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Other examples of unimodal distributions include Cauchy distribution, Student's t-distribution, chi-squared distribution and exponential distribution. Among discrete distributions, the binomial distribution and Poisson distribution can be seen as unimodal, though for some parameters they can have two adjacent values with the same probability.
The Boltzmann distribution, a discrete distribution important in statistical physics which describes the probabilities of the various discrete energy levels of a system in thermal equilibrium. It has a continuous analogue. Special cases include: The Gibbs distribution; The Maxwell–Boltzmann distribution; The Borel distribution
The shape of a distribution will fall somewhere in a continuum where a flat distribution might be considered central and where types of departure from this include: mounded (or unimodal), U-shaped, J-shaped, reverse-J shaped and multi-modal. [1] A bimodal distribution would have two high points rather than one. The shape of a distribution is ...
The Weibull distribution (usually sufficient in reliability engineering) is a special case of the three parameter exponentiated Weibull distribution where the additional exponent equals 1. The exponentiated Weibull distribution accommodates unimodal, bathtub shaped [33] and monotone failure rates.
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The theorem refines Chebyshev's inequality by including the factor of 4/9, made possible by the condition that the distribution be unimodal. It is common, in the construction of control charts and other statistical heuristics, to set λ = 3 , corresponding to an upper probability bound of 4/81= 0.04938..., and to construct 3-sigma limits to ...
If a symmetric distribution is unimodal, the mode coincides with the median and mean. All odd central moments of a symmetric distribution equal zero (if they exist), because in the calculation of such moments the negative terms arising from negative deviations from x 0 {\displaystyle x_{0}} exactly balance the positive terms arising from equal ...
A bivariate, multimodal distribution Figure 4. A non-example: a unimodal distribution, that would become multimodal if conditioned on either x or y. In statistics, a multimodal distribution is a probability distribution with more than one mode (i.e., more than one local peak of the distribution).