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In reliability analysis, the log-normal distribution is often used to model times to repair a maintainable system. [95] In wireless communication, "the local-mean power expressed in logarithmic values, such as dB or neper, has a normal (i.e., Gaussian) distribution."
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 [ 2 ] [ 3 ] f ( x ) = 1 2 π σ 2 e − ( x − μ ) 2 2 σ 2 . {\displaystyle f(x)={\frac {1}{\sqrt {2\pi \sigma ^{2 ...
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]
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
The Gaussian functions are thus those functions whose logarithm is a concave quadratic function. ... a Gaussian function ... Gaussian distribution: ...
x erf x 1 − erf x; 0: 0: 1: 0.02: 0.022 564 575: 0.977 435 425: 0.04: 0.045 111 106: 0.954 888 894: 0.06: 0.067 621 594: 0.932 378 406: 0.08: 0.090 078 126: 0.909 ...
The complex Gaussian distribution can be described with 3 parameters: [5] ... are unknown, a suitable log likelihood function for a single observation vector ...
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 ...