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abstract
abstract

... in the case of very simple sequences, such as an = n 2 or an = n1/3 where the gap distribution is conjectured to be exponential. I will survey a number of sequences where the gap distribution (and related statistics) can be computed by translating the problem to rather subtle equidistribution proble ...
ph24010 lecture2
ph24010 lecture2

... Numbers generated in sequence Same sequence every time worksheet run SEED variable sets start point in sequence Integer from 1 to 2147483647 Change seed with – Tools|Worksheet Options|Built-in variables – Seed(x) ...
Glossary Term Definition equiangular triangle A triangle with three
Glossary Term Definition equiangular triangle A triangle with three

... Two ratios that have the same value. Example: 5:4 = 10:8 Find the value of an expression. A whole number that is divisible by 2. A function whose graph is a symmetric with respect to the yaxis. A specific outcome or type of outcome. Any values of a variable that result in a denominator of 0 must be ...
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Exponential family

""Natural parameter"" links here. For the usage of this term in differential geometry, see differential geometry of curves.In probability and statistics, an exponential family is a set of probability distributions of a certain form, specified below. This special form is chosen for mathematical convenience, on account of some useful algebraic properties, as well as for generality, as exponential families are in a sense very natural sets of distributions to consider. The concept of exponential families is credited to E. J. G. Pitman, G. Darmois, and B. O. Koopman in 1935–36. The term exponential class is sometimes used in place of ""exponential family"".The exponential families include many of the most common distributions, including the normal, exponential, gamma, chi-squared, beta, Dirichlet, Bernoulli, categorical, Poisson, Wishart, Inverse Wishart and many others. A number of common distributions are exponential families only when certain parameters are considered fixed and known, e.g. binomial (with fixed number of trials), multinomial (with fixed number of trials), and negative binomial (with fixed number of failures). Examples of common distributions that are not exponential families are Student's t, most mixture distributions, and even the family of uniform distributions with unknown bounds. See the section below on examples for more discussion.Consideration of exponential-family distributions provides a general framework for selecting a possible alternative parameterisation of the distribution, in terms of natural parameters, and for defining useful sample statistics, called the natural sufficient statistics of the family. For more information, see below.
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