Review



whittle's log-likelihood function with fgn theoretical psd function  (MathWorks Inc)


Bioz Verified Symbol MathWorks Inc is a verified supplier  
  • Logo
  • About
  • News
  • Press Release
  • Team
  • Advisors
  • Partners
  • Contact
  • Bioz Stars
  • Bioz vStars
    • 90
      Buy from Supplier

    Structured Review

    MathWorks Inc whittle's log-likelihood function with fgn theoretical psd function
    Whittle's Log Likelihood Function With Fgn Theoretical Psd Function, supplied by MathWorks Inc, used in various techniques. Bioz Stars score: 90/100, based on 1 PubMed citations. ZERO BIAS - scores, article reviews, protocol conditions and more
    https://www.bioz.com/product/log-likelihood+function/pmc10662130-120-6-33
    Average 90 stars, based on 1 article reviews
    whittle's log-likelihood function with fgn theoretical psd function - by Bioz Stars, 2026-09
    90/100 stars

    Images

    Related Articles

    Plasmid Preparation:

    Article Title: A guide to Whittle maximum likelihood estimator in MATLAB
    Article Snippet: .................................................................. MATLAB code 6 : Whittle’s log-likelihood function with fGn theoretical PSD function lwHfgn = WLLFfgn (H,w,P,N) Tp = sin (pi*H)*gamma ((2*H)+1)*(abs(w).^(1-(2*H))); c = sum(P)/sum (Tp); T = c *Tp; lwHfgn=(2/N)*sum (log(T)+(P./T)); .................................................................. MATLAB code 7 : Whittle’s log-likelihood function with ARFIMA (0,d,0) theoretical PSD function lwHarf = WLLFarf (H,w,P,N) d = H-0.5; Tp=(1/(2*pi))*(2*sin (w/2)).^-(2*d); c = sum(P)/sum (Tp); T = c *Tp; lwHarf=(2/N)*sum (log(T)+(P./T)); .................................................................. In the first line, the function is used to declare the functions WLLFfgn and WLLFarf .

    Article Title: Prediction of the Formation of Biogenic Nonextractable Residues during Degradation of Environmental Chemicals from Biomass Yields.
    Article Snippet: 17 Maximum number of function evaluations (MCMCPar.ndraw) 20,000 Number of Markov chains (MCMCPar.seq) 5 Number of chain pairs to generate candidate points (MCMCPar.DEpairs) 1 Number of crossover values used (MCMCPar.nCR) 3 Thinning parameter for appending X to Z (MCMCPar.k) 10 Fraction of parallel direction updates (MCMCPar.parallelUpdate) 0.9 Perturbation for ergodicity (MCMCPar.eps) 0.05 Number of steps before calculating convergence diagnostics (MCMCPar.steps) MCMCPar.ndraw/(20 * MCMCPar.seq) = 200 Initial size of matrix Z (MCMCPar.m0) 10 * MCMCPar.n Probability of selecting a jumprate of 1 --> jump between modes (MCMCPar.pJumpRate_one) 0.20 Adaptive tuning of crossover values (MCMCPar.pCR) Yes Each Tth sample is collected in the chains (MCMCPar.T) 1 Prior sampling distribution (MCMCPar.prior) Latin Hypercube sampling (LHS) Boundary handling (MCMCPar.BoundHandling) Reflect Likelihood function -- log-likelihood function (MCMCPar.lik) Sum of squared errors (SSE) 18 Additionally, the Pattern Search algorithm was employed with the following set of options in MATLAB: 19 options = optimoptions('patternsearch', 'FunctionTolerance',1.0e-200, 'TolX',1e-200,'MeshTolerance',1e-200, 20 'MaxFunctionEvaluations', funevals,'UseCompletePoll', true,'MaxIterations',funevals) 21 The maximum number of function evaluations and iterations was set to 10,000 (funevals = 10,000).

    Article Title: A neural network for information seeking
    Article Snippet: We did this by deriving the log likelihood function, its gradient, and its Hessian, and using them as input to the Trust Region Reflective Algorithm for function optimization to find the parameters that locally maximized the log likelihood (using its implementation in the fmincon function in Matlab).



