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The probability density function is (,) = ((+)) (),where I 0 (z) is the modified Bessel function of the first kind with order zero.. In the context of Rician fading, the distribution is often also rewritten using the Shape Parameter =, defined as the ratio of the power contributions by line-of-sight path to the remaining multipaths, and the Scale parameter = +, defined as the total power ...
In probability theory, Rice's formula counts the average number of times an ergodic stationary process X(t) per unit time crosses a fixed level u. [1] Adler and Taylor describe the result as "one of the most important results in the applications of smooth stochastic processes." [2] The formula is often used in engineering. [3]
Numerous approximation methods for the situation where u is large and f(t) is a Gaussian process have been proposed such as Rice's formula. [1] [2] First-excursion probabilities can be used to describe deflection to a critical point experienced by structures during "random loadings, such as earthquakes, strong gusts, hurricanes, etc." [3]
Rice was born in Shedds, Oregon (later renamed Shedd). He received a bachelor's degree in electrical engineering from Oregon State University and did graduate work at Caltech and at Columbia University. He worked for nearly forty years at Bell Labs. [3] At Bell Labs, Rice discovered the Rice distribution and Rice's formula.
The saddlepoint approximation method, initially proposed by Daniels (1954) [1] is a specific example of the mathematical saddlepoint technique applied to statistics, in particular to the distribution of the sum of independent random variables.
The nth forward difference of a function f(x) is given by [] = = () (+)where () is the binomial coefficient.. The Nørlund–Rice integral is given by = () =! () () where f is understood to be meromorphic, α is an integer, , and the contour of integration is understood to circle the poles located at the integers α, ..., n, but encircles neither integers 0, ..., nor any of the poles of f.
This rule is also called the oversmoothed rule [7] or the Rice rule, [8] so called because both authors worked at Rice University. The Rice rule is often reported with the factor of 2 outside the cube root, () /, and may be considered a different rule. The key difference from Scott's rule is that this rule does not assume the data is normally ...
Bayesian statistics (/ ˈ b eɪ z i ə n / BAY-zee-ən or / ˈ b eɪ ʒ ən / BAY-zhən) [1] is a theory in the field of statistics based on the Bayesian interpretation of probability, where probability expresses a degree of belief in an event.