Asymptotic expansions for infinite weighted convolutions of heavy tail distributions and application / / Ph. Barbe, W.P. McCormick |
Autore | Barbe Philippe |
Pubbl/distr/stampa | Providence, Rhode Island : , : American Mathematical Society, , 2009 |
Descrizione fisica | 1 online resource (133 p.) |
Disciplina | 519.2/4 |
Collana | Memoirs of the American Mathematical Society |
Soggetto topico |
Distribution (Probability theory) - Mathematical models
Asymptotic expansions Stochastic processes |
Soggetto genere / forma | Electronic books. |
ISBN | 1-4704-0528-8 |
Formato | Materiale a stampa ![]() |
Livello bibliografico | Monografia |
Lingua di pubblicazione | eng |
Nota di contenuto |
""Contents""; ""1. Introduction""; ""1.1. Prolegomenom""; ""1.2. Mathematical overview and heuristics""; ""2. Main result""; ""2.1. Some notation""; ""2.2. Asymptotic scales""; ""2.3. The Laplace characters""; ""2.4. Smoothly varying functions of finite order""; ""2.5. Asymptotic expansion for in finite weighted convolution""; ""3. Implementing the expansion""; ""3.1. How many terms are in the expansion?""; ""3.2. [sub(*)]-Asymptotic scales and functions of class m""; ""3.3. Tail calculus: From Laplace characters to linear algebra""; ""3.4. Some examples""
""3.5. Two terms expansion and second order regular variation""""3.6. Some open questions""; ""4. Applications""; ""4.1. ARMA models""; ""4.2. Tail index estimation""; ""4.3. Randomly weighted sums""; ""4.4. Compound sums""; ""4.5. Queueing theory""; ""4.6. Branching processes""; ""4.7. Infinitely divisible distributions""; ""4.8. Implicit transient renewal equation and iterative systems""; ""5. Preparing the proof""; ""5.1. Properties of Laplace characters""; ""5.2. Properties of smoothly varying functions of finite order""; ""6. Proof in the positive case"" ""6.1. Decomposition of the convolution into integral and multiplication operators""""6.2. Organizing the proof""; ""6.3. Regular variation and basic tail estimates""; ""6.4. The fundamental estimate""; ""6.5. Basic lemmas""; ""6.6. Inductions""; ""6.7. Conclusion""; ""7. Removing the sign restriction on the random variables""; ""7.1. Elementary properties of U[sub(H)]""; ""7.2. Basic expansion of U[sub(H)]""; ""7.3. A technical lemma""; ""7.4. Conditional expansion and removing conditioning""; ""8. Removing the sign restriction on the constants"" ""8.1. Neglecting terms involving the multiplication operators""""8.2. Substituting H[sup((k))] and G[sup((k))] by their expansions""; ""9. Removing the smoothness restriction""; ""Appendix. Maple code""; ""Bibliography"" |
Record Nr. | UNINA-9910480112803321 |
Barbe Philippe
![]() |
||
Providence, Rhode Island : , : American Mathematical Society, , 2009 | ||
![]() | ||
Lo trovi qui: Univ. Federico II | ||
|
Asymptotic expansions for infinite weighted convolutions of heavy tail distributions and application / / Ph. Barbe, W.P. McCormick |
Autore | Barbe Philippe |
Pubbl/distr/stampa | Providence, Rhode Island : , : American Mathematical Society, , 2009 |
Descrizione fisica | 1 online resource (133 p.) |
Disciplina | 519.2/4 |
Collana | Memoirs of the American Mathematical Society |
Soggetto topico |
Distribution (Probability theory) - Mathematical models
Asymptotic expansions Stochastic processes |
ISBN | 1-4704-0528-8 |
Formato | Materiale a stampa ![]() |
Livello bibliografico | Monografia |
Lingua di pubblicazione | eng |
Nota di contenuto |
