{"product_id":"loss-models-9781119523789","title":"Loss Models","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003e\u003cp\u003e\u003cb\u003eA guide that provides in-depth coverage of modeling techniques used throughout many branches of actuarial science, revised and updated\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003eNow in its fifth edition, \u003ci\u003eLoss Models: From Data to Decisions \u003c\/i\u003eputs the focus on material tested in the Society of Actuaries (SOA) newly revised Exams STAM (Short-Term Actuarial Mathematics) and LTAM (Long-Term Actuarial Mathematics). Updated to reflect these exam changes, this vital resource offers actuaries, and those aspiring to the profession, a practical approach to the concepts and techniques needed to succeed in the profession. The techniques are also valuable for anyone who uses loss data to build models for assessing risks of any kind.\u003c\/p\u003e \u003cp\u003e\u003ci\u003eLoss Models\u003c\/i\u003e contains a wealth of examples that highlight the real-world applications of the concepts presented, and puts the emphasis on calculations and spreadsheet implementation. With a focus on the loss process, the book reviews the essential quantitative techniques such a\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTable of Contents\u003c\/b\u003e\u003cbr\u003e\u003c\/p\u003e\u003cp\u003ePreface xiii\u003c\/p\u003e \u003cp\u003eAbout the Companion Website xv\u003c\/p\u003e \u003cp\u003e\u003cb\u003ePart I Introduction\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e\u003cb\u003e1 Modeling 3\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e1.1 The Model-Based Approach 3\u003c\/p\u003e \u003cp\u003e1.1.1 The Modeling Process 3\u003c\/p\u003e \u003cp\u003e1.1.2 The Modeling Advantage 5\u003c\/p\u003e \u003cp\u003e1.2 The Organization of This Book 6\u003c\/p\u003e \u003cp\u003e\u003cb\u003e2 Random Variables 9\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e2.1 Introduction 9\u003c\/p\u003e \u003cp\u003e2.2 Key Functions and Four Models 11\u003c\/p\u003e \u003cp\u003e2.2.1 Exercises 19\u003c\/p\u003e \u003cp\u003e\u003cb\u003e3 Basic Distributional Quantities 21\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e3.1 Moments 21\u003c\/p\u003e \u003cp\u003e3.1.1 Exercises 28\u003c\/p\u003e \u003cp\u003e3.2 Percentiles 29\u003c\/p\u003e \u003cp\u003e3.2.1 Exercises 31\u003c\/p\u003e \u003cp\u003e3.3 Generating Functions and Sums of Random Variables 31\u003c\/p\u003e \u003cp\u003e3.3.1 Exercises 33\u003c\/p\u003e \u003cp\u003e3.4 Tails of Distributions 33\u003c\/p\u003e \u003cp\u003e3.4.1 Classification Based on Moments 33\u003c\/p\u003e \u003cp\u003e3.4.2 Comparison Based on Limiting Tail Behavior 34\u003c\/p\u003e \u003cp\u003e3.4.3 Classification Based on the Hazard Rate Function 35\u003c\/p\u003e \u003cp\u003e3.4.4 Classification Based on the Mean Excess Loss Function 36\u003c\/p\u003e \u003cp\u003e3.4.5 Equilibrium Distributions and Tail Behavior 38\u003c\/p\u003e \u003cp\u003e3.4.6 Exercises 39\u003c\/p\u003e \u003cp\u003e3.5 Measures of Risk 41\u003c\/p\u003e \u003cp\u003e3.5.1 Introduction 41\u003c\/p\u003e \u003cp\u003e3.5.2 Risk Measures and Coherence 41\u003c\/p\u003e \u003cp\u003e3.5.3 Value at Risk 43\u003c\/p\u003e \u003cp\u003e3.5.4 