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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12 citations
TL;DR: In this article, the authors provide a probabilistic phase-type representation for the first order moment distributions and an alternative representation, with an analytically appealing form, for the latter.
Abstract: Moment distributions of phase-type and matrix-exponential distributions are shown to remain within their respective classes. We provide a probabilistic phase-type representation for the former case and an alternative representation, with an analytically appealing form, for the latter. First order moment distributions are of special interest in areas like demography and economics, and we calculate explicit formulas for the Lorenz curve and Gini index used in these disciplines.
12 citations
TL;DR: In this paper, another version of the generalized exponential geometric distribution different to that of Silva et al. (2010) is proposed, which is a three-parameter lifetime distribution with decreasing, increasing, and bathtub failure rate function.
Abstract: In this article, another version of the generalized exponential geometric distribution different to that of Silva et al. (2010) is proposed. This new three-parameter lifetime distribution with decreasing, increasing, and bathtub failure rate function is created by compounding the generalized exponential distribution of Gupta and Kundu (1999) with a geometric distribution. Some basic distributional properties, moment-generating function, rth moment, and Renyi entropy of the new distribution are studied. The model parameters are estimated by the maximum likelihood method and the asymptotic distribution of estimators is discussed. Finally, an application of the new distribution is illustrated using the two real data sets.
12 citations
TL;DR: In this paper, the Weibull distribution is proposed as a model for response times and the authors show that it performs better than the often-suggested power-law and logarithmic functions.
Abstract: The Weibull distribution is proposed as a model for response times. Theoretical support is offered by classical results for extreme-value distributions. Fits of the Weibull distribution to response time data in different contexts show that this distribution (and the exponential distribution on small time-scales) perform better than the often-suggested power-law and logarithmic function. This study suggests that the power-law can be viewed as an approximation, at neural level, for the aggregate strength of superposed memory traces that have different decay rates in distinct parts of the brain. As we predict, this view does not find support at the level of induced response processes. The distinction between underlying and induced processes might also be considered in other fields, such as engineering, biology and physics.
12 citations
TL;DR: In this paper, it was shown that if |α− s/r| ≤ 1/r2 and 3 ≤ r ≤ (x/log x)1/2, for some coprime integers s and r, then, uniformly for all f ∈ F, we have
Abstract: where e(t) stands for e2πit. New bounds for F (x, α) have been announced by the author in [Ba1] and the purpose of this paper is to supply proofs for these estimates. The problem of obtaining bounds for F (x, α) uniform in f ∈ F has been first considered by H. Daboussi. He showed [Da1] (see also [DD1] and [DD2]) that if |α− s/r| ≤ 1/r2 and 3 ≤ r ≤ (x/log x)1/2, for some coprime integers s and r, then, uniformly for all f ∈ F , we have
12 citations