Testing Special Cases of the GB2 Distribution
William Griffiths & R. Carter Hill
Abstract
We examine the power of hypothesis tests leading to four widely used special cases of the four-parameter generalized beta distribution of the second kind (GB2). These are the Singh-Maddala, Dagum, beta-2 and Fisk distributions. For the Singh-Maddala, Dagum, and Fisk distributions, the power of Wald tests is nonmonotonic when the true parameter values are greater than those in the null hypothesis. As the difference between the hypothesized values of the parameters and their actual values increases, the power increases and then declines. Wald tests on log-transformations of the parameters are more powerful than those on the original parameters; their power functions are also nonmonotonic but the decline in power begins at higher values of the parameters. The likelihood ratio and Lagrange multiplier tests have power functions that increase monotonically for true parameter values beyond the hypothesized values, and are more powerful than their Wald counterparts, but only marginally so relative to the Wald test on the log-transformed parameters. For parameter values less than the hypothesized values there are no large differences in the power of all four tests. Tests for the remaining distribution, the beta-2 distribution, have power functions that are well behaved and exhibit only small differences. We provide an extensive online supplement containing several theoretical results as well as further insights into the power behavior of the tests.
1 citation
Evidence weight
Balanced mode · F 0.40 / M 0.15 / V 0.05 / R 0.40
| F · citation impact | 0.16 × 0.4 = 0.06 |
| M · momentum | 0.53 × 0.15 = 0.08 |
| V · venue signal | 0.50 × 0.05 = 0.03 |
| R · text relevance † | 0.50 × 0.4 = 0.20 |
† Text relevance is estimated at 0.50 on the detail page — for your query’s actual relevance score, open this paper from a search result.