Negation operation is important in intelligent information processing. Different existing arithmetic negation, an exponential negation presented this paper. The new can be seen as a kind of geometry negation. Some basic properties the proposed are investigated, and we find that fix point uniform probability distribution, which reaches maximum entropy. entropy increase operation, all distributio...

We consider the second-order asymptotic properties of‎  ‎the bootstrap of L_1 regression estimators by looking at‎ ‎the difference between the L_1 estimator and ‎its first-order approximation‎, ‎where the latter‎ ‎is the minimizer of a quadratic approximation to the‎ ‎L_1 objective function‎. ‎It is shown that the bootstrap ‎distribution of the normed difference does not converge‎ ‎(eit...

An efficient method for finding a better maximizer of computationally extensive probability distributions is proposed on the basis of a Bayesian optimization technique. A key idea of the proposed method is to use extreme values of acquisition functions by Gaussian processes for the next training phase, which should be located near a local maximum or a global maximum of the probability distribut...

The univariate Kummer-beta family of distributions has been proposed and studied recently by K. W. Ng and Samuel Kotz. This distribution is an univariate extension of the beta distribution. In this article, we derive the distributions of the product and the quotient of independent Kummer-beta variables.