol. X, 1838 publication-title: J Biol Phys doi: 10.1007/BF02309004 – year: 2018 ident: 10.1016/j.cnsns.2024.108261_b4 article-title: Analytic solution of a stochastic richards equation driven by Brownian motion – year: 1997 ident: 10.1016/j.cnsns.2024.108261_b6 – year: 2001 ident: 10.1016/j.cnsns.2024.108261_b19 – volume: 1 start-page: 763 year: 2006 ident: 10.1016/j.cnsns.2024.108261_b18 article-title: Estimation of diffusion parameters in diffusion processes and their asymptotic normality publication-title: Int J Contemp Math Sci – ident: 10.1016/j.cnsns.2024.108261_b23 – volume: 4 start-page: 178 issue: 2 year: 2007 ident: 10.1016/j.cnsns.2024.108261_b13 article-title: Modeling, analysis and discretization of stochastic logistic equations publication-title: Int J Numer Anal Model – volume: 10 start-page: 290 year: 1959 ident: 10.1016/j.cnsns.2024.108261_b1 article-title: A flexible growth function for empirical use publication-title: J Exp Bot doi: 10.1093/jxb/10.2.290 – volume: 72 start-page: 121 year: 2019 ident: 10.1016/j.cnsns.2024.108261_b5 article-title: Analysis of random non-autonomous logistic-type differential equations via the Karhunen–Loève expansion and the random variable transformation technique publication-title: Commun Nonlinear Sci Numer Simul doi: 10.1016/j.cnsns.2018.12.013 – volume: 26 start-page: 601 issue: 6 year: 2013 ident: 10.1016/j.cnsns.2024.108261_b11 article-title: A note on stability of stochastic logistic equation publication-title: Appl Math Lett doi: 10.1016/j.aml.2012.12.015 – volume: 116 year: 2023 ident: 10.1016/j.cnsns.2024.108261_b15 article-title: On the generalized logistic random differential equation: Theoretical analysis and numerical simulations with real-world data publication-title: Commun Nonlinear Sci Numer Simul doi: 10.1016/j.cnsns.2022.106832 – year: 2009 ident: 10.1016/j.cnsns.2024.108261_b7 – volume: 20 start-page: 645 year: 2014 ident: 10.1016/j.cnsns.2024.108261_b20 article-title: Simple simulation of diffusion bridges with application to likelihood inference for diffusions publication-title: Bernoulli doi: 10.3150/12-BEJ501 – start-page: xi+ year: 1984 ident: 10.1016/j.cnsns.2024.108261_b2 – volume: 49 start-page: 1 year: 2022 ident: 10.1016/j.cnsns.2024.108261_b17 article-title: Inference for a discretized stochastic logistic differential equation and its application to biological growth publication-title: J Appl Stat |
| SSID | ssj0016954 |
| Score | 2.4167936 |
| Snippet | In this research we aim to estimate three parameters in a stochastic generalized logistic differential equation. We assume the intrinsic growth rate and shape... |
| SourceID | crossref elsevier |
| SourceType | Index Database Publisher |
| StartPage | 108261 |
| SubjectTerms | Biological growth Diffusion bridges Expectation maximization algorithm Maximum likelihood estimation Stochastic generalized logistic differential equation |
| Title | Statistical inference for a stochastic generalized logistic differential equation |
| URI | https://dx.doi.org/10.1016/j.cnsns.2024.108261 |
| Volume | 139 |
| hasFullText | 1 |
| inHoldings | 1 |
| isFullTextHit | |
| isPrint | |
| journalDatabaseRights | – providerCode: PRVESC databaseName: ScienceDirect Freedom Collection issn: 1007-5704 databaseCode: AIEXJ dateStart: 19960101 customDbUrl: isFulltext: true dateEnd: 99991231 titleUrlDefault: https://www.sciencedirect.com omitProxy: false ssIdentifier: ssj0016954 providerName: Elsevier |
| link | http://cvtisr.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwtV1Lb9NAEF6FlgMX3ogCrfbALRjF69f6WKFQWqEKREG5WfsypEqdkkdV5afwa5nZh201CAESFyvaxOto5vN6dvzNN4S8lGUtZM7LKMlzHaXYyF1maRIpLUc6znOpVGqbTRSnp3wyKT8MBj9CLczVrGgafn1dXv5XV8MYOBtLZ__C3e2kMACfwelwBLfD8Y8cj-GjVV-2chpBRtaSJYcQ6alvAr_E1smYjppuIOJ0ZUAwGNqlrDCPbr6vO7cFMYN-PYml0jZOa0MshqFCCMHUrN2boNlwOb3wHcK6pOlsJTZiEb2Hfbpj-fls9rwNq83sq9Dz6ItleYcAW02XqvvJVGyi46ZGZLjUdkdxPJpfuMT4WOMdMMfMg0ewT3Cw9AZZZLvyxi7UmGLNCte6uF3JnS7S1lPBJSjOX6tm2aBEO0uRWsmcCvwNue1PODNOjORaVJO7RXZZkZWwYu4eHo8nJ-07qry0PfbafxI0rSx7cOtSv457erHM2X1y129C6KEDzwMyMM1Dcs9vSKhf7pePyMcelmiLJQpYooJ2WKI9LNGAJdrHEg1Yekw-vx2fvXkX-R4ckWJxEkcF0xlLdBnXsclGtYTHYWK05lxxE6P4YjkyCm5urkxuJFMatsSiznRmeGo4F8kTsgNANE8JVUKxUprExuA6SWURy1wwk8YFqhiKPfIqWKi6dFIrVeAgnlfWoBUatHIG3SN5sGLlAe6iwArc_rsTn_3ric_JnQ6fL8jOarE2--S2ugJPLA48PH4Cel2WwQ |
| 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=Statistical+inference+for+a+stochastic+generalized+logistic+differential+equation&rft.jtitle=Communications+in+nonlinear+science+%26+numerical+simulation&rft.au=Baltazar-Larios%2C+Fernando&rft.au=Delgado-Vences%2C+Francisco&rft.au=Diaz-Infante%2C+Saul&rft.au=Gomez%2C+Eduardo+Lince&rft.date=2024-12-01&rft.pub=Elsevier+B.V&rft.issn=1007-5704&rft.volume=139&rft_id=info:doi/10.1016%2Fj.cnsns.2024.108261&rft.externalDocID=S1007570424004465 |
| 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 |