Expository moments for pseudo distributions / / Haruhiko Ogasawara

• Autore: Ogasawara Haruhiko
• Pubblicazione: Singapore : , : Springer, , [2022]; ©2022
• Descrizione fisica: 1 online resource (348 pages)
• Disciplina: 519.24
• Soggetto topico: Distribution (Probability theory); Distribució (Teoria de la probabilitat)
• Soggetto genere / forma: Llibres electrònics
• 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.
• Titolo autorizzato: Expository Moments for Pseudo Distributions
• ISBN: 9789811935251; 9789811935244
• Formato: Materiale a stampa
• Livello bibliografico: Monografia
• Lingua di pubblicazione: Inglese
• Record Nr.: 996503548603316
• Lo trovi qui: Univ. di Salerno
• Serie: Behaviormetrics: Quantitative Approaches to Human Behavior