scispace - formally typeset
Search or ask a question
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.


Papers
More filters
Journal ArticleDOI
TL;DR: In this article, Gupta and Kundu developed the non-informative priors for the stress-strength reliability from one parameter gener-alized exponential distributions and showed that the proposed reference prior matches the target coverage probabilities in a frequentist sense through a simulation study and a provided example.
Abstract: This paper develops the noninformative priors for the stress-strength reliability from one parameter gener-alized exponential distributions. When this reliability is a parameter of interest, we develop the first, secondorder matching priors, reference priors in its order of importance in parameters and Jeffreys’ prior. We revealthat these probability matching priors are not the alternative coverage probability matching prior or a highestposterior density matching prior, a cumulative distribution function matching prior. In addition, we reveal thatthe one-at-a-time reference prior and Jeffreys’ prior are actually a second order matching prior. We show thatthe proposed reference prior matches the target coverage probabilities in a frequentist sense through a simulationstudy and a provided example.Keywords: Generalized exponential model, matching prior, reference prior, stress-strength relia-bility. 1. Introduction The one parameter generalized exponential distribution was introduced by Gupta and Kundu (1999)as an alternative to the gamma or Weibull distributions for analyzing lifetime data (Gupta and Kundu,2001). An advantage of employing the generalized exponential distribution is that the distributionfunction can be obtained in a closed form. Kundu and Gupta (2007) showed that the generalizedexponentialdistributionisquiteflexibleandcanbeusedveryeffectivelyinanalyzingpositivelifetimedata in place of the gamma or Weibull models. Raqab and Madi (2005) studied the Bayeian inferencefor the parameters and reliability function.Consider

1 citations

16 Jul 2009
TL;DR: The class of almost periodic functions is the uniform closure of the class of exponential polynomials as discussed by the authors, which is a special class of functions that settle the exact number of their zeros in an arbitrary rectangle of the critical strip.
Abstract: We present a result on entire exponential type almost-periodic functions that settles the exact number of their zeros in an arbitrary rectangle of the critical strip where are situated all the zeros with an error of ±2. Introduction •We say that an exponential polynomial is a function of the form Pn(z) = a1e iλ1z + · · · + ane n, with λi ∈ R, ai ∈ C, ∀i : 1 ≤ i ≤ n. We can assume, without loss of generality, aj 6= 0 ∀j : 1 ≤ j ≤ n and λi 6= λj ∀i 6= j. Moreover, we suppose λ1 < λ2 < · · · < λn. •Naturally, Pn(z) is entire of order 1 for all n ≥ 2. •Moreover, |Pn(z)| ≤ n |â| e ||, where λ̂ such that |λ̂| = max{|λk|, k = 1 . . . n} and â such that |â| = max{|ak|, k = 1 . . . n}, therefore Pn(z) is exponential type σ = |λ̂|. •We consider that an analytic function f (z) in a strip α ≤ y ≤ β (y = Im z) is said to be almost periodic function in this strip if for any 2 there exists a length l = l(2) such that every interval a < t < a + l of length l on the real axis contains at least one translation number τ = τ (2) associated with 2, i.e., a number τ satisfying the inequality |f (z + τ )− f (z)| < 2 for α ≤ y ≤ β. •The class of almost periodic functions is the uniform closure of the class of exponential polynomials. Functions of class A An entire function f with zeros {ak} satisfying

1 citations

Journal ArticleDOI
31 Dec 2010
TL;DR: In this paper, a new exponential family of distributions is derived for modeling skewed semicircular data, and the Kolmogorov-Smirnov test is adopted for a goodness of t test of the l-axial exponential family.
Abstract: For modeling(skewed) semicircular data, we derive a new exponential family of distributions. We extend it to the l-axial exponential family of distributions by a projection for modeling any arc of arbitrary length. It is straightforward to generate samples from the l-axial exponential family of distributions. Asymptotic result reveals that the linear exponential family of distributions can be used to approximate the l-axial exponential family of distributions. Some trigonometric moments are also derived in closed forms. The maximum likelihood estimation is adopted to estimate model parameters. Some hypotheses tests and confidence intervals are also developed. The Kolmogorov-Smirnov test is adopted for a goodness of t test of the l-axial exponential family of distributions. Samples of orientations are used to demonstrate the proposed model.

1 citations


Network Information
Related Topics (5)
Asymptotic distribution
16.7K papers, 564.9K citations
82% related
Random variable
29.1K papers, 674.6K citations
79% related
Estimator
97.3K papers, 2.6M citations
76% related
Statistical inference
11.2K papers, 604.4K citations
76% related
Markov chain
51.9K papers, 1.3M citations
76% related
Performance
Metrics
No. of papers in the topic in previous years
YearPapers
202319
202262
202114
202010
20196
201823