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Closure Properties for Heavy-Tailed and Related Distributions : An Overview / / by Remigijus Leipus, Jonas Šiaulys, Dimitrios Konstantinides
| Closure Properties for Heavy-Tailed and Related Distributions : An Overview / / by Remigijus Leipus, Jonas Šiaulys, Dimitrios Konstantinides |
| Autore | Leipus Remigijus |
| Edizione | [1st ed. 2023.] |
| Pubbl/distr/stampa | Cham : , : Springer Nature Switzerland : , : Imprint : Springer, , 2023 |
| Descrizione fisica | 1 online resource (99 pages) |
| Disciplina | 519.24 |
| Altri autori (Persone) |
SiaulysJonas
KonstantinidesDimitrios |
| Collana | SpringerBriefs in Statistics |
| Soggetto topico |
Probabilities
Distribution (Probability theory) Stochastic models Actuarial science Applied Probability Distribution Theory Probability Theory Stochastic Modelling in Statistics Actuarial Mathematics Distribució (Teoria de la probabilitat) |
| Soggetto genere / forma | Llibres electrònics |
| ISBN | 3-031-34553-3 |
| Formato | Materiale a stampa  |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto |
Intro -- Preface -- Contents -- Acronyms -- 1 Introduction -- 1.1 An Overview of the Book -- 1.2 Notations and Definitions -- 2 Heavy-Tailed and Related Classes of Distributions -- 2.1 Heavy-Tailed Distributions -- 2.2 Regularly Varying Distributions -- 2.3 Consistently Varying Distributions -- 2.4 Dominatedly Varying Distributions -- 2.5 Long-Tailed Distributions -- 2.6 Exponential-Like-Tailed Distributions -- 2.7 Generalized Long-Tailed Distributions -- 2.8 Subexponential Distributions -- 2.9 Strong Subexponential Distributions -- 2.10 Convolution Equivalent Distributions -- 2.11 Generalized Subexponential Distributions -- 2.12 Bibliographical Notes -- 3 Closure Properties Under Tail-Equivalence, Convolution, Finite Mixing, Maximum, and Minimum -- 3.1 Ruin Probability in the Cramér-Lundberg Risk Model in the Case of Heavy-Tailed Claims -- 3.2 Convolution Closure and Max-Sum Equivalence -- 3.3 Closure Properties for Heavy-Tailed Class of Distributions -- 3.4 Closure Properties for Regularly Varying Class of Distributions -- 3.5 Closure Properties for Consistently Varying Class of Distributions -- 3.6 Closure Properties for Dominatedly Varying Class of Distributions -- 3.7 Closure Properties for Long-Tailed Class of Distributions -- 3.8 Closure Properties for Exponential-Like-Tailed Class of Distributions -- 3.9 Closure Properties for Generalized Long-Tailed Class of Distributions -- 3.10 Closure Properties for Subexponential Class of Distributions -- 3.11 Closure Properties for Strong Subexponential Class of Distributions -- 3.12 Closure Properties for Convolution Equivalent Class of Distributions -- 3.13 Closure Properties for Generalized Subexponential Class of Distributions -- 3.14 Bibliographical Notes -- 4 Convolution-Root Closure -- 4.1 Distribution Classes Closed Under Convolution Roots.
