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Fitting and comparing seed germination models with a focus on the inverse normal distribution
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O'Neill, Michael E., Thomson, Peter C., Jacobs, Brent C., Brain, Phil, Butler, Ruth C., Turner, Heather and Mitakda, Bernadetha (2004) Fitting and comparing seed germination models with a focus on the inverse normal distribution. Australian & New Zealand Journal of Statistics , 46 (3). pp. 349-366. doi:10.1111/j.1467-842X.2004.00335.x
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Official URL: http://dx.doi.org/10.1111/j.1467-842X.2004.00335.x
Abstract
This paper reviews current methods for fitting a range of models to censored seed germination data and recommends adoption of a probability-based model for the time to germination. It shows that, provided the probability of a seed eventually germinating is not on the boundary, maximum likelihood estimates, their standard errors and the resultant deviances are identical whether only those seeds which have germinated are used or all seeds (including seeds ungerminated at the end of the experiment). The paper recommends analysis of deviance when exploring whether replicate data are consistent with a hypothesis that the underlying distributions are identical, and when assessing whether data from different treatments have underlying distributions with common parameters. The inverse normal distribution, otherwise known as the inverse Gaussian distribution, is discussed, as a natural distribution for the time to germination (including a parameter to measure the lag time to germination). The paper explores some of the properties of this distribution, evaluates the standard errors of the maximum likelihood estimates of the parameters and suggests an accurate approximation to the cumulative distribution function and the median time to germination.
| Item Type: | Journal Article | ||||
|---|---|---|---|---|---|
| Divisions: | Faculty of Science, Engineering and Medicine > Science > Statistics | ||||
| Journal or Publication Title: | Australian & New Zealand Journal of Statistics | ||||
| Publisher: | Wiley | ||||
| ISSN: | 1369-1473 | ||||
| Official Date: | 10 September 2004 | ||||
| Dates: |
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| Volume: | 46 | ||||
| Number: | 3 | ||||
| Page Range: | pp. 349-366 | ||||
| DOI: | 10.1111/j.1467-842X.2004.00335.x | ||||
| Status: | Peer Reviewed | ||||
| Publication Status: | Published | ||||
| Access rights to Published version: | Restricted or Subscription Access |
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