Tail Value at Risk 44\u003c\/p\u003e \u003cp\u003e3.5.5 Exercises 48\u003c\/p\u003e \u003cp\u003e\u003cb\u003ePart II Actuarial Models\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e\u003cb\u003e4 Characteristics of Actuarial Models 51\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e4.1 Introduction 51\u003c\/p\u003e \u003cp\u003e4.2 The Role of Parameters 51\u003c\/p\u003e \u003cp\u003e4.2.1 Parametric and Scale Distributions 52\u003c\/p\u003e \u003cp\u003e4.2.2 Parametric Distribution Families 54\u003c\/p\u003e \u003cp\u003e4.2.3 Finite Mixture Distributions 54\u003c\/p\u003e \u003cp\u003e4.2.4 Data-Dependent Distributions 56\u003c\/p\u003e \u003cp\u003e4.2.5 Exercises 59\u003c\/p\u003e \u003cp\u003e\u003cb\u003e5 Continuous Models 61\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e5.1 Introduction 61\u003c\/p\u003e \u003cp\u003e5.2 Creating New Distributions 61\u003c\/p\u003e \u003cp\u003e5.2.1 Multiplication by a Constant 62\u003c\/p\u003e \u003cp\u003e5.2.2 Raising to a Power 62\u003c\/p\u003e \u003cp\u003e5.2.3 Exponentiation 64\u003c\/p\u003e \u003cp\u003e5.2.4 Mixing 64\u003c\/p\u003e \u003cp\u003e5.2.5 Frailty Models 68\u003c\/p\u003e \u003cp\u003e5.2.6 Splicing 69\u003c\/p\u003e \u003cp\u003e5.2.7 Exercises 70\u003c\/p\u003e \u003cp\u003e5.3 Selected Distributions and Their Relationships 74\u003c\/p\u003e \u003cp\u003e5.3.1 Introduction 74\u003c\/p\u003e \u003cp\u003e5.3.2 Two Parametric Families 74\u003c\/p\u003e \u003cp\u003e5.3.3 Limiting Distributions 74\u003c\/p\u003e \u003cp\u003e5.3.4 Two Heavy-Tailed Distributions 76\u003c\/p\u003e \u003cp\u003e5.3.5 Exercises 77\u003c\/p\u003e \u003cp\u003e5.4 The Linear Exponential Family 78\u003c\/p\u003e \u003cp\u003e5.4.1 Exercises 80\u003c\/p\u003e \u003cp\u003e\u003cb\u003e6 Discrete Distributions 81\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e6.1 Introduction 81\u003c\/p\u003e \u003cp\u003e6.1.1 Exercise 82\u003c\/p\u003e \u003cp\u003e6.2 The Poisson Distribution 82\u003c\/p\u003e \u003cp\u003e6.3 The Negative Binomial Distribution 85\u003c\/p\u003e \u003cp\u003e6.4 The Binomial Distribution 87\u003c\/p\u003e \u003cp\u003e6.5 The (𝑎, 𝑏, 0) Class 88\u003c\/p\u003e \u003cp\u003e6.5.1 Exercises 91\u003c\/p\u003e \u003cp\u003e6.6 Truncation and Modification at Zero 92\u003c\/p\u003e \u003cp\u003e6.6.1 Exercises 96\u003c\/p\u003e \u003cp\u003e\u003cb\u003e7 Advanced Discrete Distributions 99\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e7.1 Compound Frequency Distributions 99\u003c\/p\u003e \u003cp\u003e7.1.1 Exercises 105\u003c\/p\u003e \u003cp\u003e7.2 Further Properties of the Compound Poisson Class 105\u003c\/p\u003e \u003cp\u003e7.2.1 Exercises 111\u003c\/p\u003e \u003cp\u003e7.3 Mixed-Frequency Distributions 111\u003c\/p\u003e \u003cp\u003e7.3.1 The General Mixed-Frequency Distribution 111\u003c\/p\u003e \u003cp\u003e7.3.2 Mixed Poisson Distributions 113\u003c\/p\u003e \u003cp\u003e7.3.3 Exercises 118\u003c\/p\u003e \u003cp\u003e7.4 The Effect of Exposure on Frequency 120\u003c\/p\u003e \u003cp\u003e7.5 An Inventory of Discrete Distributions 121\u003c\/p\u003e \u003cp\u003e7.5.1 Exercises 122\u003c\/p\u003e \u003cp\u003e\u003cb\u003e8 Frequency and Severity with Coverage Modifications 125\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e8.1 