    Similar Products

    probit log-likelihood function and maximization  (STATA Corporation)
    90
    STATA Corporation probit log-likelihood function and maximization
    Probit Log Likelihood Function And Maximization, supplied by STATA Corporation, used in various techniques. Bioz Stars score: 90/100, based on 1 PubMed citations. ZERO BIAS - scores, article reviews, protocol conditions and more
    https://www.bioz.com/product/log-likelihood+function/probit+log+likelihood+function+and+maximization/10__22434_slash_ifamr__1006-104-46-54
    Average 90 stars, based on 1 article reviews
    probit log-likelihood function and maximization - by Bioz Stars, 2026-09
    90/100 stars
    		  Buy from Supplier
    whittle's log-likelihood function with fgn theoretical psd function  (MathWorks Inc)
    90
    MathWorks Inc whittle's log-likelihood function with fgn theoretical psd function
    Whittle's Log Likelihood Function With Fgn Theoretical Psd Function, supplied by MathWorks Inc, used in various techniques. Bioz Stars score: 90/100, based on 1 PubMed citations. ZERO BIAS - scores, article reviews, protocol conditions and more
    https://www.bioz.com/product/log-likelihood+function/pmc10662130-120-6-33
    Average 90 stars, based on 1 article reviews
    whittle's log-likelihood function with fgn theoretical psd function - by Bioz Stars, 2026-09
    90/100 stars
    		  Buy from Supplier
    whittle's log-likelihood function with arfima (0,d,0) theoretical psd function  (MathWorks Inc)
    90
    MathWorks Inc whittle's log-likelihood function with arfima (0,d,0) theoretical psd function
    Whole set of α ^ estimated. On the x -axis, α is the true value of the exponents, the values computed in the generator. On the y -axis, the estimated values of α ^ computed by the corresponding analysis method are located. Red curves represent true alpha values α , and blue curves represent the estimated alpha values α ^ . The first column (A,C,E) corresponds to the signals generated via the Cholesky method, and the second column (B,D,F) corresponds to the signals generated via <t>ARFIMA</t> filtering. The first row (A,B) presents the α ^ values computed using fGn-based Whittle’s maximum likelihood estimator, the second row (C,D) presents those computed using ARFIMA-based Whittle’s maximum likelihood estimator, and the third row (E,F) presents the α ^ values computed using DFA.
    Whittle's Log Likelihood Function With Arfima (0,D,0) Theoretical Psd Function, supplied by MathWorks Inc, used in various techniques. Bioz Stars score: 90/100, based on 1 PubMed citations. ZERO BIAS - scores, article reviews, protocol conditions and more
    https://www.bioz.com/product/log-likelihood+function/pmc10662130-120-38-33
    Average 90 stars, based on 1 article reviews
    whittle's log-likelihood function with arfima (0,d,0) theoretical psd function - by Bioz Stars, 2026-09
    90/100 stars
    		  Buy from Supplier
    gradient of the negative log-likelihood function  (SAS institute)
    90
    SAS institute gradient of the negative log-likelihood function
    Whole set of α ^ estimated. On the x -axis, α is the true value of the exponents, the values computed in the generator. On the y -axis, the estimated values of α ^ computed by the corresponding analysis method are located. Red curves represent true alpha values α , and blue curves represent the estimated alpha values α ^ . The first column (A,C,E) corresponds to the signals generated via the Cholesky method, and the second column (B,D,F) corresponds to the signals generated via <t>ARFIMA</t> filtering. The first row (A,B) presents the α ^ values computed using fGn-based Whittle’s maximum likelihood estimator, the second row (C,D) presents those computed using ARFIMA-based Whittle’s maximum likelihood estimator, and the third row (E,F) presents the α ^ values computed using DFA.
    Gradient Of The Negative Log Likelihood Function, supplied by SAS institute, used in various techniques. Bioz Stars score: 90/100, based on 1 PubMed citations. ZERO BIAS - scores, article reviews, protocol conditions and more
    https://www.bioz.com/product/log-likelihood+function/gradient+of+the+negative+log+likelihood+function/pmc10074401-429-4-22
    Average 90 stars, based on 1 article reviews
    gradient of the negative log-likelihood function - by Bioz Stars, 2026-09
    90/100 stars
    		  Buy from Supplier
    log likelihood function for a discrete survival model  (Schmid GmbH)
    90
    Schmid GmbH log likelihood function for a discrete survival model
    Whole set of α ^ estimated. On the x -axis, α is the true value of the exponents, the values computed in the generator. On the y -axis, the estimated values of α ^ computed by the corresponding analysis method are located. Red curves represent true alpha values α , and blue curves represent the estimated alpha values α ^ . The first column (A,C,E) corresponds to the signals generated via the Cholesky method, and the second column (B,D,F) corresponds to the signals generated via <t>ARFIMA</t> filtering. The first row (A,B) presents the α ^ values computed using fGn-based Whittle’s maximum likelihood estimator, the second row (C,D) presents those computed using ARFIMA-based Whittle’s maximum likelihood estimator, and the third row (E,F) presents the α ^ values computed using DFA.
    Log Likelihood Function For A Discrete Survival Model, supplied by Schmid GmbH, used in various techniques. Bioz Stars score: 90/100, based on 1 PubMed citations. ZERO BIAS - scores, article reviews, protocol conditions and more
    https://www.bioz.com/product/log-likelihood+function/modeling+discrete+time+to+event+data/pm35944502-247-73-78
    Average 90 stars, based on 1 article reviews
    log likelihood function for a discrete survival model - by Bioz Stars, 2026-09
