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# Topic: Degenerate distribution

###### In the News (Wed 24 Apr 19)

 Probability distribution - Wikipedia, the free encyclopedia A probability distribution is a special case of the more general notion of a probability measure, which is a function that assigns probabilities satisfying the Kolmogorov axioms to the measurable sets of a measurable space. The rectangular distribution is a uniform distribution on [-1/2,1/2]. The triangular distribution on [a, b], a special case of which is the distribution of the sum of two uniformly distributed random variables (the convolution of two uniform distributions). en.wikipedia.org /wiki/Probability_distribution   (1336 words)

 Degenerate distribution -- Facts, Info, and Encyclopedia article   (Site not responding. Last check: 2007-10-20) In (A science (or group of related sciences) dealing with the logic of quantity and shape and arrangement) mathematics, a degenerate distribution is the (Click link for more info and facts about probability distribution) probability distribution of a discrete random variable which always has the same value. As a discrete distribution, the degenerate distribution does not have a (The amount per unit size) density. The meaning given to it by Schwartz is not the meaning of the word distribution in (The branch of applied mathematics that deals with probabilities) probability theory. www.absoluteastronomy.com /encyclopedia/d/de/degenerate_distribution.htm   (290 words)

 wikien.info: Main_Page   (Site not responding. Last check: 2007-10-20) In statistics, when a p-value is used as a test statistic for a simple null hypothesis, and the distribution of the test statistic is continuous, then the test statistic is uniformly distributed between 0 and 1 if the null hypothesis is true. Although the uniform distribution is not commonly found in nature, it is particularly useful for sampling from arbitrary distributions. The normal distribution is an important example where the inverse transform method is not efficient. www.hostingciamca.com /index.php?title=Uniform_distribution   (651 words)

 NTU Info Centre: Probability distribution   (Site not responding. Last check: 2007-10-20) The Ewens sampling formula is a probability distribution on the set of all partitions of an integer n, arising in population genetics. The F-distribution, which is the distribution of the ratio of two normally distributed random variables, used in the analysis of variance. The Levy stable distribution is often used to characterize financial data and critical behavior. www.nowtryus.com /article:Probability_distribution   (1132 words)

 6.5 -The DISTRIBUTE Directive   (Site not responding. Last check: 2007-10-20) The distribution of array elements is shown in Figure 22, along with an indication of which array elements may rest on which abstract processor (in array notation). Block distributions such as this are good for problems which have a regular domain decomposition, such as fluid dynamics and Quantum Chromodynamics. There is another type of distribution known as the cyclic distribution. www.epcc.ed.ac.uk /computing/training/document_archive/hpf-course/hpf-course.book_77.html   (580 words)

 [No title] For angles, the uniform distribution is attractive as, among all distributions on a bounded range, the uniform distribution has maximum entropy, where entropy is defined to be Shannon's information, the expected value of the log of the density. Whatever the distribution of the perimeter, we will get the same probability of an obtuse angle if, given the perimeter, the event "triangle is obtuse" is independent of the distribution of the perimeter. However, it is easier to condition on A. The conditional distribution of B and C given A is normal and the 4 components are all independent. www.math.niu.edu /~rusin/known-math/97/random.triangle   (2868 words)

 Probability Abstract Service   (Site not responding. Last check: 2007-10-20) An alternative approach to embeddability of a non-infinitely divisible $\mu$ is by considering non-classical convolution measure semigroups; for example embedding $\mu$ in a Boolean convolution measure semigroup and retaining the multinomial character of the moments.embedding $\mu$ in a Boolean convolution measure semigroup and retaining the multinomial character of the moments. As t->infty, it is perhaps evident that the distribution of Z(t) converges weakly to that of the sum of the integrals of v along the paths of two independent Brownian motions, starting at x and y and running forever.Here we prove a stronger result, namely convergence of the corresponding moment generating functions and of moments. These limit distributions have been seen previously in analysis of the Poisson-Dirichlet distribution and elsewhere; they are expressed in terms of Dickman's function, and their properties are discussed in some detail. www.economia.unimi.it /PAS/Letters/letter_80.shtml   (13044 words)