Introduction 125\u003c\/p\u003e \u003cp\u003e8.2 Deductibles 126\u003c\/p\u003e \u003cp\u003e8.2.1 Exercises 131\u003c\/p\u003e \u003cp\u003e8.3 The Loss Elimination Ratio and the Effect of Inflation for Ordinary Deductibles 132\u003c\/p\u003e \u003cp\u003e8.3.1 Exercises 133\u003c\/p\u003e \u003cp\u003e8.4 Policy Limits 134\u003c\/p\u003e \u003cp\u003e8.4.1 Exercises 136\u003c\/p\u003e \u003cp\u003e8.5 Coinsurance, Deductibles, and Limits 136\u003c\/p\u003e \u003cp\u003e8.5.1 Exercises 138\u003c\/p\u003e \u003cp\u003e8.6 The Impact of Deductibles on Claim Frequency 140\u003c\/p\u003e \u003cp\u003e8.6.1 Exercises 144\u003c\/p\u003e \u003cp\u003e\u003cb\u003e9 Aggregate Loss Models 147\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e9.1 Introduction 147\u003c\/p\u003e \u003cp\u003e9.1.1 Exercises 150\u003c\/p\u003e \u003cp\u003e9.2 Model Choices 150\u003c\/p\u003e \u003cp\u003e9.2.1 Exercises 151\u003c\/p\u003e \u003cp\u003e9.3 The Compound Model for Aggregate Claims 151\u003c\/p\u003e \u003cp\u003e9.3.1 Probabilities and Moments 152\u003c\/p\u003e \u003cp\u003e9.3.2 Stop-Loss Insurance 157\u003c\/p\u003e \u003cp\u003e9.3.3 The Tweedie Distribution 159\u003c\/p\u003e \u003cp\u003e9.3.4 Exercises 160\u003c\/p\u003e \u003cp\u003e9.4 Analytic Results 167\u003c\/p\u003e \u003cp\u003e9.4.1 Exercises 170\u003c\/p\u003e \u003cp\u003e9.5 Computing the Aggregate Claims Distribution 171\u003c\/p\u003e \u003cp\u003e9.6 The Recursive Method 173\u003c\/p\u003e \u003cp\u003e9.6.1 Applications to Compound Frequency Models 175\u003c\/p\u003e \u003cp\u003e9.6.2 Underflow\/Overflow Problems 177\u003c\/p\u003e \u003cp\u003e9.6.3 Numerical Stability 178\u003c\/p\u003e \u003cp\u003e9.6.4 Continuous Severity 178\u003c\/p\u003e \u003cp\u003e9.6.5 Constructing Arithmetic Distributions 179\u003c\/p\u003e \u003cp\u003e9.6.6 Exercises 182\u003c\/p\u003e \u003cp\u003e9.7 The Impact of Individual Policy Modifications on Aggregate Payments 186\u003c\/p\u003e \u003cp\u003e9.7.1 Exercises 189\u003c\/p\u003e \u003cp\u003e9.8 The Individual Risk Model 189\u003c\/p\u003e \u003cp\u003e9.8.1 The Model 189\u003c\/p\u003e \u003cp\u003e9.8.2 Parametric Approximation 191\u003c\/p\u003e \u003cp\u003e9.8.3 Compound Poisson Approximation 193\u003c\/p\u003e \u003cp\u003e9.8.4 Exercises 195\u003c\/p\u003e \u003cp\u003e\u003cb\u003ePart III Mathematical Statistics\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e\u003cb\u003e10 Introduction to Mathematical Statistics 201\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e10.1 Introduction and Four Data Sets 201\u003c\/p\u003e \u003cp\u003e10.2 Point Estimation 203\u003c\/p\u003e \u003cp\u003e10.2.1 Introduction 203\u003c\/p\u003e \u003cp\u003e10.2.2 Measures of Quality 204\u003c\/p\u003e \u003cp\u003e10.2.3 Exercises 214\u003c\/p\u003e \u003cp\u003e10.3 Interval Estimation 216\u003c\/p\u003e \u003cp\u003e10.3.1 Exercises 218\u003c\/p\u003e \u003cp\u003e10.4 The Construction of Parametric Estimators 218\u003c\/p\u003e \u003cp\u003e10.4.1 The Method of Moments and Percentile Matching 218\u003c\/p\u003e \u003cp\u003e10.4.2 Exercises 221\u003c\/p\u003e \u003cp\u003e10.5 Tests of Hypotheses 224\u003c\/p\u003e \u003cp\u003e10.5.1 Exercise 228\u003c\/p\u003e \u003cp\u003e\u003cb\u003e11 Maximum Likelihood