    90/100 stars
    		  Buy from Supplier
    fitglme function with a gamma distribution and a log likelihood link function  (MathWorks Inc)
    90
    MathWorks Inc fitglme function with a gamma distribution and a log likelihood link function
    Whole set of α ^ estimated. On the x -axis, α is the true value of the exponents, the values computed in the generator. On the y -axis, the estimated values of α ^ computed by the corresponding analysis method are located. Red curves represent true alpha values α , and blue curves represent the estimated alpha values α ^ . The first column (A,C,E) corresponds to the signals generated via the Cholesky method, and the second column (B,D,F) corresponds to the signals generated via <t>ARFIMA</t> filtering. The first row (A,B) presents the α ^ values computed using fGn-based Whittle’s maximum likelihood estimator, the second row (C,D) presents those computed using ARFIMA-based Whittle’s maximum likelihood estimator, and the third row (E,F) presents the α ^ values computed using DFA.
    Fitglme Function With A Gamma Distribution And A Log Likelihood Link Function, supplied by MathWorks Inc, used in various techniques. Bioz Stars score: 90/100, based on 1 PubMed citations. ZERO BIAS - scores, article reviews, protocol conditions and more
    https://www.bioz.com/product/log-likelihood+function/pm33306950-127-39-28
    Average 90 stars, based on 1 article reviews
    fitglme function with a gamma distribution and a log likelihood link function - by Bioz Stars, 2026-09
    90/100 stars
    		  Buy from Supplier
    log-likelihood function  (STATA Corporation)
    90
    STATA Corporation log-likelihood function
    Whole set of α ^ estimated. On the x -axis, α is the true value of the exponents, the values computed in the generator. On the y -axis, the estimated values of α ^ computed by the corresponding analysis method are located. Red curves represent true alpha values α , and blue curves represent the estimated alpha values α ^ . The first column (A,C,E) corresponds to the signals generated via the Cholesky method, and the second column (B,D,F) corresponds to the signals generated via <t>ARFIMA</t> filtering. The first row (A,B) presents the α ^ values computed using fGn-based Whittle’s maximum likelihood estimator, the second row (C,D) presents those computed using ARFIMA-based Whittle’s maximum likelihood estimator, and the third row (E,F) presents the α ^ values computed using DFA.
    Log Likelihood Function, supplied by STATA Corporation, used in various techniques. Bioz Stars score: 90/100, based on 1 PubMed citations. ZERO BIAS - scores, article reviews, protocol conditions and more
    https://www.bioz.com/product/log-likelihood+function/log+likelihood+function/10__1177_slash_1536867x211025797-79-4-8
    Average 90 stars, based on 1 article reviews
    log-likelihood function - by Bioz Stars, 2026-09
    90/100 stars
    		  Buy from Supplier
    log-likelihood function for the weighted negative binomial  (STATA Corporation)
    90
    STATA Corporation log-likelihood function for the weighted negative binomial
    Whole set of α ^ estimated. On the x -axis, α is the true value of the exponents, the values computed in the generator. On the y -axis, the estimated values of α ^ computed by the corresponding analysis method are located. Red curves represent true alpha values α , and blue curves represent the estimated alpha values α ^ . The first column (A,C,E) corresponds to the signals generated via the Cholesky method, and the second column (B,D,F) corresponds to the signals generated via <t>ARFIMA</t> filtering. The first row (A,B) presents the α ^ values computed using fGn-based Whittle’s maximum likelihood estimator, the second row (C,D) presents those computed using ARFIMA-based Whittle’s maximum likelihood estimator, and the third row (E,F) presents the α ^ values computed using DFA.
    Log Likelihood Function For The Weighted Negative Binomial, supplied by STATA Corporation, used in various techniques. Bioz Stars score: 90/100, based on 1 PubMed citations. ZERO BIAS - scores, article reviews, protocol conditions and more
    https://www.bioz.com/product/log-likelihood+function/log+likelihood+function+for+the+weighted+negative+binomial/pm27129112-193-10-19
    Average 90 stars, based on 1 article reviews
    log-likelihood function for the weighted negative binomial - by Bioz Stars, 2026-09
    90/100 stars
    		  Buy from Supplier
    log-likelihood functions  (MathWorks Inc)
    90
    MathWorks Inc log-likelihood functions
    Whole set of α ^ estimated. On the x -axis, α is the true value of the exponents, the values computed in the generator. On the y -axis, the estimated values of α ^ computed by the corresponding analysis method are located. Red curves represent true alpha values α , and blue curves represent the estimated alpha values α ^ . The first column (A,C,E) corresponds to the signals generated via the Cholesky method, and the second column (B,D,F) corresponds to the signals generated via <t>ARFIMA</t> filtering. The first row (A,B) presents the α ^ values computed using fGn-based Whittle’s maximum likelihood estimator, the second row (C,D) presents those computed using ARFIMA-based Whittle’s maximum likelihood estimator, and the third row (E,F) presents the α ^ values computed using DFA.
    Log Likelihood Functions, supplied by MathWorks Inc, used in various techniques. Bioz Stars score: 90/100, based on 1 PubMed citations. ZERO BIAS - scores, article reviews, protocol conditions and more
    https://www.bioz.com/product/log-likelihood+function/pmc04697432-193-1-6
    Average 90 stars, based on 1 article reviews
    log-likelihood functions - by Bioz Stars, 2026-09
    90/100 stars
    		  Buy from Supplier

