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The Actuary’s Free Study Guide for Exam 4 / Exam C

G. Stolyarov II
Summer and Fall 2009

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A Comprehensive List of Free Study Materials for Exam 4/C

Section 1: Raw Moments, Central Moments, Excess Loss Variables, and Left-Censored and Shifted Variables

Section 2: The Empirical Model and Limited Loss Variables

Section 3: Coefficient of Variation, Skewness, Kurtosis, and a Shortcut Formula for Mean Excess Loss Functions

Section 4: Percentiles, Value-at-Risk, and Tail-Value-at-Risk

Section 5: The Central Limit Theorem and Applications to Special Distributions

Section 6: Moment Generating Functions and Probability Generating Functions

Section 7: Hazard Rates and Light and Heavy Tails of Distributions

Section 8: The Equilibrium Distribution, Mean Excess Loss Functions, and Tails of Distributions

Section 9: Risk Measures and Coherence

Section 10: Parametric Distributions and Scale Parameters

Section 11: K-Point Mixtures, Variable-Component Mixture Distributions, and Data-Dependent Distributions

Section 12: Exam-Style Questions on the Central Limit Theorem, Skewness, Percentile Matching, and Ogives

Section 13: Distributions of Multiples and Powers of Random Variables

Section 14: The Gamma Function, Incomplete Gamma Function, and Exponentiation of Random Variables

Section 15: Mixture Distributions and Some Review Questions

Section 16: Mixture Distributions Involving Discrete Random Variables

Section 17: Frailty Models

Section 18: Spliced Distributions

Section 19: The Linear Exponential Family of Distributions

Section 20: Properties of Poisson, Negative Binomial, and Geometric Distributions

Section 21: Properties of the Binomial Distribution and the (a, b, 0) Class of Distributions

Section 22: The (a, b, 1) Class of Distributions

Section 23: The Logarithmic Distribution

Section 24: Assorted Exam-Style Questions for Exam 4 / Exam C - Part 1

Section 25: Applications of Ordinary Deductibles Per Payment and Per Loss

Section 26: Applications of Franchise Deductibles Per Payment and Per Loss

Section 27: Loss Elimination Ratios and Inflation Effects for Ordinary Deductibles

Section 28: Policy Limits and Associated Effects of Inflation

Section 29: Coinsurance and Treatment Thereof in Combination with Ordinary Deductibles, Policy Limits, and Inflation

Section 30: Impact of a Deductible on the Number of Payments

Section 31: Assorted Exam-Style Questions for Exam 4 / Exam C - Part 2

Section 32: The Collective Risk Model and the Individual Risk Model

Section 33: Mean, Variance, Third Central Moment, and Probability Calculations Pertaining to Aggregate Loss Random Variables

Section 34: Stop-Loss Insurance and the Net Stop-Loss Premium

Section 35: Moment Generating Functions of Aggregate Random Variables and Probability Calculations for Aggregate Random Variables With Exponential Severity

Section 36: Using Convolutions to Determine the Probability Distribution of Aggregate Random Variables

Section 37: The Method of Rounding or Mass Dispersal

Section 38: The Method of Local Moment Matching

Section 39: The Effects of Individual Policy Modifications on the Aggregate Payment Random Variable

Section 40: Properties of Aggregate Losses in the Individual Risk Model

Section 41: Parametric Approximations of Probability Distributions of Aggregate Losses in the Individual Risk Model

Section 42: The Empirical Distribution Function, the Cumulative Hazard Rate Function, and the Nelson-Åalen Estimate

Section 43: Kernel Smoothed Distributions, Ogives, and Histograms

Section 44: Exam-Style Questions on the Smoothed Empirical Estimate, the Nelson-Åalen Estimate, and Aggregate Random Variables

Section 45: Properties of Estimators

Section 46: Interval Estimators and Hypothesis Testing

Section 47: Modifications of Observations and Calculations Pertaining to the Risk Set for Modified Observations

Section 48: The Kaplan-Meier Product-Limit Estimator

Section 49: Full Credibility of Data in Limited Fluctuation Credibility Theory

Section 50: Estimating the Variances of Empirical Survival Functions and Empirical Probability Estimates

Section 51: Greenwood’s Approximation and Variances of Products of Random Variables

Section 52: Log-Transformed Confidence Intervals for Survival Functions and Cumulative Hazard Rate Functions

Section 53: Kernel Density Estimators and Uniform, Triangular, and Gamma Kernels

Section 54: Partial Credibility in Limited Fluctuation Credibility Theory

Section 55: The Kaplan-Meier Approximation for Large Data Sets and Multiple Decrements

Section 56: The Method of Moments and Maximum Likelihood Estimation

Section 57: Exam-Style Questions on Maximum Likelihood Estimation

Section 58: Fisher Information for One Parameter

Section 59: Fisher Information for Multiple Parameters

Section 60: The Delta Method for Estimating Functions of Parameters

Section 61: Non-Normal Confidence Intervals for Parameters

Section 62: Prior, Model, Marginal, Posterior, and Predictive Distributions in Bayesian Estimation

Section 63: Loss Functions and the Expected Value of the Predictive Distribution in Bayesian Estimation

Section 64: Credibility Intervals and the Bayesian Central Limit Theorem in Bayesian Estimation

Section 65: Conjugate Prior Distributions in Bayesian Estimation

Section 66: Exam-Style Questions on Bayesian Estimation

Section 67: Exam-Style Questions on Bayesian Estimation - Part 2

Section 68: Exam-Style Questions on Bühlmann Credibility

Section 69: Exam-Style Questions on Bühlmann Credibility - Part 2

Section 70: Exam-Style Questions on Bühlmann-Straub Credibility

Section 71: Distribution and Probability Density Functions for Modified Data, Difference Functions, and the Kolmogorov-Smirnov Test