Estimation 229\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e11.1 Introduction 229\u003c\/p\u003e \u003cp\u003e11.2 Individual Data 231\u003c\/p\u003e \u003cp\u003e11.2.1 Exercises 232\u003c\/p\u003e \u003cp\u003e11.3 Grouped Data 235\u003c\/p\u003e \u003cp\u003e11.3.1 Exercises 236\u003c\/p\u003e \u003cp\u003e11.4 Truncated or Censored Data 236\u003c\/p\u003e \u003cp\u003e11.4.1 Exercises 241\u003c\/p\u003e \u003cp\u003e11.5 Variance and Interval Estimation for Maximum Likelihood Estimators 242\u003c\/p\u003e \u003cp\u003e11.5.1 Exercises 247\u003c\/p\u003e \u003cp\u003e11.6 Functions of Asymptotically Normal Estimators 248\u003c\/p\u003e \u003cp\u003e11.6.1 Exercises 250\u003c\/p\u003e \u003cp\u003e11.7 Nonnormal Confidence Intervals 251\u003c\/p\u003e \u003cp\u003e11.7.1 Exercise 253\u003c\/p\u003e \u003cp\u003e\u003cb\u003e12 Frequentist Estimation for Discrete Distributions 255\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e12.1 The Poisson Distribution 255\u003c\/p\u003e \u003cp\u003e12.2 The Negative Binomial Distribution 259\u003c\/p\u003e \u003cp\u003e12.3 The Binomial Distribution 261\u003c\/p\u003e \u003cp\u003e12.4 The (𝑎, 𝑏, 1) Class 264\u003c\/p\u003e \u003cp\u003e12.5 Compound Models 268\u003c\/p\u003e \u003cp\u003e12.6 The Effect of Exposure on Maximum Likelihood Estimation 269\u003c\/p\u003e \u003cp\u003e12.7 Exercises 270\u003c\/p\u003e \u003cp\u003e\u003cb\u003e13 Bayesian Estimation 275\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e13.1 Definitions and Bayes’ Theorem 275\u003c\/p\u003e \u003cp\u003e13.2 Inference and Prediction 279\u003c\/p\u003e \u003cp\u003e13.2.1 Exercises 285\u003c\/p\u003e \u003cp\u003e13.3 Conjugate Prior Distributions and the Linear Exponential Family 290\u003c\/p\u003e \u003cp\u003e13.3.1 Exercises 291\u003c\/p\u003e \u003cp\u003e13.4 Computational Issues 292\u003c\/p\u003e \u003cp\u003e\u003cb\u003ePart IV Construction of Models\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e\u003cb\u003e14 Construction of Empirical Models 295\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e14.1 The Empirical Distribution 295\u003c\/p\u003e \u003cp\u003e14.2 Empirical Distributions for Grouped Data 300\u003c\/p\u003e \u003cp\u003e14.2.1 Exercises 301\u003c\/p\u003e \u003cp\u003e14.3 Empirical Estimation with Right Censored Data 304\u003c\/p\u003e \u003cp\u003e14.3.1 Exercises 316\u003c\/p\u003e \u003cp\u003e14.4 Empirical Estimation of Moments 320\u003c\/p\u003e \u003cp\u003e14.4.1 Exercises 326\u003c\/p\u003e \u003cp\u003e14.5 Empirical Estimation with Left Truncated Data 327\u003c\/p\u003e \u003cp\u003e14.5.1 Exercises 331\u003c\/p\u003e \u003cp\u003e14.6 Kernel Density Models 332\u003c\/p\u003e \u003cp\u003e14.6.1 Exercises 336\u003c\/p\u003e \u003cp\u003e14.7 Approximations for Large Data Sets 337\u003c\/p\u003e \u003cp\u003e14.7.1 Introduction 337\u003c\/p\u003e \u003cp\u003e14.7.2 Using Individual Data Points 339\u003c\/p\u003e \u003cp\u003e14.7.3 Interval-Based Methods 342\u003c\/p\u003e \u003cp\u003e14.7.4 Exercises 346\u003c\/p\u003e \u003cp\u003e14.8 Maximum Likelihood Estimation of Decrement Probabilities 347\u003c\/p\u003e \u003cp\u003e14.8.1 Exercise 349\u003c\/p\u003e \u003cp\u003e14.9 Estimation of Transition Intensities 350\u003c\/p\u003e \u003cp\u003e\u003cb\u003e15 