    Image Search Results


    Whole set of α ^ estimated. On the x -axis, α is the true value of the exponents, the values computed in the generator. On the y -axis, the estimated values of α ^ computed by the corresponding analysis method are located. Red curves represent true alpha values α , and blue curves represent the estimated alpha values α ^ . The first column (A,C,E) corresponds to the signals generated via the Cholesky method, and the second column (B,D,F) corresponds to the signals generated via ARFIMA filtering. The first row (A,B) presents the α ^ values computed using fGn-based Whittle’s maximum likelihood estimator, the second row (C,D) presents those computed using ARFIMA-based Whittle’s maximum likelihood estimator, and the third row (E,F) presents the α ^ values computed using DFA.

    Journal: Frontiers in Network Physiology

    Article Title: A guide to Whittle maximum likelihood estimator in MATLAB

    doi: 10.3389/fnetp.2023.1204757

    Figure Lengend Snippet: Whole set of α ^ estimated. On the x -axis, α is the true value of the exponents, the values computed in the generator. On the y -axis, the estimated values of α ^ computed by the corresponding analysis method are located. Red curves represent true alpha values α , and blue curves represent the estimated alpha values α ^ . The first column (A,C,E) corresponds to the signals generated via the Cholesky method, and the second column (B,D,F) corresponds to the signals generated via ARFIMA filtering. The first row (A,B) presents the α ^ values computed using fGn-based Whittle’s maximum likelihood estimator, the second row (C,D) presents those computed using ARFIMA-based Whittle’s maximum likelihood estimator, and the third row (E,F) presents the α ^ values computed using DFA.

    Article Snippet: .................................................................. MATLAB code 6 : Whittle’s log-likelihood function with fGn theoretical PSD function lwHfgn = WLLFfgn (H,w,P,N) Tp = sin (pi*H)*gamma ((2*H)+1)*(abs(w).^(1-(2*H))); c = sum(P)/sum (Tp); T = c *Tp; lwHfgn=(2/N)*sum (log(T)+(P./T)); .................................................................. MATLAB code 7 : Whittle’s log-likelihood function with ARFIMA (0,d,0) theoretical PSD function lwHarf = WLLFarf (H,w,P,N) d = H-0.5; Tp=(1/(2*pi))*(2*sin (w/2)).^-(2*d); c = sum(P)/sum (Tp); T = c *Tp; lwHarf=(2/N)*sum (log(T)+(P./T)); .................................................................. In the first line, the function is used to declare the functions WLLFfgn and WLLFarf .