4.2 Distribution Classes Not Closed Under Convolution Roots -- 4.3 Bibliographical Notes -- 5 Product-Convolution of Heavy-Tailed and Related Distributions -- 5.1 Product-Convolution -- 5.2 From Light Tails to Heavy Tails Through Product-Convolution -- 5.3 Product-Convolution Closure Properties for Heavy-Tailed Class of Distributions -- 5.4 Product-Convolution Closure Properties for Regularly Varying Class of Distributions -- 5.5 Product-Convolution Closure Properties for Consistently Varying Class of Distributions -- 5.6 Product-Convolution Closure Properties for Dominatedly Varying Class of Distributions -- 5.7 Product-Convolution Closure Properties for Exponential-Like-Tailed Distributions -- 5.8 Product-Convolution Closure Properties for Generalized Long-Tailed Class of Distributions -- 5.9 Product-Convolution Closure Properties for Convolution Equivalent Class of Distributions -- 5.10 Product-Convolution Closure Properties for Generalized Subexponential Class of Distributions -- 5.11 Some Extensions -- 5.12 Bibliographical Notes -- 6 Summary of Closure Properties -- References -- Index. |
| Record Nr. | UNINA-9910746099003321 |
Leipus Remigijus
|
||
| Cham : , : Springer Nature Switzerland : , : Imprint : Springer, , 2023 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
Expository moments for pseudo distributions / / Haruhiko Ogasawara
| Expository moments for pseudo distributions / / Haruhiko Ogasawara |
| Autore | Ogasawara Haruhiko |
| Pubbl/distr/stampa | Singapore : , : Springer, , [2022] |
| Descrizione fisica | 1 online resource (348 pages) |
| Disciplina | 519.24 |
| Collana | Behaviormetrics: quantitative approaches to human behavior |
| Soggetto topico |
Distribution (Probability theory)
Distribució (Teoria de la probabilitat) |
| Soggetto genere / forma | Llibres electrònics |
| ISBN |
9789811935251
9789811935244 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto |
Intro -- Preface -- Contents -- 1 The Sectionally Truncated Normal Distribution -- 1.1 Introduction -- 1.2 The Probability Density Function (PDF) and the Moment Generating Function for the Sectionally Truncated Normal Vector -- 1.3 Partial Derivatives of the Cumulative Distribution Function of the Normal Random Vector -- 1.4 Moments and Cumulants of the STN-Distributed Vector Using the MGF -- 1.5 The Product Sum of Natural Numbers and the Hermite Polynomials -- References -- 2 Normal Moments Under Stripe Truncation and the Real-Valued Poisson Distribution -- 2.1 Introduction -- 2.2 Closed Formulas for Moments of Integer-Valued Orders -- 2.3 Series Expressions of \overline{I}_{k}^{(r)} \,(k = 0,1, \ldots -- r = 1, \ldots ,R) for Moments of Integer-Valued Orders -- 2.4 The Real-Valued Poisson Distribution for Series Expressions of \overline{I}_{k}^{(r)} \,(k = 0,1, \ldots -- r = 1,...,R) for Absolute Moments -- 2.4.1 Generalization of the Poisson Distribution -- 2.4.2 The Real-Valued Poisson Distribution -- 2.4.3 Applications to the Series Expressions of the Moments of the Normal Distribution -- 2.5 Remarks -- References -- 3 The Basic Parabolic Cylinder Distribution and Its Multivariate Extension -- 3.1 Introduction -- 3.2 The BPC Distribution of the Third Kind and Its CDF -- 3.3 Moments of the BPC Distribution -- 3.4 The Mode and the Shapes of the PDFs of the BPC Distribution -- 3.5 The Multivariate BPC Distribution -- 3.6 Numerical Illustrations -- 3.7 Discussion -- 3.8 R-Functions -- 3.8.1 The R-Function wpc for the Weighted Parabolic Cylinder Function -- 3.8.2 The R-Functions bpc1n and bpc2n for the Normalizers of the Uni- and Bivariate BPC Distributions -- 3.8.3 The R-Functions dbpc1 and dbpc2 for the PDFs of the Uni- and Bivariate BPC Distributions -- 3.8.4 The R-Function bpc2d for the CDF of the Bivariate BPC Distribution -- References.
4 The Pseudo-Normal (PN) Distribution -- 4.1 Introduction -- 4.2 The PDF of the PN Distribution -- 4.3 The Moment Generating Functions (MGFs) -- 4.3.1 The MGF of the PN-Distributed Vector -- 4.3.2 The MGF of {{\bf Y}}^{{{\rm T}}} {{\bf CY}} -- 4.3.3 The MGF of {{\bf YY}}^{{{\rm T}}} -- 4.4 Closed Properties of the PN -- 4.4.1 The Closure of Affine Transformations of the PN-Distributed Vector -- 4.4.2 Marginal and Conditional Distributions -- 4.4.3 Independent Random Vectors and Sums -- 4.4.4 Summary -- 4.5 Moments and Cumulants of the PN -- 4.5.1 General Results for Cumulants -- 4.5.2 Moments and Cumulants When q = 1 -- 4.6 The Distribution Function of the PN -- References -- 5 The Kurtic-Normal (KN) Distribution -- 5.1 Introduction -- 5.2 The Limiting Distributions