""Contents""; ""1. Introduction""; ""1.1. Prolegomenom""; ""1.2. Mathematical overview and heuristics""; ""2. Main result""; ""2.1. Some notation""; ""2.2. Asymptotic scales""; ""2.3. The Laplace characters""; ""2.4. Smoothly varying functions of finite order""; ""2.5. Asymptotic expansion for in finite weighted convolution""; ""3. Implementing the expansion""; ""3.1. How many terms are in the expansion?""; ""3.2. [sub(*)]-Asymptotic scales and functions of class m""; ""3.3. Tail calculus: From Laplace characters to linear algebra""; ""3.4. Some examples""
""3.5. Two terms expansion and second order regular variation""""3.6. Some open questions""; ""4. Applications""; ""4.1. ARMA models""; ""4.2. Tail index estimation""; ""4.3. Randomly weighted sums""; ""4.4. Compound sums""; ""4.5. Queueing theory""; ""4.6. Branching processes""; ""4.7. Infinitely divisible distributions""; ""4.8. Implicit transient renewal equation and iterative systems""; ""5. Preparing the proof""; ""5.1. Properties of Laplace characters""; ""5.2. Properties of smoothly varying functions of finite order""; ""6. Proof in the positive case"" ""6.1. Decomposition of the convolution into integral and multiplication operators""""6.2. Organizing the proof""; ""6.3. Regular variation and basic tail estimates""; ""6.4. The fundamental estimate""; ""6.5. Basic lemmas""; ""6.6. Inductions""; ""6.7. Conclusion""; ""7. Removing the sign restriction on the random variables""; ""7.1. Elementary properties of U[sub(H)]""; ""7.2. Basic expansion of U[sub(H)]""; ""7.3. A technical lemma""; ""7.4. Conditional expansion and removing conditioning""; ""8. Removing the sign restriction on the constants"" ""8.1. Neglecting terms involving the multiplication operators""""8.2. Substituting H[sup((k))] and G[sup((k))] by their expansions""; ""9. Removing the smoothness restriction""; ""Appendix. Maple code""; ""Bibliography"" |
Record Nr. | UNINA-9910788853703321 |
Barbe Philippe
![]() |
||
Providence, Rhode Island : , : American Mathematical Society, , 2009 | ||
![]() | ||
Lo trovi qui: Univ. Federico II | ||
|
Asymptotic expansions for infinite weighted convolutions of heavy tail distributions and application / / Ph. Barbe, W.P. McCormick |
Autore | Barbe Philippe |
Pubbl/distr/stampa | Providence, Rhode Island : , : American Mathematical Society, , 2009 |
Descrizione fisica | 1 online resource (133 p.) |
Disciplina | 519.2/4 |
Collana | Memoirs of the American Mathematical Society |
Soggetto topico |
Distribution (Probability theory) - Mathematical models
Asymptotic expansions Stochastic processes |
ISBN | 1-4704-0528-8 |
Formato | Materiale a stampa ![]() |
Livello bibliografico | Monografia |
Lingua di pubblicazione | eng |
Nota di contenuto |
""Contents""; ""1. Introduction""; ""1.1. Prolegomenom""; ""1.2. Mathematical overview and heuristics""; ""2. Main result""; ""2.1. Some notation""; ""2.2. Asymptotic scales""; ""2.3. The Laplace characters""; ""2.4. Smoothly varying functions of finite order""; ""2.5. Asymptotic expansion for in finite weighted convolution""; ""3. Implementing the expansion""; ""3.1. How many terms are in the expansion?""; ""3.2. [sub(*)]-Asymptotic scales and functions of class m""; ""3.3. Tail calculus: From Laplace characters to linear algebra""; ""3.4. Some examples""
""3.5. Two terms expansion and second order regular variation""""3.6. Some open questions""; ""4. Applications""; ""4.1. ARMA models""; ""4.2. Tail index estimation""; ""4.3. Randomly weighted sums""; ""4.4. Compound sums""; ""4.5. Queueing theory""; ""4.6. Branching processes""; ""4.7. Infinitely divisible distributions""; ""4.8. Implicit transient renewal equation and iterative systems""; ""5. Preparing the proof""; ""5.1. Properties of Laplace characters""; ""5.2. Properties of smoothly varying functions of finite order""; ""6. Proof in the positive case"" ""6.1. Decomposition of the