    Techniques: Generated

    Periodogram of choleskyfgn (A) , arfima0d0 (B) , whitenoise (C) , and empirical (D) signals with the theoretical power spectral density of fGn (orange curve) and ARFIMA (0, d ,0) (yellow curve). The theoretical power spectral densities were computed with the estimated values of H and d obtained via whittle.m. Those values, entered in MATLAB code 2 and 3, are presented in .

    Journal: Frontiers in Network Physiology

    Article Title: A guide to Whittle maximum likelihood estimator in MATLAB

    doi: 10.3389/fnetp.2023.1204757

    Figure Lengend Snippet: Periodogram of choleskyfgn (A) , arfima0d0 (B) , whitenoise (C) , and empirical (D) signals with the theoretical power spectral density of fGn (orange curve) and ARFIMA (0, d ,0) (yellow curve). The theoretical power spectral densities were computed with the estimated values of H and d obtained via whittle.m. Those values, entered in MATLAB code 2 and 3, are presented in .

    Article Snippet: .................................................................. MATLAB code 6 : Whittle’s log-likelihood function with fGn theoretical PSD function lwHfgn = WLLFfgn (H,w,P,N) Tp = sin (pi*H)*gamma ((2*H)+1)*(abs(w).^(1-(2*H))); c = sum(P)/sum (Tp); T = c *Tp; lwHfgn=(2/N)*sum (log(T)+(P./T)); .................................................................. MATLAB code 7 : Whittle’s log-likelihood function with ARFIMA (0,d,0) theoretical PSD function lwHarf = WLLFarf (H,w,P,N) d = H-0.5; Tp=(1/(2*pi))*(2*sin (w/2)).^-(2*d); c = sum(P)/sum (Tp); T = c *Tp; lwHarf=(2/N)*sum (log(T)+(P./T)); .................................................................. In the first line, the function is used to declare the functions WLLFfgn and WLLFarf .

    Techniques:

    Periodogram of choleskyfgn (A) , arfima0d0 (B) , whitenoise (C) , and empirical (D) signals (blue curve) with the adjusted theoretical power spectral density of fGn (orange curve) and ARFIMA (0, d ,0) (yellow curve). The H and d values are the same as those used in the previous figure.

    Journal: Frontiers in Network Physiology

    Article Title: A guide to Whittle maximum likelihood estimator in MATLAB

    doi: 10.3389/fnetp.2023.1204757

    Figure Lengend Snippet: Periodogram of choleskyfgn (A) , arfima0d0 (B) , whitenoise (C) , and empirical (D) signals (blue curve) with the adjusted theoretical power spectral density of fGn (orange curve) and ARFIMA (0, d ,0) (yellow curve). The H and d values are the same as those used in the previous figure.

    Article Snippet: .................................................................. MATLAB code 6 : Whittle’s log-likelihood function with fGn theoretical PSD function lwHfgn = WLLFfgn (H,w,P,N) Tp = sin (pi*H)*gamma ((2*H)+1)*(abs(w).^(1-(2*H))); c = sum(P)/sum (Tp); T = c *Tp; lwHfgn=(2/N)*sum (log(T)+(P./T)); .................................................................. MATLAB code 7 : Whittle’s log-likelihood function with ARFIMA (0,d,0) theoretical PSD function lwHarf = WLLFarf (H,w,P,N) d = H-0.5; Tp=(1/(2*pi))*(2*sin (w/2)).^-(2*d); c = sum(P)/sum (Tp); T = c *Tp; lwHarf=(2/N)*sum (log(T)+(P./T)); .................................................................. In the first line, the function is used to declare the functions WLLFfgn and WLLFarf .

    Techniques:

    Whittle’s log-likelihood functions of choleskyfgn (A) , arfima0d0 (B) , whitenoise (C) , and empirical (D) signals. The blue curves correspond to Whittle’s likelihood function calculated using the fGn theoretical spectrum, while the orange curves correspond to the same function calculated using the ARFIMA (0, d ,0) theoretical spectrum.

    Journal: Frontiers in Network Physiology

    Article Title: A guide to Whittle maximum likelihood estimator in MATLAB

    doi: 10.3389/fnetp.2023.1204757

    Figure Lengend Snippet: Whittle’s log-likelihood functions of choleskyfgn (A) , arfima0d0 (B) , whitenoise (C) , and empirical (D) signals. The blue curves correspond to Whittle’s likelihood function calculated using the fGn theoretical spectrum, while the orange curves correspond to the same function calculated using the ARFIMA (0, d ,0) theoretical spectrum.