 The distribution of #tex2html_wrap_inline4760#   (Site not responding. Last check: 2007-10-20) We show that the covariance of the counters for overlapping M- tuples causes this asymptotic distribution to degenerate to a lower dimension. In order to construct a useful test statistic for the degenerate multivariate normal distribution we compute a onedimensional fingerprint which is related to the distance between theoretical and empirical distribution function of the counter vector. The technique used to derive the asymptotic distribution of the test statistic can be extended to a large class of statistical problems. random.mat.sbg.ac.at /~ste/dipl/node34.html   (279 words)

 Nat' Academies Press, Statistical Models and Analysis in Auditing: A Study of Statistical Models and Methods for ... If F. the degenerate distribution, is chosen in the first stage, the observed value of the outcome is zero; otherwise the observed value is drawn from the other distribution. The distribution of Eros can, therefore, be Rewed as a mixture of two distinguishable distributions, one win a discrete probability mass at zero and He over a continuous distribution of non-zero positive and/or negative error amounts. The distribution is a mixture of a mass point at O and a nontrivial continuous distnbution of decay score. www.nap.edu /books/POD283/html/1.html   (2794 words)

 Queueing theory - Open Encyclopedia   (Site not responding. Last check: 2007-10-20) M stands for "Markovian", implying exponential distribution for service times or inter-arrival times. D stands for "degenerate" distribution, or "deterministic" service times. Ek stands for an Erlang distribution with k as the shape parameter. open-encyclopedia.com /Queueing_theory   (254 words)

 Large deviations and quasi-stationarity for density-dependent birth-death processes   (Site not responding. Last check: 2007-10-20) , so the probability of sets not containing the degenerate point will tend to 0; large deviations is concerned with obtaining the exponential decay rate of these probabilities. no longer exists), the same elementary computations are still applicable to the quasi-stationary distribution, and we show that the quasi-stationary distributions obey the same large deviations principle as in the recurrent case. In addition, we address some questions related to the estimated time to absorption and obtain a large deviations principle for the invariant distribution in higher dimensions by studying a quasi-potential. www.austms.org.au /Publ/Jamsb/V40P2/abs/1571/1571.html   (182 words)

 Channels of Distribution Distribution opportunities: Distribution provides a number of opportunities for the marketer that may normally be associated with other elements of the marketing mix. In view of the need for markets to be balanced, the same distribution strategy is unlikely to be successful for each firm. In general, for convenience products, intense distribution is desirable, but only brands that have a certain amount of power—e.g., an established brand name—can hope to gain national intense distribution. www.consumerpsychologist.com /distribution.htm   (8748 words)

 [No title] Also, in the “standard” case, the OLS estimators have to be multiplied by some increasing function of T to obtain a non-degenerate limiting distribution. The F statistic must be divided by T to obtain a non-divergent distribution (but one which is not F even then). A DW statistic which is “significant” on usual criteria suggests that the regression model is mispecified, perhaps because it is a spurious regression. homepages.strath.ac.uk /~hbs96127/Rennes3a.doc   (853 words)

 Approaches to Performance Evaluation: Analytical Queueing Models The time taken by a station to process the customer can also be modeled with a probability distribution function. Exponential Distribution, with parameters depending on the length of the queue, model the queues. The service time is exponentially distributed with the same mean for all classes of customer. www.doc.ic.ac.uk /~nd/surprise_97/journal/vol2/wll1/queues.html   (842 words)

 Kendall's Notation for Classification of Queue Types   (Site not responding. Last check: 2007-10-20) If E is included, D must be, to ensure that one is not confused between the two, but an infinity symbol is allowed for D. D / M / n - This would describe a queue with a degenerate distribution for the interarrival times of customers, an exponential distribution for service times of customers, and n servers. M / M / m / K / N - This would describe a queueing system with an exponential distribution for the interarrival times of customers and the service times of customers, m servers, a maximum of K customers in the queueing system at once, and N potential customers in the calling population. www.new-destiny.co.uk /andrew/past_work/queueing_theory/Andy/kendall.html   (255 words)

