# Schedule and Textbooks Information

## Fall 2023 Schedule and Textbook Information for STAT 479

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### STAT 479 - Textbook(s) for Fall 2023

Textbook information is not available at this time.

### STAT 479 - Schedule information for Fall 2023

CRN | Section | Instructor | Day | Time | Room |
---|---|---|---|---|---|

25706 | 001 | Mengyi Xu | TR | 3:00-4:15pm | SCHM 113 |

#### STAT 479 - Course Outline

Specifically, the candidate is expected to be able to perform the tasks listed below:A. Severity Models

- Calculate the basic distributional quantities:
- a) Moments,
- b) Percentiles,
- c) Generating functions.

- Describe how changes in parameters affect the distribution.
- Recognize classes of distributions and their relationships.
- Apply the following techniques for creating new families of distributions:
- a) Multiplication by a constant,
- b) Raising to a power,
- c) Exponentiation,
- d) Mixing.
- Identify the applications in which each distribution is used and reasons why.
- Apply the distribution to an application, given the parameters.
- Calculate various measures of tail weight and interpret the results to compare the tail weights.
- Explain the properties of the lognormal distribution.

- a. For the Poisson, Mixed Poisson, Binomial, Negative Binomial, Geometric distribution and mixtures thereof (as well as compound distributions):
- Describe how changes in parameters affect the distribution,
- Calculate moments,
- Identify the applications for which each distribution is used and reasons why,
- Apply the distribution to an application given the parameters.

- Compute relevant parameters and statistics for collective risk models.
- Evaluate compound models for aggregate claims.
- Compute aggregate claims distributions.

- Evaluate the impacts of coverage modifications:
- a) Deductibles,
- b) Limits, and
- c) Coinsurance.
- Calculate Loss Elimination Ratios.
- Evaluate effects of inflation on losses.

- Calculate risk measures VaR, CTE and explain their use and limitations

- Calculate survival and ruin probabilities using discrete models.
- Describe the considerations included in a ruin model

- Estimate failure time and loss distributions using
- a) Kaplan-Meier estimator, including approximations for large data sets
- b) Nelson-Aalen estimator
- c) Kernel density estimators
- Estimate the variance of estimators and confidence intervals for failure time and loss distributions.
- Estimate failure time and loss distributions with the Cox proportional hazards model and other basic models with covariates.
- Apply the following concepts in estimating failure time and loss distribution
- a) Unbiasedness
- b) Consistency
- c) Mean squared error

- 1. Estimate the parameters of failure time and loss distributions using
- a) Maximum likelihood
- b) Method of moments
- c) Percentile matching
- d) Bayesian procedures
- Estimate the parameters of failure time and loss distributions with censored and/or truncated data using maximum likelihood.
- Estimate the variance of estimators and the confidence intervals for the parameters and functions of parameters of failure time and loss distributions.
- Apply the following concepts in estimating failure time and loss distributions
- a) Unbiasedness
- b) Asymptotic unbiasedness
- c) Consistency
- d) Mean squared error
- e) Uniform minimum variance
- Determine the acceptability of a fitted model using
- a) Graphical procedures
- b) Kolmogorov-Smirnov test
- c) Anderson-Darling test
- d) Chi-square goodness-of-fit test
- e) Likelihood ratio test