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Fitting distributions using maximum likelihood: Methods and packages

机译：使用最大似然拟合分布：方法和包

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The most powerful tests of response time (RT) models often involve the whole shape of the RT distribution, thus avoiding mimicking that can occur at the level of RT means and variances. Nonpara-metric distribution estimation is, in principle, the most appropriate approach, but such estimators are sometimes difficult to obtain. On the other hand, distribution fitting, given an algebraic function, is both easy and compact. We review the general approach to performing distribution fitting with maximum likelihood (ML) and a method based on quantiles (quantile maximum probability, QMP). We show that QMP has both small bias and good efficiency when used with common distribution functions (the ex-Gaussian, Gumbel, lognormal, Wald, and Weibull distributions). In addition, we review some software packages performing ML (PASTIS, QMPE, DISFIT, and MATHEMATICA) and compare their results. In general, the differences between packages have little influence on the optimal solution found, but the form of the distribution function has: Both the lognormal and the Wald distributions have nonlinear dependencies between the parameter estimates that tend to increase the overall bias in parameter recovery and to decrease efficiency. We conclude by laying out a few pointers on how to relate descriptive models of RT to cognitive models of RT. A program that generated the random deviates used in our studies may be downloaded from www.psychonomic.org/archive/.
机译：响应时间（RT）模型最强大的测试通常涉及RT分布的整个形状，因此避免了在RT均值和方差水平上可能发生的模仿。原则上，非参数分布估计是最合适的方法，但是有时很难获得这种估计量。另一方面，具有代数功能的分布拟合既简单又紧凑。我们回顾了使用最大似然（ML）进行分布拟合的一般方法和基于分位数（分位数最大概率，QMP）的方法。我们证明，当与常见的分布函数（前高斯分布，Gumbel，对数正态分布，Wald和Weibull分布）一起使用时，QMP具有较小的偏差和良好的效率。此外，我们回顾了一些执行ML的软件包（PASTIS，QMPE，DISFIT和MATHEMATICA）并比较了它们的结果。通常，程序包之间的差异对找到的最佳解几乎没有影响，但是分布函数的形式具有：对数正态分布和Wald分布在参数估计值之间都具有非线性依赖性，这往往会增加参数恢复的总体偏差。降低效率。最后，我们就如何将RT的描述性模型与RT的认知模型联系起来提出了一些建议。可以从www.psychonomic.org/archive/下载产生我们研究中使用的随机偏差的程序。

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