 Why study white dwarfs?   (Site not responding. Last check: 2007-10-20) The study of degenerate stars is important because it can in principle be used to reconstruct the entire history of star formation in the Galactic disc. To do this both the luminosity function and the mass distribution of degenerate stars need to be determined precisely, and we need to understand the relationship between the initial mass and final mass of a star. The width of this distribution puts constraints on the theories of stellar formation in the Solar neighbourhood (Fusi-Pecci and Renzini 1976), so accurate determinations are vital. www.star.ucl.ac.uk /~cmj/thesis/node16.html   (196 words)

 Mutation rates in mammalian genomes -- Kumar and Subramanian 99 (2): 803 -- Proceedings of the National Academy of ... The expected amount of variance in the distribution of multigene distances for a given pair of species is the sum of the estimation This distribution of neutral distance is equivalent to The normal distribution curve is drawn by using the observed mean and the expected variance under the null hypothesis of uniform neutral mutation rate among genes. www.pnas.org /cgi/content/full/99/2/803   (4036 words)

 Wilmott Forums - Beta distribution If we have the beta function b(A,B,p,q) and n (which presumably is given by one of p or q) must lie between 0 and 1, then am I correct in thinking that the upper and lower bounds A and B, must be set to 0 and 1 respectively? 1.25*x^0.25, from x = 0 to 1, is a degenerate Beta distribution with A = 1.25 and B = 0. It is a degenerate one, with B = 0 and A = n, but none of the Beta distribution results will hold because you will find yourself dividing by zero. www.wilmott.com /messageview.cfm?catid=8&threadid=24314   (437 words)

 Prior distributions and Bayes factors The interaction terms are equal to zero under the independence hypothesis I. This degenerate distribution on the interaction terms can be viewed as the limit of the above N(0, denotes the degenerate prior on the interaction terms under the independence hypothesis. www-math.bgsu.edu /~albert/latexhtml/two_way/node6.html   (318 words)

 [No title]   (Site not responding. Last check: 2007-10-20) The probability distribution for an observation from the population of individuals in q + 1 mutually and exhaustive categories is known as the multinomial distribution. Then the multivariate vector Y = ( EMBED Equation.3 ) is said to have a multinomial distribution and we write Y = ( EMBED Equation.3 ) ~ Multinomial (n,  EMBED Equation.3 ) and P[Y = ( EMBED Equation.3 )] =  EMBED Equation.3  EMBED Equation.3 . Control region for future observations The goal is to use data , collected when a process is stable, to set a control region for a future observation X or future observations. web.syr.edu /~pinchen/Lecture7.doc   (1583 words)

 Mathematical Statistics with Mathematica - Index as limit distribution of a Binomial 93, 281, 299 asymptotic distribution of MLE of (m, s2) 372-374 as limit distribution of Binomial 95, 280, 300 www.mathstatica.com /book/bookindex.html   (313 words)

 Large deviations and quasi-stationarity for density-dependent birth-death processes   (Site not responding. Last check: 2007-10-20) be the unique stationary distribution (on [0, 1]) of X Typically, these distributions converge weakly to a degenerate distribution as N \rightarrow \infty, so the probability of sets not containing the degenerate point will tend to 0; large deviations is concerned with obtaining the exponential decay rate of these probabilities. In the one-dimensional case, a large deviations principle for the stationary distribution \Pi anziamj.austms.org.au /V40/part2/Chan.html   (216 words)

 Table of contents for Library of Congress control number 2003041157   (Site not responding. Last check: 2007-10-20) Table of contents for Library of Congress control number 2003041157 Table of contents for A primer on statistical distributions / N. Balakrishnan and V.B. Nevzorov. Bibliographic record and links to related information available from the Library of Congress catalog www.loc.gov /catdir/toc/wiley031/2003041157.html   (55 words)

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