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In reliability analysis, the log-normal distribution is often used to model times to repair a maintainable system. [82] In wireless communication, "the local-mean power expressed in logarithmic values, such as dB or neper, has a normal (i.e., Gaussian) distribution."
This leads directly to the probability mass function of a Log(p)-distributed random variable: = for k ≥ 1, and where 0 < p < 1. Because of the identity above, the distribution is properly normalized. The cumulative distribution function is
In probability theory and statistics, a normal distribution or Gaussian distribution is a type of continuous probability distribution for a real-valued random variable. The general form of its probability density function is f ( x ) = 1 2 π σ 2 e − ( x − μ ) 2 2 σ 2 . {\displaystyle f(x)={\frac {1}{\sqrt {2\pi \sigma ^{2}}}}e^{-{\frac ...
It is much easier than to convert logs to their natural values, to add them and again to convert them to logs. Moreover, Gaussian logs yield greater accuracy of result than the traditional computing method and help 5-digit log values to be sufficiently accurate for this method. […] The use of "Gaussians" by Bruce is original in the field of ...
If () is a general scalar-valued function of a normal vector, its probability density function, cumulative distribution function, and inverse cumulative distribution function can be computed with the numerical method of ray-tracing (Matlab code). [17]
The theorem was proved independently by Jacques Hadamard [1] and Charles Jean de la Vallée Poussin [2] in 1896 using ideas introduced by Bernhard Riemann (in particular, the Riemann zeta function). The first such distribution found is π(N) ~ N / log(N) , where π(N) is the prime-counting function (the number of primes less than or ...
The Gaussian functions are thus those functions whose logarithm is a concave quadratic function. ... a Gaussian function ... Gaussian distribution: ...
The log-likelihood is also particularly useful for exponential families of distributions, which include many of the common parametric probability distributions. The probability distribution function (and thus likelihood function) for exponential families contain products of factors involving exponentiation. The logarithm of such a function is a ...