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 |