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Statistical Testing: User Requirements Document

 

Prepared by:

Introduction

Purpose of the document

This document collects the specific requirements concerning Goodness-of-Fit testing.

Scope of the software

The Statistical Testing project will provide tools for the statistical comparison of distributions; the system will be usable in the context of other software projects, like, for instance,  the Geant4 Test & Analysis Project.

Product perspective

This software product is meant to be a component of a software system for statistical tools for HEP data analysis. Since it adopts a component-based architecture, this software can be of interest also in a wider context.

General capabilities

- The user shall be able to compare binned distributions.

- The user shall be able to compare unbinned distributions.

- The user shall be able to compare binned and unbinned distributions, simply converting one kind into the other.

- The user shall be able to choose among a variety of goodness-of-fit tests.

General constraints

It will be based on AIDA interfaces, without any dependency on any specific analysis tool.

User characteristics

Users of the product are espected to be:

In addition, other potential users may be:

Operational environment

The software will operate in the same environment as the development of the Geant4 Toolkit.

Assumptions and dependencies

The system will depend on AIDA interfaces

Specific requirements: capability requirements

Comparing one-dimensional distributions - two-sample problem

UR 1.1 The user shall be able to compare one-dimensional binned distributions by means of integrating chi-squared test (gamma function).

UR 1.2 The user shall be able to compare one-dimensional binned distributions by means of Anderson-Darling test.

UR 1.3 The user shall be able to compare one-dimensional binned distributions by means of Fisz-Cramer-von Mises test.

UR 1.4 The user shall be able to compare one-dimensional binned distributions by means of Tiku test.

UR 1.5 The user shall be able to compare one-dimensional unbinned distributions by means of Kolmogorov-Smirnov test with Goodman'approximation.

UR 1.6 The user shall be able to compare one-dimensional unbinned distributions by means of Kolmogorov-Smirnov test.

UR 1.7 The user shall be able to compare one-dimensional unbinned distributions by means of Kolmogorov-Smirnov test with the Anderson-Darling weighting function.

UR 1.8 The user shall be able to compare one-dimensional unbinned distributions by means of Kolmogorov-Smirnov test with the Buning weighting function.

UR 1.9 The user shall be able to compare one-dimensional unbinned distributions by means of Anderson-Darling test.

UR 1.10 The user shall be able to compare one-dimensional unbinned distributions by means of Fisz-Cramer-von Mises test.

UR 1.11 The user shall be able to compare one-dimensional unbinned distributions by means of Fisz-Cramer-von Mises test with the Buning weighting function.

UR 1.12 The user shall be able to compare one-dimensional unbinned distributions by means of Kuiper test.

UR 1.13 The user shall be able to compare one-dimensional unbinned distributions by means of Tiku test.

UR 1.14 The user shall be able to compare one-dimensional unbinned distributions by means of Watson test.

UR 1.15 The user shall be able to compare one-dimensional binned distributions by means of approximated chi-squared test (incomplete gamma function).

UR 1.16 The user shall be able to compare one-dimensional binned distributions by means of chi-squared test (GSL).

UR 1.17 The user shall be able to compare one-dimensional binned distributions by means of approximated Anderson-Darling test.

UR 1.18 The user shall be able to compare one-dimensional unbinned distributions by means of approximated Anderson-Darling test.

UR 1.19 The user shall be able to compare one-dimensional unbinned distributions by means of Girone test.

UR 1.20 The user shall be able to select the type of test.

UR 1.21 The user will be told if the test he/she chooses is not appropriate to compare his/her distributions.

Note: Requirements for other bayesian tests are currently under consideration.


Specific requirements: constraint requirements

UR A.1 The code shall be in ISO C++.

UR A.2 The system shall be based on AIDA interfaces.

UR A.3 The system shall have a user layer for ROOT objects

UR A.4 The system shall not depend on any concrete analysis system.

UR A.5 The system should work on Geant4 supported platforms.

History

09 Jan 2003 S. Donadio, B. Mascialino, MG Pia Created
28 May 2003 S. Donadio, B. Mascialino Added UR1.10, UR4.6, UR4.7, UR4.8
14 March 2004 S. Donadio, B. Mascialino, P.Viarengo Added UR for Tiku algorithm
18 January 2006
B. Mascialino
Added requirements for weighted tests
10 April 2006
B. Mascialino
Modified names of tests for 2nd release


Last modified 10 April 2006 - Barbara Mascialino