Model Selection 353\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e15.1 Introduction 353\u003c\/p\u003e \u003cp\u003e15.2 Representations of the Data and Model 354\u003c\/p\u003e \u003cp\u003e15.3 Graphical Comparison of the Density and Distribution Functions 355\u003c\/p\u003e \u003cp\u003e15.3.1 Exercises 360\u003c\/p\u003e \u003cp\u003e15.4 Hypothesis Tests 360\u003c\/p\u003e \u003cp\u003e15.4.1 The Kolmogorov–Smirnov Test 360\u003c\/p\u003e \u003cp\u003e15.4.2 The Anderson–Darling Test 363\u003c\/p\u003e \u003cp\u003e15.4.3 The Chi-Square Goodness-of-Fit Test 363\u003c\/p\u003e \u003cp\u003e15.4.4 The Likelihood Ratio Test 367\u003c\/p\u003e \u003cp\u003e15.4.5 Exercises 369\u003c\/p\u003e \u003cp\u003e15.5 Selecting a Model 371\u003c\/p\u003e \u003cp\u003e15.5.1 Introduction 371\u003c\/p\u003e \u003cp\u003e15.5.2 Judgment-Based Approaches 372\u003c\/p\u003e \u003cp\u003e15.5.3 Score-Based Approaches 373\u003c\/p\u003e \u003cp\u003e15.5.4 Exercises 381\u003c\/p\u003e \u003cp\u003e\u003cb\u003ePart V Credibility\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e\u003cb\u003e16 Introduction to Limited Fluctuation Credibility 387\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e16.1 Introduction 387\u003c\/p\u003e \u003cp\u003e16.2 Limited Fluctuation Credibility Theory 389\u003c\/p\u003e \u003cp\u003e16.3 Full Credibility 390\u003c\/p\u003e \u003cp\u003e16.4 Partial Credibility 393\u003c\/p\u003e \u003cp\u003e16.5 Problems with the Approach 397\u003c\/p\u003e \u003cp\u003e16.6 Notes and References 397\u003c\/p\u003e \u003cp\u003e16.7 Exercises 397\u003c\/p\u003e \u003cp\u003e\u003cb\u003e17 Greatest Accuracy Credibility 401\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e17.1 Introduction 401\u003c\/p\u003e \u003cp\u003e17.2 Conditional Distributions and Expectation 404\u003c\/p\u003e \u003cp\u003e17.3 The Bayesian Methodology 408\u003c\/p\u003e \u003cp\u003e17.4 The Credibility Premium 415\u003c\/p\u003e \u003cp\u003e17.5 The Bühlmann Model 418\u003c\/p\u003e \u003cp\u003e17.6 The Bühlmann–Straub Model 422\u003c\/p\u003e \u003cp\u003e17.7 Exact Credibility 427\u003c\/p\u003e \u003cp\u003e17.8 Notes and References 431\u003c\/p\u003e \u003cp\u003e17.9 Exercises 432\u003c\/p\u003e \u003cp\u003e\u003cb\u003e18 Empirical Bayes Parameter Estimation 445\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e18.1 Introduction 445\u003c\/p\u003e \u003cp\u003e18.2 Nonparametric Estimation 448\u003c\/p\u003e \u003cp\u003e18.3 Semiparametric Estimation 459\u003c\/p\u003e \u003cp\u003e18.4 Notes and References 460\u003c\/p\u003e \u003cp\u003e18.5 Exercises 460\u003c\/p\u003e \u003cp\u003e\u003cb\u003ePart VI Simulation\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e\u003cb\u003e19 Simulation 467\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e19.1 Basics of Simulation 467\u003c\/p\u003e \u003cp\u003e19.1.1 The Simulation Approach 468\u003c\/p\u003e \u003cp\u003e19.1.2 Exercises 472\u003c\/p\u003e \u003cp\u003e19.2 Simulation for Specific Distributions 472\u003c\/p\u003e \u003cp\u003e19.2.1 Discrete Mixtures 472\u003c\/p\u003e \u003cp\u003e19.2.2 Time or Age of Death from a Life Table 473\u003c\/p\u003e \u003cp\u003e19.2.3 Simulating from the (𝑎, 𝑏, 0) Class 474\u003c\/p\u003e \u003cp\u003e19.2.4 