    Article Snippet: .................................................................. MATLAB code 6 : Whittle’s log-likelihood function with fGn theoretical PSD function lwHfgn = WLLFfgn (H,w,P,N) Tp = sin (pi*H)*gamma ((2*H)+1)*(abs(w).^(1-(2*H))); c = sum(P)/sum (Tp); T = c *Tp; lwHfgn=(2/N)*sum (log(T)+(P./T)); .................................................................. MATLAB code 7 : Whittle’s log-likelihood function with ARFIMA (0,d,0) theoretical PSD function lwHarf = WLLFarf (H,w,P,N) d = H-0.5; Tp=(1/(2*pi))*(2*sin (w/2)).^-(2*d); c = sum(P)/sum (Tp); T = c *Tp; lwHarf=(2/N)*sum (log(T)+(P./T)); .................................................................. In the first line, the function is used to declare the functions WLLFfgn and WLLFarf .

    Techniques:

    Box plot of α ^ squared error values obtained via fGn-based Whittle’s likelihood (A) , ARFIMA-based Whittle’s likelihood (B) , and DFA (C) . The lower and upper edges of the boxes represent the 25 and 75 percentiles, respectively. The horizontal black line represents the median. The whiskers extend to the most extreme points not considered as outliers. The outliers are plotted as individual points. The orange diamond represents the MSE value.

    Journal: Frontiers in Network Physiology

    Article Title: A guide to Whittle maximum likelihood estimator in MATLAB

    doi: 10.3389/fnetp.2023.1204757

    Figure Lengend Snippet: Box plot of α ^ squared error values obtained via fGn-based Whittle’s likelihood (A) , ARFIMA-based Whittle’s likelihood (B) , and DFA (C) . The lower and upper edges of the boxes represent the 25 and 75 percentiles, respectively. The horizontal black line represents the median. The whiskers extend to the most extreme points not considered as outliers. The outliers are plotted as individual points. The orange diamond represents the MSE value.

    Article Snippet: .................................................................. MATLAB code 6 : Whittle’s log-likelihood function with fGn theoretical PSD function lwHfgn = WLLFfgn (H,w,P,N) Tp = sin (pi*H)*gamma ((2*H)+1)*(abs(w).^(1-(2*H))); c = sum(P)/sum (Tp); T = c *Tp; lwHfgn=(2/N)*sum (log(T)+(P./T)); .................................................................. MATLAB code 7 : Whittle’s log-likelihood function with ARFIMA (0,d,0) theoretical PSD function lwHarf = WLLFarf (H,w,P,N) d = H-0.5; Tp=(1/(2*pi))*(2*sin (w/2)).^-(2*d); c = sum(P)/sum (Tp); T = c *Tp; lwHarf=(2/N)*sum (log(T)+(P./T)); .................................................................. In the first line, the function is used to declare the functions WLLFfgn and WLLFarf .

    Techniques:

    Box plot of α ^ squared error values obtained using ARFIMA-based Whittle’s likelihood for four sets of length: 32 (A) , 64 (B) , 128 (C) , and 256 (D) . The lower and upper edges of the boxes represent the 25 and 75 percentiles, respectively. The horizontal black line represents the median. The whiskers extend to the most extreme points not considered as outliers. The outliers are plotted as individual points. The orange diamond represents the MSE value. The vertical scale of the top left graph is 20 times larger than the other three panels.

    Journal: Frontiers in Network Physiology

    Article Title: A guide to Whittle maximum likelihood estimator in MATLAB

    doi: 10.3389/fnetp.2023.1204757

    Figure Lengend Snippet: Box plot of α ^ squared error values obtained using ARFIMA-based Whittle’s likelihood for four sets of length: 32 (A) , 64 (B) , 128 (C) , and 256 (D) . The lower and upper edges of the boxes represent the 25 and 75 percentiles, respectively. The horizontal black line represents the median. The whiskers extend to the most extreme points not considered as outliers. The outliers are plotted as individual points. The orange diamond represents the MSE value. The vertical scale of the top left graph is 20 times larger than the other three panels.

