[Abstract]
We discussed the simulator and test statistic of continuous Bernoulli distribution which is important to test the pervasive error of variational autoencoders in deep learning. We provided the sufficient statistic, the point estimator, the confidence interval, test statistic, goodness of fit, and one-way test for continuous Bernoulli distribution. Besides, continuous binomial distribution can be derived, so the the confidence interval and the test can be worked under two continuous Bernoulli populations. Continuous trinomial distribution can also be find. Please download the computer software of this book from
https://github.com/meiyulee/continuous_Bernoulli