# Tests of Goodness of Fit and Distribution Selection

1. Elisa T. Lee and
2. John Wenyu Wang

Published Online: 30 JUN 2003

DOI: 10.1002/0471458546.ch9

## Statistical Methods for Survival Data Analysis, Third Edition

#### How to Cite

Lee, E. T. and Wang, J. W. (2003) Tests of Goodness of Fit and Distribution Selection, in Statistical Methods for Survival Data Analysis, Third Edition, John Wiley & Sons, Inc., Hoboken, NJ, USA. doi: 10.1002/0471458546.ch9

#### Author Information

1. Department of Biostatistics and Epidemiology and Center for American Indian Health Research, College of Public Health, University of Oklahoma Health Sciences Center, Oklahoma City, Oklahoma, USA

#### Publication History

1. Published Online: 30 JUN 2003
2. Published Print: 4 APR 2003

#### Book Series:

1. Wiley Series in Probability and Statistics

#### ISBN Information

Print ISBN: 9780471369974

Online ISBN: 9780471458548

## SEARCH

### Keywords:

• goodness-of-fit tests;
• distribution selection;
• statistics;
• asymptotic likelihood inferences;
• family of distributions;
• BIC procedures;
• AIC procedures;
• known parameters;
• tests for appropriateness;
• Hollander and Proschan's test for appropriateness

### Summary

In this chapter we discuss several analytical procedures for testing the goodness of fit of a family of distributions or a given distribution with known parameters and consequently, the selection of an appropriate family of distributions. We begin by introducing several of the most widely used statistics for testing goodness of fit. We then discuss statistics for testing whether a family of distributions is appropriate and how to select a family of distributions based on certain criteria. We present statistics for testing whether a distribution with given parameters is appropriate. All of the test statistics discussed are based on asymptotic likelihood inferences. Finally, we introduce the test statistic of Hollander and Proschan for testing whether a distribution with given parameters is appropriate. Computer codes for BMDP or SAS that can be used to carry out the test procedures are provided. The chapter concludes with a problem solving section.