of the KN -- 5.3 Moments and Cumulants of the KN -- References -- 6 The Normal-Normal (NN) Distribution -- 6.1 Introduction -- 6.2 The MGFs of the NN -- 6.3 Closed Properties of the NN -- 6.4 Cumulants of the NN -- 6.5 Alternative Expressions of the PDF of the NN: Mixture, Convolution and Regression -- 6.6 Moment-Equating for the PN and NN -- 6.6.1 The SN and NN -- 6.6.2 The Multivariate PN and NN with Exchangeable Variables -- Reference -- 7 The Decompositions of the PN- and NN-Distributed Variables -- 7.1 Decomposition of the PN -- 7.2 Decomposition of the NN -- 7.3 Multivariate Hermite Polynomials -- 7.4 Normal-Reduced and Normal-Added PN and NN -- References -- 8 The Truncated Pseudo-Normal (TPN) and Truncated Normal-Normal (TNN) Distributions -- 8.1 Introduction -- 8.2 Moment Generating Functions for the TPN Distribution -- 8.3 Properties of the TPN -- 8.3.1 Affine Transformation of the TPN Vector -- 8.3.2 Marginal and Conditional Distributions of the TPN Vector -- 8.4 Moments and Cumulants of the TPN -- 8.4.1 A Non-recursive Formula -- 8.4.2 A Formula Using the MGF. 8.4.3 The Case of Sectionally Truncated SN with p = q = 1 -- 8.5 The Truncated Normal-Normal Distribution -- References -- 9 The Student t- and Pseudo t- (PT) Distributions: Various Expressions of Mixtures -- 9.1 Introduction -- 9.2 The t-Distribution -- 9.3 The Multivariate t-Distribution -- 9.4 The Pseudo t (PT)-Distribution -- 9.4.1 The PDF of the PT -- 9.4.2 Moments and Cumulants of the PT -- References -- 10 Multivariate Measures of Skewness and Kurtosis -- 10.1 Preliminaries -- 10.2 Multivariate Cumulants and Multiple Commutators -- 10.3 Multivariate Measures of Skewness and Kurtosis -- 10.3.1 Multivariate Measures of Skewness -- 10.3.2 Multivariate Measures of Excess Kurtosis -- 10.4 Elimination Matrices and Non-duplicated Multivariate Skewness and Kurtosis -- References -- Index. |
| Record Nr. | UNISA-996503548603316 |
|
Ogasawara Haruhiko
|
||
| Singapore : , : Springer, , [2022] | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. di Salerno | ||
| ||
Expository moments for pseudo distributions / / Haruhiko Ogasawara
| Expository moments for pseudo distributions / / Haruhiko Ogasawara |
| Autore | Ogasawara Haruhiko |
| Pubbl/distr/stampa | Singapore : , : Springer, , [2022] |
| Descrizione fisica | 1 online resource (348 pages) |
| Disciplina | 519.24 |
| Collana | Behaviormetrics: quantitative approaches to human behavior |
| Soggetto topico |
Distribution (Probability theory)
Distribució (Teoria de la probabilitat) |
| Soggetto genere / forma | Llibres electrònics |
| ISBN |
9789811935251
9789811935244 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto |
Intro -- Preface -- Contents -- 1 The Sectionally Truncated Normal Distribution -- 1.1 Introduction -- 1.2 The Probability Density Function (PDF) and the Moment Generating Function for the Sectionally Truncated Normal Vector -- 1.3 Partial Derivatives of the Cumulative Distribution Function of the Normal Random Vector -- 1.4 Moments and Cumulants of the STN-Distributed Vector Using the MGF -- 1.5 The Product Sum of Natural Numbers and the Hermite Polynomials -- References -- 2 Normal Moments Under Stripe Truncation and the Real-Valued Poisson Distribution -- 2.1 Introduction -- 2.2 Closed Formulas for Moments of Integer-Valued Orders -- 2.3 Series Expressions of \overline{I}_{k}^{(r)} \,(k = 0,1, \ldots -- r = 1, \ldots ,R) for Moments of Integer-Valued Orders -- 2.4 The Real-Valued Poisson Distribution for Series Expressions of \overline{I}_{k}^{(r)} \,(k = 0,1, \ldots -- r = 1,...,R) for Absolute Moments -- 2.4.1 Generalization of the Poisson Distribution -- 2.4.2 The Real-Valued Poisson Distribution -- 2.4.3 Applications to the Series Expressions of the Moments of the Normal Distribution -- 2.5 Remarks -- References -- 3 The Basic Parabolic Cylinder Distribution and Its Multivariate Extension -- 3.1 Introduction -- 3.2 The BPC Distribution of the Third Kind and Its CDF -- 3.3 Moments of the BPC Distribution -- 3.4 The Mode and the Shapes of the PDFs of the BPC Distribution -- 3.5 The Multivariate BPC Distribution -- 3.6 Numerical Illustrations -- 3.7 Discussion -- 3.8 R-Functions -- 3.8.1 The R-Function wpc for the Weighted Parabolic Cylinder Function -- 3.8.2 The R-Functions bpc1n and bpc2n for the Normalizers of the Uni- and Bivariate BPC Distributions -- 3.8.3 The R-Functions dbpc1 and dbpc2 for the PDFs of the Uni- and Bivariate BPC Distributions -- 3.8.4 The R-Function bpc2d for the CDF of the Bivariate BPC Distribution -- References.
