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AMOOF2 Update Sept 1st

September 1st, 2012
by Yvonne Chueh on 8 June 2014

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Transcript of AMOOF2 Update Sept 1st

Advanced Mathematical Programmers
September 1st, 2012
AMOOF 2.0
AMOOF2 Project Contributors
The AMP Team
Client & Proposer
Cameron Spencer
Jim Smigaj
Noble Brown
Sean Fardell
Kris Hepler
Zachary Haberman
Dr. Yvonne C. Chueh
Project Background
Actuarial and Insurance fields may require complex probability distribution fitting under increasing needs/mandates for stochastic modeling e.g. PBA, AG43
No low/no cost and efficient software available for extensive and customized actuarial data/model research and final analysis
Inspiration by the open source AMOOF software used by company model efficiency research
AMOOF2 receives sponsorship from TAF through individual grant competition.
New research and computational innovation to incorporate Bias Correction for small sample bias rising from MLE curve fitting approach.
CS Advisor
Dr. James Schwing
Project Solution
Software Engineering
I/E System
Graphics System
PDF System
Solver System
GUI System
Statistics System
PDF System
I/E System
Imports Data Sets - 100%
Handles Importing and Exporting:
Exports Reports - 100%
Exports Statistics - 100%
Exports Images - 100%
Interacts with:
GUI System
Overall Completion: 100%
In .CSV, .DOCX format
Imports and Exports - 100%
Handles All User Interactions:
Color Scheme - 100%
Functionality - 85%
Displaying Statistics - 100%
Interacts with:
All Other Systems
Overall Completion: 90%
Bias Correction Information - 95%
Single PDFs Implemented - 100%
Holds PDFs and all related formulas:
Mixed PDFs Implemented - 60%
Special Gamma Function - 100%
Interacts with:
GUI System
Overall Completion: 85%
Descriptive Statistics - 100%
Handles All Descriptive Statistics:
Relative Error Calculation - 100%
Value at Risk - 100%
Interacts with:
GUI System
Overall Completion: 99%
Conditional Tail Expectation - 99%
PDF System
Calculating Single PDFs - 100%
Interfaces between AMOOF2 and EXCEL:
Calculating Mixed PDFs - 67%
Interacts with:
GUI System
Overall Completion: 89%
Safe Garbage Collection - 100%
PDF System
4:3 Ratio Histogram - 70%
Produces the Histogram:
16:9 Ratio Histogram - 70%
Function Line Overlay - 70%
Interacts with:
GUI System
Overall Completion: 70%
Total Implementation: 66.63%
Demonstration
Programming Specifics
Project Status
Conclusion
Questions
Reflection and Strategy Pattern
Singleton Pattern
Reflection and Factory Pattern
Modular Design
PDF Implementation
Exporting and Importing
Controller Object
The Systems
Integration
CTE and VaR Integration
Implementing VaR and CTE integration
PDF Integration
Integration: Precision v.s. Speed constraints
Integration: The Programming
Integration: CTE and VaR
Revision Count (As of 9/1/2012): 459++?
Number of Classes: 45
Lines of Code (Just the Code!): 3,700+

Planned date of completion:
July 17, Pari integrator integrated
July 17, Tab 4 "O" completed
July 24, Mixed pdfs, options working
July 31, Report and histogram integrated
July 31, Tab 5 "F" and Help Tab completed
Post July: Correct documentation, add formulas to website, add documentation to website, maintenance mode, stable release by end of August

For software development status and download for testing, visit
http://amp-software.net/amoof/download.php
Develop the AMOOF 2.0 Software Suite running .NET and COM environment
Decouple the AMOOF software from Excel using Solver Fundation's resources--Not successful after attempts
Implement PDF selection, graphing features to
aid user flexibility, high-computation outcome
reporting

Research and implement small sample bias adjustment rising from MLE
Major setbacks/challenges causing late delivery
e.g. Solver foundation not supporting Special
math functions for frequently used Gamma
and PolyGamma

Numerical precision constraints/issue 16-50-
300 digits implies speed and precision
tradeoff

Initial value inputs for optimization process required to fit PDF--interactive user input


Very complicated probability distribution problem to implement correctly and effectively
Incorporates various fields Mathematics


Incorporates many areas of Computer Science
Area under curve from a to b
Dynamic Gaussian Integration method
Integration error measured and tracked
Partitions stop when the error small enough, Trapezoidal rule v.s. Simpsons for error estimation
Test and compare with Wolfram Mathematica 8 results
High-Precision Riemann Sums (Gaussian Quadrature Integration) calculating VaRs and CTEs
PARI (50-300 digit precision) v.s. C# (calculation speed 16 digit) tradeoff
Integration: CTE and VaR
High-Precision Riemann Sums (Gaussian algorithms) calculating VaRs and CTEs

Locating the tail regions for integration depending on the parametric PDF found
and data may be tricky
Waiting for Final Implementations of User Help Documents and Mixed PDF Functions

Release Version for Testing Available at http://amoof.amp-software.net/download.php
Improper integral for right/Left tail: Precision challenge, Numerical analysis of accuracy
Two tail areas: Precision challenge

Math library requires doubles (16 digits)

Tail integration 50-300 digit needed
Contact Person:
Yvonne Chueh chueh@cwu.edu
Analytic MLE Estimator for 22 PDFs in Closed Form (if exists) completed in Wolfram Mathematica 8.

CSCK MLE Bias Estimators for 22 PDFs in Closed Form (if exist) and Special Math function also completed in Wolfram Matheamtica 8.

AMOOF2 User-Interactive GUI incorporates these findings to enhance the speed and accuracy.
Small Sample Bias Research
Sponsor
Researcher
Dr. Paul H. Johnson, Jr.
CWU Computer Science 2012
Sponsor:
User-interactive spreadsheet input to ensure solver runs properly regardless Excel version,
Access spreadsheet using C#
hosting website
https://bitbucket.org/AMOOF3/amoof-3.0/downloads
Optimal Probability Density Functions for Actuarial Model Outcomes
Central Washington University
AMOOF 2.0
Demonstration
………….
PDF22
PDF2
PDF1
………….
PDF22
PDF2
………….
PDF22
PDF2
PDF1
PDF8
PDF7

Model Efficiency

Only generates PDF objects selected for calculation.
With
………….
PDF22
PDF2
PDF1
………….
PDF22
PDF2
PDF1
………….
PDF22
PDF2
PDF1
PDF8
PDF7
PDF3
Permanent Storage
Memory (RAM)
Without
Permanent Storage
Memory (RAM)
Use of Reflection
AMOOF 2.0: Multiple PDFs
Graphical User Interface
Research & Analysis
Available Fall 2012
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