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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TL;DR: In this article, a method to generate normal random variable using a generalized exponential distribution is proposed, which is compared with the other existing methods and it is observed that the proposed method is quite competitive with most of the existing methods in terms of the KS − distances and corresponding p-values.
Abstract: A convenient method to generate normal random variable using a generalized exponential distribution is proposed. The new method is compared with the other existing methods and it is observed that the proposed method is quite competitive with most of the existing methods in terms of the KS − distances and the corresponding p-values.
6 citations
6 citations
TL;DR: In this article, the authors show that the exponential function used in ESTAR models is ill-suited as a regime weighting function because of two undesirable properties: the first is that it can be well approximated by a quadratic function in the threshold variable whenever the transition function parameter γ, which governs the shape of the function, is small.
Abstract: Exponential smooth transition autoregressive (ESTAR) models have been widely used in the empirical international finance literature. We show that the exponential function used in ESTAR models is ill-suited as a regime weighting function because of two undesirable properties. The first is that it can be well approximated by a quadratic function in the threshold variable whenever the transition function parameter γ, which governs the shape of the function, is ‘small’. This leads to identification issues with respect to the transition function parameter and the slope vector in ESTAR models. The second is that the exponential function becomes an indicator function over the entire range of the threshold variable, except at the point where the threshold variable is equal to the location parameter µ. This results in a high propensity to spuriously overfit a small number of observations around µ, leading to an ‘outlier fitting effect’ of the exponential function. We show the effect of both of these problems on estimation of ESTAR models by means of an empirical replication of the well known study by Taylor et al. (2001), and an extensive simulation exercise, where we vary the magnitude of the threshold parameter as well as the sample size.
6 citations
6 citations
01 Oct 1983
TL;DR: In this article, the problem of selecting populations, from two-parameters exponential populations, which are better than a standard under an ordering prior is investigated, and the comparison of these procedures based on the expected number of bad populations in the selected subset is investigated.
Abstract: : The problem of selecting populations, from two-parameters exponential populations, which are better than a standard under an ordering prior is investigated. If the negative exponential distribution is the model for lifetime, then the problem is to select all those populations for which the guarantee lifetimes are larger than that of a standard. Comparisons of these procedures based on the expected number of bad populations in the selected subset is investigated. Tables of associated constants for the proposed procedures are given. (Author)
6 citations