Section 72: Exam-Style Questions on the Kolmogorov-Smirnov Test and Bühlmann Credibility

Section 73: Nonparametric and Semiparametric Empirical Bayes Estimation of Bühlmann And Bühlmann-Straub Credibility Factors

Section 74: Exam-Style Questions on Nonparametric Empirical Bayes Estimation of Bühlmann and Bühlmann-Straub Credibility Factors

Section 75: Exam-Style Questions on Semiparametric Empirical Bayes Estimation of Bühlmann and Bühlmann-Straub Credibility Factors and the Chi-Square Goodness of Fit Test

Section 76: The Anderson-Darling Test

Section 77: The Likelihood Ratio Test

Section 78: The Schwarz Bayesian Criterion and Exam-Style Questions on Hypothesis Testing of Models

Section 79: Basics of Simulation and the Inversion Method

Section 80: Exam-Style Questions on the Inversion Method

Section 81: Exam-Style Questions on Simulation

Section 82: Estimates for Value-at-Risk and Tail Value-at-Risk for Simulated Samples

Section 83: The Bootstrap Method for Estimating Mean Square Error

Section 84: Simulations of Cumulative Distribution Functions and Exam-Style Questions on Simulation

Section 85: Assorted Exam-Style Questions for Exam 4/C - Part 3

Section 86: Assorted Exam-Style Questions for Exam 4/C - Part 4

Section 87: The Life Table Methodology for Estimating Risk Sets and Assorted Exam-Style Questions for Exam 4/C

Section 88: Assorted Exam-Style Questions for Exam 4/C - Part 5

Section 89: Assorted Exam-Style Questions for Exam 4/C - Part 6

Section 90: Assorted Exam-Style Questions for Exam 4/C - Part 7

Section 91: Assorted Exam-Style Questions for Exam 4/C - Part 8

Section 92: Assorted Exam-Style Questions for Exam 4/C - Part 9

Section 93: The Continuity Correction for Normal Approximations and Exam-Style Questions on Mixed and Aggregate Distributions

Section 94: Assorted Exam-Style Questions for Exam 4/C - Part 10

Section 95: Assorted Exam-Style Questions for Exam 4/C - Part 11

Section 96: Assorted Exam-Style Questions for Exam 4/C - Part 12

Section 97: Assorted Exam-Style Questions for Exam 4/C - Part 13

Section 98: Assorted Exam-Style Questions for Exam 4/C - Part 14

Section 99: Assorted Exam-Style Questions for Exam 4/C - Part 15

Section 100: Assorted Exam-Style Questions for Exam 4/C - Part 16

Section 101: Assorted Exam-Style Questions for Exam 4/C - Part 17

Section 102: Assorted Exam-Style Questions for Exam 4/C - Part 18

Section 103: Assorted Exam-Style Questions for Exam 4/C - Part 19

Section 104: Assorted Exam-Style Questions for Exam 4/C - Part 20

Section 105: Assorted Exam-Style Questions for Exam 4/C - Part 21  

Section 106: Assorted Exam-Style Questions for Exam 4/C - Part 22

Section 107: Assorted Exam-Style Questions for Exam 4/C - Part 23

Section 108: Assorted Exam-Style Questions for Exam 4/C - Part 24

Section 109: Assorted Exam-Style Questions for Exam 4/C - Part 25

Section 110: Assorted Exam-Style Questions for Exam 4/C - Part 26

Section 111: Assorted Exam-Style Questions for Exam 4/C - Part 27

Section 112: Assorted Exam-Style Questions for Exam 4/C - Part 28

Section 113: Assorted Exam-Style Questions for Exam 4/C - Part 29

Section 114: Assorted Exam-Style Questions for Exam 4/C - Part 30

Section 115: Assorted Exam-Style Questions for Exam 4/C - Part 31

Section 116: Assorted Exam-Style Questions for Exam 4/C - Part 32

G. Stolyarov II is an actuary, science fiction novelist, independent philosophical essayist, poet, amateur mathematician, composer, contributor to Enter Stage Right, Le Quebecois Libre, Rebirth of Reason, and the Ludwig von Mises Institute, Senior Writer for The Liberal Institute, former weekly columnist for GrasstopsUSA.com, and Editor-in-Chief of The Rational Argumentator, a magazine championing the principles of reason, rights, and progress. Mr. Stolyarov’s new blog, The Progress of Liberty, offers a combination of commentary, multimedia presentations, educational materials, and suggestions for effective activism in favor of individual freedom. Mr. Stolyarov also publishes his articles on Helium.com and Associated Content to assist the spread of rational ideas. He holds the highest Clout Level (10) possible on Associated Content. Mr. Stolyarov has also written a science fiction novel, Eden against the Colossus, a non-fiction treatise, A Rational Cosmology, and a play, Implied Consent. You can watch his YouTube Videos. Mr. Stolyarov can be contacted at gennadystolyarovii@yahoo.com.

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Learn about Mr. Stolyarov’s novel, Eden against the Colossus, here.

Read Mr. Stolyarov’s comprehensive treatise, A Rational Cosmology, explicating such terms as the universe, matter, space, time, sound, light, life, consciousness, and volition, here.

Read Mr. Stolyarov’s four-act play, Implied Consent, a futuristic intellectual drama on the sanctity of human life, here.

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