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.

Evaluation of exponential product kernel for quadratic time-frequency distributions applied to ultrasonic signals

Abstract: The display of energy of ultrasonic backscattered echoes simultaneously on a joint time-frequency (t-f) plane reveals critical information pertaining to time of arrival and frequency of echoes. The quadratic t-f distributions play important role in displaying the energy of the signal on a joint t-f plane. The t-f energy distribution of the signal is dependent on a weighting function, kernel, of generalized quadratic t-f distribution. This kernel, a function of product of time lag and frequency lag variables, controls the t-f concentration of the signal and the suppression of artifacts generated by the quadratic t-f distribution. A generalized exponential product (GEP) kernel function is explored in this paper, Exponential (i.e., Choi-Williams) distribution is a special case of this generalized exponential distribution. A whole family of Quadratic exponential distributions can be generated by varying the parameters of the generalized exponential product kernel. We evaluate these parameters on the basis of optimum concentration of the ultrasonic backscattered echoes, resolution of defect echoes, suppression of the cross-terms artifacts, and performance in the presence of noise. These parameters are evaluated by reducing the cross-terms and keeping auto-terms on the ambiguity plane close to the ideal. It is shown that by controlling the parameters of the generalized exponential product kernel we can achieve better performance in the form of time-frequency concentration, and resolution for multiple echoes as compared to exponential distribution. The application of GEP kernel to ultrasonic experimental data, with properly chosen parameters, not only discern the defect echo embedded in grain echoes but diminish the cross-terms generated by the bilinear structure of the t-f distribution.

The Generalized Exponential Extended Exponentiated Family of Distributions: Theory, Properties, and Applications

Abstract: Here, we propose a new generalized exponential extended exponentiated (NGE3) family of distributions. Some statistical properties of proposed family are gained. The most extreme probability method, maximum likelihood (ML), is utilized for parameter estimation. We explore an exceptional model called NGE3-Exponential (NGE3E). NGE3E is estimated with ML, and the performance of estimators is demonstrated by utilizing a simulation. Moreover, two applications are given to show the significance and adaptability of the proposed model in comparison to some generalized models (GMs).

A new Exponential Naive Bayes Classifier with Fuzzy Parameters

Abstract: It is difficult to classify data which follow the exponential distribution. For this reason, in this paper we propose a new classifier based on that distribution, named Exponential Naive Bayes network with Fuzzy Parameters (ENB-FP), where those parameters are given by fuzzy numbers. In order to know performance of ENB-FP, tests using data from six different statistical distributions were performed. ENB-FP have achieved an agreement degree of “almost perfect”, according to Kappa Coeficient, in five of them. A brief comparison with another fuzzy classifier recently proposed was performed as well. According to the Kappa Coefficient, the ENB-FP outperformed that classifier when using data from exponential distribution and provided a competitive approach for the other five distributions.

Simulation uses of the exponential distribution

Abstract: : This paper indicates how exponential random variables can be effeciently used in a variety of simulation problems. One of the problems is the simulation of order statistics from a normal population. The authors discuss the general problem of simulating order statistics and then consider the normal case. They start by showing how the Von-Neumann rejection approach via the exponential can be modified to become an efficient algorithm for generating a normal and then present a method for generating normal order statistics. They show how to use the exponential to efficiently simulate random permutations with weights. They consider the problem of simulating a 2-dimensional Poissin process both for a homogeneous and nonhomogeneous Poisson process. (Author)

Binomial Mixtures of some Standard Distributions

Abstract: In this paper, binomial mixture of some standard distributions such as binomial, Poisson, normal, log-normal, chi-square, F, t, beta, gamma, exponential, rectangular, and Erlang are defined and their different characteristics are provided.