convolution into integral and multiplication operators""""6.2. Organizing the proof""; ""6.3. Regular variation and basic tail estimates""; ""6.4. The fundamental estimate""; ""6.5. Basic lemmas""; ""6.6. Inductions""; ""6.7. Conclusion""; ""7. Removing the sign restriction on the random variables""; ""7.1. Elementary properties of U[sub(H)]""; ""7.2. Basic expansion of U[sub(H)]""; ""7.3. A technical lemma""; ""7.4. Conditional expansion and removing conditioning""; ""8. Removing the sign restriction on the constants"" ""8.1. Neglecting terms involving the multiplication operators""""8.2. Substituting H[sup((k))] and G[sup((k))] by their expansions""; ""9. Removing the smoothness restriction""; ""Appendix. Maple code""; ""Bibliography"" |
Record Nr. | UNINA-9910817264803321 |
Barbe Philippe
![]() |
||
Providence, Rhode Island : , : American Mathematical Society, , 2009 | ||
![]() | ||
Lo trovi qui: Univ. Federico II | ||
|
Intermediate probability [[electronic resource] ] : a computational approach / / Marc S. Paolella |
Autore | Paolella Marc S |
Pubbl/distr/stampa | Chichester, England ; ; Hoboken, NJ, : John Wiley, c2007 |
Descrizione fisica | 1 online resource (431 p.) |
Disciplina | 519.2 |
Soggetto topico |
Distribution (Probability theory) - Mathematical models
Probabilities |
ISBN |
1-281-00209-7
9786611002091 0-470-03506-4 0-470-03505-6 |
Formato | Materiale a stampa ![]() |
Livello bibliografico | Monografia |
Lingua di pubblicazione | eng |
Nota di contenuto |
Intermediate Probability; Chapter Listing; Contents; Preface; Part I Sums of Random Variables; 1 Generating functions; 1.1 The moment generating function; 1.1.1 Moments and the m.g.f.; 1.1.2 The cumulant generating function; 1.1.3 Uniqueness of the m.g.f.; 1.1.4 Vector m.g.f.; 1.2 Characteristic functions; 1.2.1 Complex numbers; 1.2.2 Laplace transforms; 1.2.3 Basic properties of characteristic functions; 1.2.4 Relation between the m.g.f. and c.f.; 1.2.5 Inversion formulae for mass and density functions; 1.2.6 Inversion formulae for the c.d.f.; 1.3 Use of the fast Fourier transform
1.3.1 Fourier series1.3.2 Discrete and fast Fourier transforms; 1.3.3 Applying the FFT to c.f. inversion; 1.4 Multivariate case; 1.5 Problems; 2 Sums and other functions of several random variables; 2.1 Weighted sums of independent random variables; 2.2 Exact integral expressions for functions of two continuous random variables; 2.3 Approximating the mean and variance; 2.4 Problems; 3 The multivariate normal distribution; 3.1 Vector expectation and variance; 3.2 Basic properties of the multivariate normal; 3.3 Density and moment generating function; 3.4 Simulation and c.d.f. calculation 3.5 Marginal and conditional normal distributions3.6 Partial correlation; 3.7 Joint distribution of X and S2 for i.i.d. normal samples; 3.8 Matrix algebra; 3.9 Problems; Part II Asymptotics and Other Approximations; 4 Convergence concepts; 4.1 Inequalities for random variables; 4.2 Convergence of sequences of sets; 4.3 Convergence of sequences of random variables; 4.3.1 Convergence in probability; 4.3.2 Almost sure convergence; 4.3.3 Convergence in r-mean; 4.3.4 Convergence in distribution; 4.4 The central limit theorem; 4.5 Problems; 5 Saddlepoint approximations; 5.1 Univariate 5.1.1 Density saddlepoint approximation5.1.2 Saddlepoint approximation to the c.d.f.; 5.1.3 Detailed illustration: the normal-Laplace sum; 5.2 Multivariate; 5.2.1 Conditional distributions; 5.2.2 Bivariate c.d.f. approximation; 5.2.3 Marginal distributions; 5.3 The hypergeometric functions 1F1 and 2F1; 5.4 Problems; 6 Order statistics; 6.1 Distribution theory for i.i.d. samples; 6.1.1 Univariate; 6.1.2 