We characterize the existence of the maximum likelihood estimator for discrete exponential families. Our criterion is simple to apply as we show in various settings, most notably for exponential models of random graphs. As an application, we point out the size of independent identically distributed samples for which the maximum likelihood estimator exists with high probability.

翻译：我们描述离散指数式家庭的最大可能性估计值的存在。 我们的标准很简单, 正如我们在各种设置中显示的那样, 最突出的是随机图形的指数模型。 作为应用, 我们指出独立分布相同的样本的大小, 其最大可能性估计值存在概率很高。