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Integral geometry sprang from the principle that the mathematically natural probability models are those that are invariant under certain transformation groups. This topic emphasises systematic development of formulas for calculating expected values associated with the geometric objects derived from random points, and can in part be viewed as a ...
The geometric distribution is the only memoryless discrete probability distribution. [4] It is the discrete version of the same property found in the exponential distribution . [ 1 ] : 228 The property asserts that the number of previously failed trials does not affect the number of future trials needed for a success.
In probability theory and statistics, the hypergeometric distribution is a discrete probability distribution that describes the probability of successes (random draws for which the object drawn has a specified feature) in draws, without replacement, from a finite population of size that contains exactly objects with that feature, wherein each draw is either a success or a failure.
Geometric Brownian motion is used to model stock prices in the Black–Scholes model and is the most widely used model of stock price behavior. [4] Some of the arguments for using GBM to model stock prices are: The expected returns of GBM are independent of the value of the process (stock price), which agrees with what we would expect in ...
In graph theory, a random geometric graph (RGG) is the mathematically simplest spatial network, namely an undirected graph constructed by randomly placing N nodes in some metric space (according to a specified probability distribution) and connecting two nodes by a link if and only if their distance is in a given range, e.g. smaller than a certain neighborhood radius, r.
In the case when the 3 parameters , and are positive integers, the Beta negative binomial can also be motivated by an urn model - or more specifically a basic Pólya urn model. Consider an urn initially containing α {\displaystyle \alpha } red balls (the stopping color) and β {\displaystyle \beta } blue balls.
Geometric discrepancy theory; The theorem of van Aardenne-Ehrenfest; Arithmetic progressions (Roth, Sarkozy, Beck, Matousek & Spencer) Beck–Fiala theorem [2] Six Standard Deviations Suffice (Spencer) [3]
In the early 1960s a stochastic geometry model [5] was developed to study wireless networks. This model is considered to be pioneering and the origin of continuum percolation. [6] Network models based on geometric probability were later proposed and used in the late 1970s [7] and continued throughout the 1980s [8] [9] for examining packet radio ...
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