Topic
Uniform distribution (continuous)
About: Uniform distribution (continuous) is a research topic. Over the lifetime, 2946 publications have been published within this topic receiving 48300 citations.
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TL;DR: The dip test as mentioned in this paper measures multimodality in a sample by the maximum difference, over all sample points, between the empirical distribution function, and the unimodal distribution function that minimizes that maximum difference.
Abstract: The dip test measures multimodality in a sample by the maximum difference, over all sample points, between the empirical distribution function, and the unimodal distribution function that minimizes that maximum difference. The uniform distribution is the asymptotically least favorable unimodal distribution, and the distribution of the test statistic is determined asymptotically and empirically when sampling from the uniform.
1,800 citations
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07 Sep 2000
TL;DR: In this paper, a Markov chain is constructed by alternating uniform sampling in the vertical direction with uniform sampling from the horizontal ''slice'' defined by the current vertical position, or more generally with some update that leaves the uniform distribution over this slice invariant Variations on such slice sampling methods are easily implemented for univariate distributions, and can be used to sample from a multivariate distribution by updating each variable in turn.
Abstract: Markov chain sampling methods that automatically adapt to characteristics of the distribution being sampled can be constructed by exploiting the principle that one can sample from a distribution by sampling uniformly from the region under the plot of its density function A Markov chain that converges to this uniform distribution can be constructed by alternating uniform sampling in the vertical direction with uniform sampling from the horizontal `slice' defined by the current vertical position, or more generally, with some update that leaves the uniform distribution over this slice invariant Variations on such `slice sampling' methods are easily implemented for univariate distributions, and can be used to sample from a multivariate distribution by updating each variable in turn This approach is often easier to implement than Gibbs sampling, and more efficient than simple Metropolis updates, due to the ability of slice sampling to adaptively choose the magnitude of changes made It is therefore attractive for routine and automated use Slice sampling methods that update all variables simultaneously are also possible These methods can adaptively choose the magnitudes of changes made to each variable, based on the local properties of the density function More ambitiously, such methods could potentially allow the sampling to adapt to dependencies between variables by constructing local quadratic approximations Another approach is to improve sampling efficiency by suppressing random walks This can be done using `overrelaxed' versions of univariate slice sampling procedures, or by using `reflective' multivariate slice sampling methods, which bounce off the edges of the slice
1,285 citations
TL;DR: The class of combinatorial problems involving the random generation from a uniform distribution is considered in this article, where it is shown that almost uniform generation and randomized approximate counting are inter-reducible, and hence, of similar complexity.
899 citations
TL;DR: In this article, it is shown that a worthwhile criterion can be based on desired statistical properties of the plot, rather than on comparison of plotting positions with estimates of probability for individual sample values.
619 citations