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Mode (statistics) In statistics, the mode is the value that appears most often in a set of data values. [1] If X is a discrete random variable, the mode is the value x at which the probability mass function takes its maximum value (i.e., x=argmaxxi P (X = xi) ). In other words, it is the value that is most likely to be sampled.
Log-normal distribution. In probability theory, a log-normal (or lognormal) distribution is a continuous probability distribution of a random variable whose logarithm is normally distributed. Thus, if the random variable X is log-normally distributed, then Y = ln (X) has a normal distribution.
Triangular. In probability theory and statistics, the triangular distribution is a continuous probability distribution with lower limit a, upper limit b, and mode c, where a < b and a ≤ c ≤ b .
Probability theory. 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. The parameter is the mean or expectation of the distribution (and also its median and mode ), while ...
Letting α = β, the expression for the mode simplifies to 1/2, showing that for α = β > 1 the mode (resp. anti-mode when α, β < 1), is at the center of the distribution: it is symmetric in those cases. See Shapes section in this article for a full list of mode cases, for arbitrary values of α and β. For several of these cases, the ...
Normal mode. A normal mode of a dynamical system is a pattern of motion in which all parts of the system move sinusoidally with the same frequency and with a fixed phase relation. The free motion described by the normal modes takes place at fixed frequencies. These fixed frequencies of the normal modes of a system are known as its natural ...
The gamma distribution is the maximum entropy probability distribution (both with respect to a uniform base measure and a base measure) for a random variable X for which E[X] = kθ = α/β is fixed and greater than zero, and E[ln X] = ψ(k) + ln θ = ψ(α) − ln β is fixed ( ψ is the digamma function ). [1]
Molecular vibration. A molecular vibration is a periodic motion of the atoms of a molecule relative to each other, such that the center of mass of the molecule remains unchanged. The typical vibrational frequencies range from less than 10 13 Hz to approximately 10 14 Hz, corresponding to wavenumbers of approximately 300 to 3000 cm −1 and ...