05905nam 2200553 450 99647937090331620230717151949.03-030-97963-6(MiAaPQ)EBC6975909(Au-PeEL)EBL6975909(CKB)21957562900041(OCoLC)1314629464(PPN)269154973(EXLCZ)992195756290004120221126d2022 uy 0engurcnu||||||||txtrdacontentcrdamediacrrdacarrierApplied probability from random experiments to random sequences and statistics /Valérie Girardin and Nikolaos LimniosCham, Switzerland :Springer,[2022]©20221 online resource (265 pages)Print version: Girardin, Valérie Applied Probability Cham : Springer International Publishing AG,c2022 9783030979621 Intro -- Preface -- Contents -- Notation -- 1 Events and Probability Spaces -- 1.1 Sample Space -- 1.2 Measure Spaces -- 1.2.1 σ-Algebras -- Properties of σ-Algebras -- 1.2.2 Measures -- Properties of Measures -- Dirac Measure -- Counting Measure -- Lebesgue Measure -- 1.3 Probability Spaces -- 1.3.1 General Case -- 1.3.2 Conditional Probabilities -- 1.3.3 Discrete Case: Combinatorial Analysis and Entropy -- Properties of Shannon Entropy -- 1.4 Independence of Finite Collections -- 1.5 Exercises -- 2 Random Variables -- 2.1 Random Variables -- 2.1.1 Measurable Functions -- Properties of Measurable Functions -- 2.1.2 Distributions and Distribution Functions -- Properties of Distribution Functions -- Properties of Quantiles -- 2.2 Expectation -- 2.2.1 Lebesgue Integral -- Properties of Lebesgue Integrals -- 2.2.2 Expectation -- 2.3 Discrete Random Variables -- 2.3.1 General Properties -- 2.3.2 Classical Discrete Distributions -- Dirac Distribution -- Uniform Distribution -- Bernoulli Distribution -- Binomial Distribution -- Hyper-Geometric Distribution -- Geometric and Negative Binomial Distributions -- Poisson Distribution -- 2.4 Continuous Random Variables -- 2.4.1 Absolute Continuity of Measures -- 2.4.2 Densities -- Properties of Densities of Random Variables -- 2.4.3 Classical Distributions with Densities -- Uniform Distribution -- Gaussian Distribution -- Gamma, Exponential, Chi-Squared, Erlang Distributions -- Log-Normal Distribution -- Weibull Distribution -- Inverse-Gaussian Distribution -- Beta Distribution -- Fisher Distribution -- Student and Cauchy Distributions -- 2.4.4 Determination of Distributions -- 2.5 Analytical Tools -- 2.5.1 Generating Functions -- Properties of Generating Functions -- 2.5.2 Fourier Transform and Characteristic Functions -- Properties of Characteristic Functions -- 2.5.3 Laplace Transform.Properties of Laplace Transforms -- 2.5.4 Moment Generating Functions and Cramér Transform -- Properties of Cramér Transform -- 2.6 Reliability and Survival Analysis -- 2.7 Exercises and Complements -- 3 Random Vectors -- 3.1 Relations Between Random Variables -- 3.1.1 Covariance -- Properties of Covariance and Correlation Coefficients -- 3.1.2 Independence of Random Variables -- 3.1.3 Stochastic Order Relation -- 3.1.4 Entropy -- Properties of Entropy -- 3.2 Characteristics of Random Vectors -- 3.2.1 Product of Probability Spaces -- 3.2.2 Distribution of Random Vectors -- Properties of Multi-dimensional Distribution Functions -- Properties of Densities of Random Vectors -- Properties of Covariance Matrices -- 3.2.3 Independence of Random Vectors -- Properties of Covariance Matrices of Two Vectors -- 3.3 Functions of Random Vectors -- 3.3.1 Order Statistics -- 3.3.2 Sums of Independent Variables or Vectors -- Properties of Convolution -- 3.3.3 Determination of Distributions -- 3.4 Gaussian Vectors -- 3.5 Exercises and Complements -- 4 Random Sequences -- 4.1 Enumerable Sequences -- 4.1.1 Sequences of Events -- Properties of Superior and Inferior Limits of Events -- 4.1.2 Independence of Sequences -- 4.2 Stochastic Convergence -- 4.2.1 Different Types of Convergence -- 4.2.2 Convergence Criteria -- 4.2.3 Links Between Convergences -- 4.2.4 Convergence of Sequences of Random Vectors -- 4.3 Limit Theorems -- 4.3.1 Asymptotics of Discrete Distributions -- 4.3.2 Laws of Large Numbers -- 4.3.3 Central Limit Theorem -- 4.4 Stochastic Simulation Methods -- 4.4.1 Generating Random Variables -- 4.4.2 Monte Carlo Simulation Method -- 4.5 Exercises and Complements -- 5 Introduction to Statistics -- 5.1 Non-parametric Statistics -- 5.1.1 Empirical Distribution Function -- 5.1.2 Confidence Intervals -- 5.1.3 Non-parametric Testing -- 5.2 Parametric Statistics.5.2.1 Point Estimation -- 5.2.2 Maximum Likelihood Method -- 5.2.3 Precision of the Estimators -- 5.2.4 Parametric Confidence Intervals -- 5.2.5 Testing in a Parametric Model -- 5.3 The Linear Model -- 5.3.1 Linear and Quadratic Approximations -- 5.3.2 The Simple Linear Model -- 5.3.3 ANOVA -- For Two Samples -- One Way Model -- Two Way Model -- 5.4 Exercises and Complements -- Further Reading -- Measure and Probability -- Probability Theory and Statistics -- Applications -- Index.Distribution (Probability theory)StatisticsStochastic processesProbabilitatsthubEstadística matemàticathubLlibres electrònicsthubDistribution (Probability theory)Statistics.Stochastic processes.ProbabilitatsEstadística matemàtica519.2Girardin Valérie768207Limnios N.MiAaPQMiAaPQMiAaPQBOOK996479370903316Applied Probability2070204UNISA04859nas1 22004573i 450 VEA001543620231121125918.00774-2908P 00077041P 19970927b19282017||||0itac50 balatmulbeazu||||||||z01i xxxe z01nHumanistica LovaniensiaUniversitas catholica Lovaniensis, Seminarium philologiae humanisticae1 (1928)-66 (2017)LovaniiLibrairie universitaire1928-2017volumi24 cmAnnualeInizia nel 1928 come serie monograficaNon pubblicato dal 1962 al 1967Da vol. 20 (1971) il complemento del titolo varia in: Journal of neo-latin studiesL'editore varia in: Vander, poi: The Hague : Nijhoff, poi: Leuven : University PressDisponibile anche onlineContinua in formato digitale001PUV03035952001 Roma humanisticastudia in honorem Iosaei Ruysschaertcollegit et edidit Iosephus Ijsewijn34 AHumanistica LovaniensiaSBN0094084Letteratura latina umanisticaPeriodiciFIRSBLC071196I470.05Lingue italiche. Latino. Pubblicazioni in serie.20ITIT-0119970927IT-RM0285 IT-FR0017 http://humanistica.be/index.php/humanistica/issue/archiveBiblioteca Dell'Istituto Nazionale Di Studi RomaniRM0285 29 (1980), 34 A (1985), 40 (1991);Biblioteca umanistica Giorgio ApreaFR0017 1993-NVEA0015436Biblioteca umanistica Giorgio Aprea1993- 52PER.STR. 124 a 52FLS0000303575 VPN RS 55 (2006)C 20160407201604071993- 52PER.STR. 124 a 52FLS0000311255 VPN RS 56 (2007)C 20160407201604071993- 52PER.STR. 124 a 52FLS0000352625 VPN RS 57 (2008)C 20160407201604071993- 52PER.STR. 124 a 52SBA0000124325 VPN RS 58 (2009)C 20160407201604071993- 52PER.STR. 124 a 52SBA0000129355 VPN RS 59 (2010)C 20160407201604071993- 52PER.STR. 124 a 52SBA0000143095 VPN RS 60 (2011)C 20121012201210121993- 52PER.STR. 124 a 52SBA0000153255 VPN RS 61 (2012)C 20130522201305221993- 52PER.STR. 124 a 52SBA0000184775 VPN RS 62 (2013)C 20150521201505211993- 52PER.STR. 124 a 52SBA0000184785 VPN RS 63 (2014)C 20150521201505211993- 52PER.STR. 124 a 52SBA0000200405 VPN RS 64 (2015)C 2016040720160407Vol. 54 (2005) 52PER.STR. 124a 52VP 0000209195 VP Descr.Fascicoli:Vol. 54 (2005)C 2006040520121204Vol. 53 (2004) 52PER.STR. 124a 52VP 0000209185 VP Descr.Fascicoli:Vol. 53 (2004)C 2005061620121204Vol. 52 (2003) 52PER.STR. 124a 52VP 0000138695 VP Inventario:FLS Descr.Fascicoli:Vol. 52 (2003)C 2004121620121204Vol. 51 (2002) 52PER.STR. 124a 52VP 0000138685 VP Inventario:FLS Descr.Fascicoli:Vol. 51 (2002)C 2004121620121204Vol. 50 (2001) 52PER.STR. 124a 52VP 0000138675 VP Inventario:FLS Descr.Fascicoli:Vol. 50 (2001)C 2004121620121204Vol. 49 (2000) 52PER.STR. 124a 52VP 0000138665 VP Inventario:FLS Descr.Fascicoli:Vol. 49 (2000)C 2004121620121204Vol. 48 (1999) 52PER.STR. 124a 52VP 0000138655 VP Inventario:FLS Descr.Fascicoli:Vol. 48 (1999)C 2004121620121204Vol. 47 (1998) 52PER.STR. 124a 52VP 0000138645 VP Inventario:FLS Descr.Fascicoli:Vol. 47 (1998)C 2004121620121204Vol. 46 (1997) 52PER.STR. 124a 52VP 0000138635 VP Inventario:FLS Descr.Fascicoli:Vol. 46 (1997)C 2004121620121204Vol. 45 (1996) 52PER.STR. 124a 52VP 0000138625 VP Inventario:FLS Descr.Fascicoli:Vol. 45 (1996)C 2004121620121204Vol. 44 (1995) 52PER.STR. 124a 52VP 0000138615 VP Inventario:FLS Descr.Fascicoli:Vol. 44 (1995)C 2004121620121204Vol. 43 (1994) 52PER.STR. 124a 52VP 0000138605 VP Inventario:FLS Descr.Fascicoli:Vol. 43 (1994)C 2004121620121204Vol. 42 (1993) 52PER.STR. 124a 52VP 0000138595 VP Inventario:FLS Descr.Fascicoli:Vol. 42 (1993)C 20041216201212041 06 07 13 52Humanistica lovaniensia892550UNICAS