Topic
Natural exponential family
About: Natural exponential family is a research topic. Over the lifetime, 1973 publications have been published within this topic receiving 60189 citations. The topic is also known as: NEF.
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01 Jan 2017
TL;DR: In this paper, the generalized exponential distribution (PAL) was introduced as a new lifetime distribution and the maximum likelihood estimates and asymptotic variance-covariance matrix were obtained.
Abstract: In this paper, The PAL generalized exponential distribution is introduced as a new lifetime distribution. Some properties of the new distribution are studied. The maximum likelihood estimates and asymptotic variance-covariance matrix are obtained. Also, approximate Bayes estimates are computed using the Gibbs sampling procedure. Finally, an application to real data set is given.
01 Jan 2005
TL;DR: This paper proposes exponential type nonlinearities in order to blindly separate instantaneous mixtures of signals with mixed kurtosis signs to neutralize the effect of outliers while the higher order terms inherently present in the exponential function result in fast convergence especially for signals with bounded support.
Abstract: This paper proposes exponential type nonlinearities in order to blindly separate instantaneous mixtures of signals with mixed kurtosis signs. These nonlinear functions are applied only in a certain range around zero in order to ensure that the relative gradient algorithm remains locally stable. The proposed truncated nonlinearities neutralize the effect of outliers while the higher order terms inherently present in the exponential function result in fast convergence especially for signals with bounded support. By varying the truncation threshold, signals with both sub-Gaussian and super-Gaussian probability distributions can be separated. Furthermore, when the sources consist of signals with mixed kurtosis signs we propose to estimate the characteristic function online in order to classify the signals as sub-Gaussian or super-Gaussian and consequently choose an adequate value of the truncation threshold. Some computer simulations are presented to demonstrate the effectiveness of the proposed idea.
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TL;DR: An algorithm for the evaluation of the complex exponential function is proposed which is quasi-linear in time and linear in space and based on a modified binary splitting method for the hypergeometric series and a modified Karatsuba method for its fast evaluation.
Abstract: An algorithm for the evaluation of the complex exponential function is proposed which is quasi-linear in time and linear in space. This algorithm is based on a modified binary splitting method for the hypergeometric series and a modified Karatsuba method for the fast evaluation of the exponential function. The time complexity of this algorithm is equal to that of the ordinary algorithm for the evaluation of the exponential function based on the series expansion: O(M(n)log(n) 2 ).