4 The Pseudo-Normal (PN) Distribution -- 4.1 Introduction -- 4.2 The PDF of the PN Distribution -- 4.3 The Moment Generating Functions (MGFs) -- 4.3.1 The MGF of the PN-Distributed Vector -- 4.3.2 The MGF of {{\bf Y}}^{{{\rm T}}} {{\bf CY}} -- 4.3.3 The MGF of {{\bf YY}}^{{{\rm T}}} -- 4.4 Closed Properties of the PN -- 4.4.1 The Closure of Affine Transformations of the PN-Distributed Vector -- 4.4.2 Marginal and Conditional Distributions -- 4.4.3 Independent Random Vectors and Sums -- 4.4.4 Summary -- 4.5 Moments and Cumulants of the PN -- 4.5.1 General Results for Cumulants -- 4.5.2 Moments and Cumulants When q = 1 -- 4.6 The Distribution Function of the PN -- References -- 5 The Kurtic-Normal (KN) Distribution -- 5.1 Introduction -- 5.2 The Limiting Distributions of the KN -- 5.3 Moments and Cumulants of the KN -- References -- 6 The Normal-Normal (NN) Distribution -- 6.1 Introduction -- 6.2 The MGFs of the NN -- 6.3 Closed Properties of the NN -- 6.4 Cumulants of the NN -- 6.5 Alternative Expressions of the PDF of the NN: Mixture, Convolution and Regression -- 6.6 Moment-Equating for the PN and NN -- 6.6.1 The SN and NN -- 6.6.2 The Multivariate PN and NN with Exchangeable Variables -- Reference -- 7 The Decompositions of the PN- and NN-Distributed Variables -- 7.1 Decomposition of the PN -- 7.2 Decomposition of the NN -- 7.3 Multivariate Hermite Polynomials -- 7.4 Normal-Reduced and Normal-Added PN and NN -- References -- 8 The Truncated Pseudo-Normal (TPN) and Truncated Normal-Normal (TNN) Distributions -- 8.1 Introduction -- 8.2 Moment Generating Functions for the TPN Distribution -- 8.3 Properties of the TPN -- 8.3.1 Affine Transformation of the TPN Vector -- 8.3.2 Marginal and Conditional Distributions of the TPN Vector -- 8.4 Moments and Cumulants of the TPN -- 8.4.1 A Non-recursive Formula -- 8.4.2 A Formula Using the MGF. 8.4.3 The Case of Sectionally Truncated SN with p = q = 1 -- 8.5 The Truncated Normal-Normal Distribution -- References -- 9 The Student t- and Pseudo t- (PT) Distributions: Various Expressions of Mixtures -- 9.1 Introduction -- 9.2 The t-Distribution -- 9.3 The Multivariate t-Distribution -- 9.4 The Pseudo t (PT)-Distribution -- 9.4.1 The PDF of the PT -- 9.4.2 Moments and Cumulants of the PT -- References -- 10 Multivariate Measures of Skewness and Kurtosis -- 10.1 Preliminaries -- 10.2 Multivariate Cumulants and Multiple Commutators -- 10.3 Multivariate Measures of Skewness and Kurtosis -- 10.3.1 Multivariate Measures of Skewness -- 10.3.2 Multivariate Measures of Excess Kurtosis -- 10.4 Elimination Matrices and Non-duplicated Multivariate Skewness and Kurtosis -- References -- Index. |
| Record Nr. | UNINA-9910637717803321 |
|
Ogasawara Haruhiko
|
||
| Singapore : , : Springer, , [2022] | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
Pioneering works on extreme value theory : in honor of Masaaki Sibuya / / Nobuaki Hoshino, Shuhei Mano, Takaaki Shimura, editors
| Pioneering works on extreme value theory : in honor of Masaaki Sibuya / / Nobuaki Hoshino, Shuhei Mano, Takaaki Shimura, editors |
| Edizione | [1st ed. 2021.] |
| Pubbl/distr/stampa | Singapore : , : Springer, , [2021] |
| Descrizione fisica | 1 online resource (IX, 134 p. 28 illus., 2 illus. in color.) |
| Disciplina | 519.24 |
| Collana | SpringerBriefs in Statistics |
| Soggetto topico |
Extreme value theory
Distribució (Teoria de la probabilitat) |
| Soggetto genere / forma | Llibres electrònics |
