This work is a detailed description of different discrete and continuous univariate and multivariate distributions with applications in economics and different financial problems and other scenarios in which these recently developed statistical models have been applied in recent years, including actuarial statistics (with emphasis on credibility theory, ruin theory, calculation of insurance premiums, etc.), stochastic frontier analysis (estimation of technical efficiency), duration models (intraday rate of trading), population geography, income and wealth distribution, physical economy, tourism and sports, among others. Each distribution is dealt with in a separate chapter along with descriptions of all possible applications. The authors also provide a detailed analysis of the proposed probabilistic families, discussing their relationship with existing models, statistical properties, analyzing their strengths and weaknesses, similarities and differences, different estimation methods along with comments on possible applications and extensions. Simulation methods are given for most of the models presented. Many of the probabilistic models shown along with their applications in the fields indicated are a result of numerous research articles published by the authors although others are also provided, mainly based on classical formulations, which have been the starting point of more general models. This volume contains an extensive updated bibliography selected from magazines and books on statistics, mathematics, economics, actuarial sciences and computer science. This book is an essential manual for researchers, professionals, professionals and, in general, for graduate students in computer science, engineering, bioinformatics, statistics and mathematics, since the concise writing style makes the book accessible to a wide audience.
Author(s): Emilio Gómez-Déniz, Enrique Calderín-Ojeda
Edition: 1
Publisher: CRC Press | Taylor & Francis Group
Year: 2022
Language: English
Commentary: TruePDF
Pages: 189
Tags: Statistical Theory & Methods; Statistics For Business, Finance & Economics
Cover
Title Page
Copyright Page
Preface
Table of Contents
List of Figures
List of Tables
1. Basic Statistical Distributions
1.1 Introduction
1.2 Univariate discrete distributions
1.2.1 Bernoulli distribution
1.2.2 Binomial distribution
1.2.3 Moment and probability generating functions
1.2.4 Poisson distribution
1.2.5 Negative binomial distribution
1.2.6 The geometric distribution
1.2.7 Logarithmic distribution
1.3 Univariate continuous distributions
1.3.1 Normal distribution
1.3.2 Lognormal distribution
1.3.3 Gamma distribution
1.3.4 Exponential distribution
1.3.5 Weibull distribution
1.3.6 Inverse Gaussian distribution
1.3.7 Family of Pareto distributions
1.3.8 Classical Pareto distribution
1.3.9 Pareto type II or Lomax distribution
1.3.10 Beta distribution
1.4 Deriving new distributions
1.4.1 Mixture of distribution
1.4.2 Composite models
1.4.3 General composite models
1.5 Multivariate distributions
1.5.1 Bivariate Poisson distribution
1.5.2 Bivariate Poisson distribution. An alternative parametrization
1.6 Multivariate continuous distributions
1.6.1 The multivariate normal distribution
1.6.2 Bivariate exponential distribution
1.7 Criteria for model validation
1.7.1 Hypothesis testing
1.7.2 Other measures of model selection
1.7.3 Graphical methods of model selection
Exercises
2. Statistical Distributions in Insurance and Finance
2.1 Introduction
2.2 Individual and collective risk models
2.2.1 Individual risk model
2.2.2 Collective risk model
2.2.3 Compound Poisson distribution
2.2.4 Compound negative binomial distribution
2.3 Classes of discrete probability distributions
2.3.1 The (a, b, 0) class of distributions
2.3.2 The (a, b, 1) class of distributions
2.4 A recursive expression for the aggregate claims distribution
2.5 Premium calculation principles
2.5.1 Examples
2.5.2 Properties of premium calculation principles
2.6 Risk measures
2.6.1 Value at Risk (VaR)
2.6.2 Tail Value at Risk (TVaR)
2.6.3 Conditional Tail Expectation (CTE) and Expected Shortall (ES)
2.6.4 Properties of risk measures
2.7 Reinsurance
2.7.1 Type of reinsurance
2.8 Comparing risks
2.8.1 Stochastic dominance
2.8.2 Stochastic dominance and stop-loss premiums
2.8.3 Stop-Loss order and Stop-Loss Reinsurance
Exercises
3. Statistical Distributions in Tourism
3.1 Introduction
3.2 Data
3.3 The length of stay variable
3.3.1 Models
3.3.2 Numerical illustration
3.4 The expenditure variable
3.5 Compound models
3.5.1 The compound Poisson model
3.5.2 The compound positive negative binomial model
3.6 Bivariate model
3.6.1 Some methods of estimation
3.7 Generalized additive model
Exercises
4. Statistical Distributions in Other Fields
4.1 Introduction
4.2 Stochastic frontier analysis
4.2.1 The general model
4.2.2 The normal-exponential model
4.2.3 The normal-half normal model
4.2.4 The normal-truncated normal model
4.2.5 An example
4.3 Geography: The size distribution of cities
4.3.1 The composite lognormal-Pareto
4.3.2 Data
4.3.3 Numerical results
4.4 ACD models
4.4.1 The general model
4.4.2 Specific models
4.4.3 Extensions
4.4.4 An empirical example
4.5 Income
4.5.1 Basic elements
4.5.2 Inequality measures and population functions
4.5.3 Lorenz ordering
4.5.4 Estimation
4.5.5 Leimkuhler curve
Exercises
Bibliography
Index