Multivariate; 6.1.3 Sample range and midrange; 6.2 Further examples; 6.3 Distribution theory for dependent samples; 6.4 Problems; Part III More Flexible and Advanced Random Variables 7 Generalizing and mixing7.1 Basic methods of extension; 7.1.1 Nesting and generalizing constants; 7.1.2 Asymmetric extensions; 7.1.3 Extension to the real line; 7.1.4 Transformations; 7.1.5 Invention of flexible forms; 7.2 Weighted sums of independent random variables; 7.3 Mixtures; 7.3.1 Countable mixtures; 7.3.2 Continuous mixtures; 7.4 Problems; 8 The stable Paretian distribution; 8.1 Symmetric stable; 8.2 Asymmetric stable; 8.3 Moments; 8.3.1 Mean; 8.3.2 Fractional absolute moment proof I; 8.3.3 Fractional absolute moment proof II; 8.4 Simulation; 8.5 Generalized central limit theorem 9 Generalized inverse Gaussianand generalized hyperbolic distributions |
Record Nr. | UNINA-9910143585303321 |
Paolella Marc S
![]() |
||
Chichester, England ; ; Hoboken, NJ, : John Wiley, c2007 | ||
![]() | ||
Lo trovi qui: Univ. Federico II | ||
|
Intermediate probability [[electronic resource] ] : a computational approach / / Marc S. Paolella |
Autore | Paolella Marc S |
Pubbl/distr/stampa | Chichester, England ; ; Hoboken, NJ, : John Wiley, c2007 |
Descrizione fisica | 1 online resource (431 p.) |
Disciplina | 519.2 |
Soggetto topico |
Distribution (Probability theory) - Mathematical models
Probabilities |
ISBN |
1-281-00209-7
9786611002091 0-470-03506-4 0-470-03505-6 |
Formato | Materiale a stampa ![]() |
Livello bibliografico | Monografia |
Lingua di pubblicazione | eng |
Nota di contenuto |
Intermediate Probability; Chapter Listing; Contents; Preface; Part I Sums of Random Variables; 1 Generating functions; 1.1 The moment generating function; 1.1.1 Moments and the m.g.f.; 1.1.2 The cumulant generating function; 1.1.3 Uniqueness of the m.g.f.; 1.1.4 Vector m.g.f.; 1.2 Characteristic functions; 1.2.1 Complex numbers; 1.2.2 Laplace transforms; 1.2.3 Basic properties of characteristic functions; 1.2.4 Relation between the m.g.f. and c.f.; 1.2.5 Inversion formulae for mass and density functions; 1.2.6 Inversion formulae for the c.d.f.; 1.3 Use of the fast Fourier transform
1.3.1 Fourier series1.3.2 Discrete and fast Fourier transforms; 1.3.3 Applying the FFT to c.f. inversion; 1.4 Multivariate case; 1.5 Problems; 2 Sums and other functions of several random variables; 2.1 Weighted sums of independent random variables; 2.2 Exact integral expressions for functions of two continuous random variables; 2.3 Approximating the mean and variance; 2.4 Problems; 3 The multivariate normal distribution; 3.1 Vector expectation and variance; 3.2 Basic properties of the multivariate normal; 3.3 Density and moment generating function; 3.4 Simulation and c.d.f. calculation 3.5 Marginal and conditional normal distributions3.6 Partial correlation; 3.7 Joint distribution of X and S2 for i.i.d. normal samples; 3.8 Matrix algebra; 3.9 Problems; Part II Asymptotics and Other Approximations; 4 Convergence concepts; 4.1 Inequalities for random variables; 4.2 Convergence of sequences of sets; 4.3 Convergence of sequences of random variables; 4.3.1 Convergence in probability; 4.3.2 Almost sure convergence; 4.3.3 Convergence in r-mean; 4.3.4 Convergence in distribution; 4.4 The central limit theorem; 4.5 Problems; 5 Saddlepoint approximations; 5.1 Univariate 5.1.1 Density saddlepoint approximation5.1.2 Saddlepoint approximation to the c.d.f.; 5.1.3 Detailed illustration: the normal-Laplace sum; 5.2 Multivariate; 5.2.1 Conditional distributions; 5.2.2 Bivariate c.d.f. approximation; 5.2.3 Marginal distributions; 5.3 The hypergeometric functions 1F1 and 2F1; 5.4 