| ISBN | 981-16-0768-0 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto | Chap. 1 Estimation of generalized beta distributions (Authors: Sibuya and Mano) -- Chap. 2 On Some Resampling Procedures with the Empirical Beta Copula (Kiriliouk, Segers and Tsukahara) -- Chap. 3 Regression Analysis for Imbalanced Binary Data: Multi-Dimensional Case (Sei) -- Chap. 4 An Analysis of Extremes: Semiparametric Efficiency in Regression (Ozeki and Doksum) -- Chap. 5 Future Change in Relationships among Extreme Precipitation Statistics Using “d4PDF” (Tanaka) -- Chap. 6 History and Perspectives of Hydrological Frequency Analysis in Japan (Takara). |
| Record Nr. | UNISA-996466395903316 |
| Singapore : , : Springer, , [2021] | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. di Salerno | ||
| ||
Pioneering works on extreme value theory : in honor of Masaaki Sibuya / / Nobuaki Hoshino, Shuhei Mano, Takaaki Shimura, editors
| Pioneering works on extreme value theory : in honor of Masaaki Sibuya / / Nobuaki Hoshino, Shuhei Mano, Takaaki Shimura, editors |
| Edizione | [1st ed. 2021.] |
| Pubbl/distr/stampa | Singapore : , : Springer, , [2021] |
| Descrizione fisica | 1 online resource (IX, 134 p. 28 illus., 2 illus. in color.) |
| Disciplina | 519.24 |
| Collana | SpringerBriefs in Statistics |
| Soggetto topico |
Extreme value theory
Distribució (Teoria de la probabilitat) |
| Soggetto genere / forma | Llibres electrònics |
| ISBN | 981-16-0768-0 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto | Chap. 1 Estimation of generalized beta distributions (Authors: Sibuya and Mano) -- Chap. 2 On Some Resampling Procedures with the Empirical Beta Copula (Kiriliouk, Segers and Tsukahara) -- Chap. 3 Regression Analysis for Imbalanced Binary Data: Multi-Dimensional Case (Sei) -- Chap. 4 An Analysis of Extremes: Semiparametric Efficiency in Regression (Ozeki and Doksum) -- Chap. 5 Future Change in Relationships among Extreme Precipitation Statistics Using “d4PDF” (Tanaka) -- Chap. 6 History and Perspectives of Hydrological Frequency Analysis in Japan (Takara). |
| Record Nr. | UNINA-9910483209703321 |
| Singapore : , : Springer, , [2021] | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
Weak Convergence and Empirical Processes : With Applications to Statistics / / by A. W. van der Vaart, Jon A. Wellner
| Weak Convergence and Empirical Processes : With Applications to Statistics / / by A. W. van der Vaart, Jon A. Wellner |
| Autore | van der Vaart A W |
| Edizione | [2nd ed. 2023.] |
| Pubbl/distr/stampa | Cham : , : Springer International Publishing : , : Imprint : Springer, , 2023 |
| Descrizione fisica | 1 online resource (693 pages) |
| Disciplina | 519 |
| Altri autori (Persone) | WellnerJon A |
| Collana | Springer Series in Statistics |
| Soggetto topico |
Statistics
Applied Statistics Statistical Theory and Methods Bayesian Inference Processos estocàstics Convergència (Matemàtica) Distribució (Teoria de la probabilitat) Mostreig (Estadística) |
| Soggetto genere / forma | Llibres electrònics |
| ISBN | 3-031-29040-2 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto | Preface -- Reading Guide -- Part I: Stochastic Convergence -- Part 2: Empirical Processes -- Part 3: Statistical Applications -- Appendix -- References -- Author Index -- Subject Index -- List of Symbols. |
| Record Nr. | UNINA-9910734858903321 |
|
van der Vaart A W
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| Cham : , : Springer International Publishing : , : Imprint : Springer, , 2023 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
