论文标题
用均匀分布截断指数
Truncating the Exponential with a Uniform Distribution
论文作者
论文摘要
对于指数分布的持续时间的样本，我们针对的是点估计和参数的置信区间。仅当持续时间在特定时间间隔内结束时才观察到持续时间，该时间间隔由均匀分布确定。因此，数据是一个被截断的经验过程，当仅观察到样本的一小部分时，我们可以通过泊松过程近似，就像我们的应用一样。我们从标准参数中得出了点过程的可能性，确认潜在样本的大小为第二个参数，并得出两者的最大似然估计器。指数参数的估计量的一致性和渐近正态性来自M估计的标准结果。我们将设计与观察到的持续时间进行简单的随机样品假设进行比较。从理论上讲，对数似然的衍生物在截断设计中的小参数值不那么陡峭，这表明较大的计算量对于根发现和较大的标准误差。在社会和经济科学和模拟中的应用中，我们确实在确认截断时会发现中等增加的标准错误。
For a sample of Exponentially distributed durations we aim at point estimation and a confidence interval for its parameter. A duration is only observed if it has ended within a certain time interval, determined by a Uniform distribution. Hence, the data is a truncated empirical process that we can approximate by a Poisson process when only a small portion of the sample is observed, as is the case for our applications. We derive the likelihood from standard arguments for point processes, acknowledging the size of the latent sample as the second parameter, and derive the maximum likelihood estimator for both. Consistency and asymptotic normality of the estimator for the Exponential parameter are derived from standard results on M-estimation. We compare the design with a simple random sample assumption for the observed durations. Theoretically, the derivative of the log-likelihood is less steep in the truncation-design for small parameter values, indicating a larger computational effort for root finding and a larger standard error. In applications from the social and economic sciences and in simulations, we indeed, find a moderately increased standard error when acknowledging truncation.