Problems; 6 Order statistics; 6.1 Distribution theory for i.i.d. samples; 6.1.1 Univariate; 6.1.2 Multivariate; 6.1.3 Sample range and midrange; 6.2 Further examples; 6.3 Distribution theory for dependent samples; 6.4 Problems; Part III More Flexible and Advanced Random Variables 7 Generalizing and mixing7.1 Basic methods of extension; 7.1.1 Nesting and generalizing constants; 7.1.2 Asymmetric extensions; 7.1.3 Extension to the real line; 7.1.4 Transformations; 7.1.5 Invention of flexible forms; 7.2 Weighted sums of independent random variables; 7.3 Mixtures; 7.3.1 Countable mixtures; 7.3.2 Continuous mixtures; 7.4 Problems; 8 The stable Paretian distribution; 8.1 Symmetric stable; 8.2 Asymmetric stable; 8.3 Moments; 8.3.1 Mean; 8.3.2 Fractional absolute moment proof I; 8.3.3 Fractional absolute moment proof II; 8.4 Simulation; 8.5 Generalized central limit theorem 9 Generalized inverse Gaussianand generalized hyperbolic distributions |
Record Nr. | UNINA-9910829851403321 |
Paolella Marc S
![]() |
||
Chichester, England ; ; Hoboken, NJ, : John Wiley, c2007 | ||
![]() | ||
Lo trovi qui: Univ. Federico II | ||
|
Intermediate probability : a computational approach / / Marc S. Paolella |
Autore | Paolella Marc S |
Pubbl/distr/stampa | Chichester, England ; ; Hoboken, NJ, : John Wiley, c2007 |
Descrizione fisica | 1 online resource (431 p.) |
Disciplina | 519.2 |
Soggetto topico |
Distribution (Probability theory) - Mathematical models
Probabilities |
ISBN |
1-281-00209-7
9786611002091 0-470-03506-4 0-470-03505-6 |
Formato | Materiale a stampa ![]() |
Livello bibliografico | Monografia |
Lingua di pubblicazione | eng |
Nota di contenuto |
Intermediate Probability; Chapter Listing; Contents; Preface; Part I Sums of Random Variables; 1 Generating functions; 1.1 The moment generating function; 1.1.1 Moments and the m.g.f.; 1.1.2 The cumulant generating function; 1.1.3 Uniqueness of the m.g.f.; 1.1.4 Vector m.g.f.; 1.2 Characteristic functions; 1.2.1 Complex numbers; 1.2.2 Laplace transforms; 1.2.3 Basic properties of characteristic functions; 1.2.4 Relation between the m.g.f. and c.f.; 1.2.5 Inversion formulae for mass and density functions; 1.2.6 Inversion formulae for the c.d.f.; 1.3 Use of the fast Fourier transform
1.3.1 Fourier series1.3.2 Discrete and fast Fourier transforms; 1.3.3 Applying the FFT to c.f. inversion; 1.4 Multivariate case; 1.5 Problems; 2 Sums and other functions of several random variables; 2.1 Weighted sums of independent random variables; 2.2 Exact integral expressions for functions of two continuous random variables; 2.3 Approximating the mean and variance; 2.4 Problems; 3 The multivariate normal distribution; 3.1 Vector expectation and variance; 3.2 Basic properties of the multivariate normal; 3.3 Density and moment generating function; 3.4 Simulation and c.d.f. calculation 3.5 Marginal and conditional normal distributions3.6 Partial correlation; 3.7 Joint distribution of X and S2 for i.i.d. normal samples; 3.8 Matrix algebra; 3.9 Problems; Part II Asymptotics and Other Approximations; 4 Convergence concepts; 4.1 Inequalities for random variables; 4.2 Convergence of sequences of sets; 4.3 Convergence of sequences of random variables; 4.3.1 Convergence in probability; 4.3.2 Almost sure convergence; 4.3.3 Convergence in r-mean; 4.3.4 Convergence in distribution; 4.4 The central limit theorem; 4.5 Problems; 5 Saddlepoint approximations; 5.1 Univariate 5.1.1 Density saddlepoint approximation5.1.2 Saddlepoint approximation to the c.d.f.; 5.1.3 Detailed illustration: the normal-Laplace sum; 5.2 Multivariate; 5.2.1 Conditional distributions; 5.2.2 Bivariate c.d.f. approximation; 5.2.3 Marginal