    Article Snippet: .................................................................. MATLAB code 6 : Whittle’s log-likelihood function with fGn theoretical PSD function lwHfgn = WLLFfgn (H,w,P,N) Tp = sin (pi*H)*gamma ((2*H)+1)*(abs(w).^(1-(2*H))); c = sum(P)/sum (Tp); T = c *Tp; lwHfgn=(2/N)*sum (log(T)+(P./T)); .................................................................. MATLAB code 7 : Whittle’s log-likelihood function with ARFIMA (0,d,0) theoretical PSD function lwHarf = WLLFarf (H,w,P,N) d = H-0.5; Tp=(1/(2*pi))*(2*sin (w/2)).^-(2*d); c = sum(P)/sum (Tp); T = c *Tp; lwHarf=(2/N)*sum (log(T)+(P./T)); .................................................................. In the first line, the function is used to declare the functions WLLFfgn and WLLFarf .

    Techniques:

    Comparison of α ^ estimated via ARFIMA-based Whittle’s likelihood and DFA on gait data made available by J. Hausdorff on the PhysioNet platform ( <xref ref-type= Goldberger et al., 2000 ; Hausdorff, 2001 ). The results highlighted in red correspond to anti-persistent series, i.e., with α lower than 0.5." width="100%" height="100%">

    Journal: Frontiers in Network Physiology

    Article Title: A guide to Whittle maximum likelihood estimator in MATLAB

    doi: 10.3389/fnetp.2023.1204757

    Figure Lengend Snippet: Comparison of α ^ estimated via ARFIMA-based Whittle’s likelihood and DFA on gait data made available by J. Hausdorff on the PhysioNet platform ( Goldberger et al., 2000 ; Hausdorff, 2001 ). The results highlighted in red correspond to anti-persistent series, i.e., with α lower than 0.5.

    Article Snippet: .................................................................. MATLAB code 6 : Whittle’s log-likelihood function with fGn theoretical PSD function lwHfgn = WLLFfgn (H,w,P,N) Tp = sin (pi*H)*gamma ((2*H)+1)*(abs(w).^(1-(2*H))); c = sum(P)/sum (Tp); T = c *Tp; lwHfgn=(2/N)*sum (log(T)+(P./T)); .................................................................. MATLAB code 7 : Whittle’s log-likelihood function with ARFIMA (0,d,0) theoretical PSD function lwHarf = WLLFarf (H,w,P,N) d = H-0.5; Tp=(1/(2*pi))*(2*sin (w/2)).^-(2*d); c = sum(P)/sum (Tp); T = c *Tp; lwHarf=(2/N)*sum (log(T)+(P./T)); .................................................................. In the first line, the function is used to declare the functions WLLFfgn and WLLFarf .

    Techniques: Comparison

    log-power spectral density of Hausdorff data rearranged into three groups: persistent behavior (A) , anti-persistent behavior (B) , and mixed behavior (C) . log-power spectral density of an artificial ARFIMA(p,d,q) signal with parameters (2, −0.35.1) generated using ARFIMApdq.m (D) .

    Journal: Frontiers in Network Physiology

    Article Title: A guide to Whittle maximum likelihood estimator in MATLAB

    doi: 10.3389/fnetp.2023.1204757

    Figure Lengend Snippet: log-power spectral density of Hausdorff data rearranged into three groups: persistent behavior (A) , anti-persistent behavior (B) , and mixed behavior (C) . log-power spectral density of an artificial ARFIMA(p,d,q) signal with parameters (2, −0.35.1) generated using ARFIMApdq.m (D) .

    Article Snippet: .................................................................. MATLAB code 6 : Whittle’s log-likelihood function with fGn theoretical PSD function lwHfgn = WLLFfgn (H,w,P,N) Tp = sin (pi*H)*gamma ((2*H)+1)*(abs(w).^(1-(2*H))); c = sum(P)/sum (Tp); T = c *Tp; lwHfgn=(2/N)*sum (log(T)+(P./T)); .................................................................. MATLAB code 7 : Whittle’s log-likelihood function with ARFIMA (0,d,0) theoretical PSD function lwHarf = WLLFarf (H,w,P,N) d = H-0.5; Tp=(1/(2*pi))*(2*sin (w/2)).^-(2*d); c = sum(P)/sum (Tp); T = c *Tp; lwHarf=(2/N)*sum (log(T)+(P./T)); .................................................................. In the first line, the function is used to declare the functions WLLFfgn and WLLFarf .

    Techniques: Generated