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 paper, the minimum variance unbiased estimators for the functions of scale and truncation parameters as well as the reliability function of the truncated exponential family distribution were derived, and uniformly most powerful unbiased tests of hypotheses were formulated.
Abstract: Blackwell-Rao-Lehmann-Scheffe' theory is used to derive the minimum variance unbiased estimators for the functions of scale and truncation parameters as well as the reliability function of the truncated exponential family distribution. Uniformly most powerful unbiased tests of hypotheses are formulated. Finally, a particular model of this family, viz., the truncated exponential model is discussed.
11 citations
Journal Article•
TL;DR: In this paper, the authors proposed new classes of weighted distributions by incorporating exponential distribution in Azzalini's method, resulting in weighted models generated by exponential distribution are: the weighted gamma-exponential model and the weighted generalized exponential-exp exponential model.
Abstract: In this paper, we propose new classes of weighted distributions by incorporating exponential distribution in Azzalini’s method. Resulting weighted models generated by exponential distribution are: the weighted gamma-exponential model and the weighted generalized exponential-exponential model. The moment properties of the proposed distributions are studied.Maximum likelihood estimators (MLEs) of the unknown parameterscannot be obtained in explicit forms and they have to be obtained by solving some numerical methods. Two data sets have been analyzed for illustrative purposes, which show that the proposed models can be used quite effectively in analyzing real data.
11 citations
TL;DR: The exact distributions of R=X+Y, P=XY and W=X/(X-Y) and the corresponding moment properties when X and Y follow Lawrence and Lewis's bivariate exponential distribution are derived.
11 citations
TL;DR: In this paper, a generalized mixture of gamma distributions in terms of the confluent hypergeometric function, as the waiting time distribution, was obtained for renewal theory and various applications of the model to reliability.
Abstract: In the present paper, we study the properties of finite mixture of exponential model in the context of renewal theory. We obtain a generalized mixture of gamma distributions in terms of the confluent hypergeometric function, as the waiting time distribution. We present various applications of the model to reliability.
11 citations
TL;DR: In this article, a maximin argument based on information theory is used to derive a new approach to density approximation from summary statistics which is not restricted by the assumption of validity of an underlying exponential family.
Abstract: In the case of exponential families, it is a straightforward matter to approximate a density function by use of summary statistics; however, an appropriate approach to such approximation is far less clear when an exponential family is not assumed. In this paper, a maximin argument based on information theory is used to derive a new approach to density approximation from summary statistics which is not restricted by the assumption of validity of an underlying exponential family. Information-theoretic criteria are developed to assess loss of predictive power of summary statistics under such minimal knowledge. Under these criteria, optimal density approximations in the maximin sense are obtained and shown to be related to exponential families. Conditions for existence of optimal density approximations are developed. Applications of the proposed approach are illustrated, and methods for estimation of densities are provided in the case of simple random sampling. Large-sample theory for estimates is developed.
11 citations