distributions; 5.3 The hypergeometric functions 1F1 and 2F1; 5.4 Problems; 6 Order statistics; 6.1 Distribution theory for i.i.d. samples; 6.1.1 Univariate; 6.1.2 Multivariate; 6.1.3 Sample range and midrange; 6.2 Further examples; 6.3 Distribution theory for dependent samples; 6.4 Problems; Part III More Flexible and Advanced Random Variables 7 Generalizing and mixing7.1 Basic methods of extension; 7.1.1 Nesting and generalizing constants; 7.1.2 Asymmetric extensions; 7.1.3 Extension to the real line; 7.1.4 Transformations; 7.1.5 Invention of flexible forms; 7.2 Weighted sums of independent random variables; 7.3 Mixtures; 7.3.1 Countable mixtures; 7.3.2 Continuous mixtures; 7.4 Problems; 8 The stable Paretian distribution; 8.1 Symmetric stable; 8.2 Asymmetric stable; 8.3 Moments; 8.3.1 Mean; 8.3.2 Fractional absolute moment proof I; 8.3.3 Fractional absolute moment proof II; 8.4 Simulation; 8.5 Generalized central limit theorem 9 Generalized inverse Gaussianand generalized hyperbolic distributions |
Record Nr. | UNINA-9910876673803321 |
Paolella Marc S
![]() |
||
Chichester, England ; ; Hoboken, NJ, : John Wiley, c2007 | ||
![]() | ||
Lo trovi qui: Univ. Federico II | ||
|
Riesz probability distributions / / Abdelhamid Hassairi |
Autore | Hassairi Abdelhamid |
Pubbl/distr/stampa | Berlin ; ; Boston, MA : , : Walter de Gruyter GmbH, , [2021] |
Descrizione fisica | 1 online resource (XVI, 276 p.) |
Disciplina | 519.24 |
Collana | De Gruyter Series in Probability and Stochastics |
Soggetto topico |
Distribution (Probability theory) - Data processing
Distribution (Probability theory) - Mathematical models |
ISBN |
9783110713374
3-11-071337-3 |
Formato | Materiale a stampa ![]() |
Livello bibliografico | Monografia |
Lingua di pubblicazione | eng |
Nota di contenuto | Frontmatter -- Preface -- Acknowledgment -- Contents -- 1 Jordan algebras and symmetric cones -- 2 Generalized power -- 3 Riesz probability distributions -- 4 Riesz natural exponential families -- 5 Tweedie scale -- 6 Moments and constancy of regression -- 7 Beta Riesz probability distributions -- 8 Beta–Wishart distributions -- 9 Beta–hypergeometric distributions -- 10 Riesz–Dirichlet distributions -- 11 Riesz inverse Gaussian distribution -- Bibliography -- Index -- Index of notations |
Record Nr. | UNINA-9910554230403321 |
Hassairi Abdelhamid
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Berlin ; ; Boston, MA : , : Walter de Gruyter GmbH, , [2021] | ||
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Lo trovi qui: Univ. Federico II | ||
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Wind power forecasting error distributions over multiple timescales [[electronic resource] /] / Bri-Mathias Hodge, Michael Milligan |
Autore | Hodge Bri-Mathias |
Pubbl/distr/stampa | Golden, Colo. : , : National Renewable Energy Laboratory, , [2011] |
Descrizione fisica | 1 online resource (15 unnumbered slides) : illustrations (chiefly color) |
Altri autori (Persone) | MilliganMichael R |
Collana | NREL/PR |
Soggetto topico |
Wind power - Forecasting - Mathematical models
Distribution (Probability theory) - Mathematical models |
Formato | Materiale a stampa ![]() |
Livello bibliografico | Monografia |
Lingua di pubblicazione | eng |
Altri titoli varianti | Wind Power Forecasting Error Distributions over Multiple Timescales |
Record Nr. | UNINA-9910703288303321 |
Hodge Bri-Mathias
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Golden, Colo. : , : National Renewable Energy Laboratory, , [2011] | ||
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Lo trovi qui: Univ. Federico II | ||
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