Normal and Lognormal Distributions 476\u003c\/p\u003e \u003cp\u003e19.2.5 Exercises 477\u003c\/p\u003e \u003cp\u003e19.3 Determining the Sample Size 477\u003c\/p\u003e \u003cp\u003e19.3.1 Exercises 479\u003c\/p\u003e \u003cp\u003e19.4 Examples of Simulation in Actuarial Modeling 480\u003c\/p\u003e \u003cp\u003e19.4.1 Aggregate Loss Calculations 480\u003c\/p\u003e \u003cp\u003e19.4.2 Examples of Lack of Independence 480\u003c\/p\u003e \u003cp\u003e19.4.3 Simulation Analysis of the Two Examples 481\u003c\/p\u003e \u003cp\u003e19.4.4 The Use of Simulation to Determine Risk Measures 484\u003c\/p\u003e \u003cp\u003e19.4.5 Statistical Analyses 484\u003c\/p\u003e \u003cp\u003e19.4.6 Exercises 486\u003c\/p\u003e \u003cp\u003e\u003cb\u003eA An Inventory of Continuous Distributions 489\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003eA.1 Introduction 489\u003c\/p\u003e \u003cp\u003eA.2 The Transformed Beta Family 493\u003c\/p\u003e \u003cp\u003eA.2.1 The Four-Parameter Distribution 493\u003c\/p\u003e \u003cp\u003eA.2.2 Three-Parameter Distributions 493\u003c\/p\u003e \u003cp\u003eA.2.3 Two-Parameter Distributions 494\u003c\/p\u003e \u003cp\u003eA.3 The Transformed Gamma Family 496\u003c\/p\u003e \u003cp\u003eA.3.1 Three-Parameter Distributions 496\u003c\/p\u003e \u003cp\u003eA.3.2 Two-Parameter Distributions 497\u003c\/p\u003e \u003cp\u003eA.3.3 One-Parameter Distributions 499\u003c\/p\u003e \u003cp\u003eA.4 Distributions for Large Losses 499\u003c\/p\u003e \u003cp\u003eA.4.1 Extreme Value Distributions 499\u003c\/p\u003e \u003cp\u003eA.4.2 Generalized Pareto Distributions 500\u003c\/p\u003e \u003cp\u003eA.5 Other Distributions 501\u003c\/p\u003e \u003cp\u003eA.6 Distributions with Finite Support 502\u003c\/p\u003e \u003cp\u003e\u003cb\u003eB An Inventory of Discrete Distributions 505\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003eB.1 Introduction 505\u003c\/p\u003e \u003cp\u003eB.2 The (𝑎, 𝑏, 0) Class 506\u003c\/p\u003e \u003cp\u003eB.3 The (𝑎, 𝑏, 1) Class 507\u003c\/p\u003e \u003cp\u003eB.3.1 The Zero-Truncated Subclass 507\u003c\/p\u003e \u003cp\u003eB.3.2 The Zero-Modified Subclass 509\u003c\/p\u003e \u003cp\u003eB.4 The Compound Class 509\u003c\/p\u003e \u003cp\u003eB.4.1 Some Compound Distributions 510\u003c\/p\u003e \u003cp\u003eB.5 A Hierarchy of Discrete Distributions 511\u003c\/p\u003e \u003cp\u003e\u003cb\u003eC Frequency and Severity Relationships 513\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e\u003cb\u003eD The Recursive Formula 515\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e\u003cb\u003eE Discretization of the Severity Distribution 517\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003eE.1 The Method of Rounding 517\u003c\/p\u003e \u003cp\u003eE.2 Mean Preserving 518\u003c\/p\u003e \u003cp\u003eE.3 Undiscretization of a Discretized Distribution 518\u003c\/p\u003e \u003cp\u003eReferences 521\u003c\/p\u003e \u003cp\u003eIndex 529\u003c\/p\u003e","brand":"John Wiley \u0026 Sons Inc","offers":[{"title":"Default Title","offer_id":48866400764247,"sku":"9781119523789","price":116.96,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9781119523789.jpg?v=1722278466","url":"https:\/\/bookcurl.com\/products\/loss-models-9781119523789","provider":"Book Curl","version":"1.0","type":"link"}