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Given a probability distribution (density) function with random variable and
, a mode of is a real number such that:
-
,
-
for all
.
The mode of is the set of all modes of (It is also customary to say denote the mode of to be elements within the mode of ). If the mode contains one element, then we say that is unimodal. If it has two elements, then is called bimodal. When has more than two modes, it is called multimodal.
- if
is the sample space for the random variable , then the mode of the distribution function is 4.
- if
is the sample space for , then the modes of are 6 and 11 and is bimodal.
- For a binomial distribution with mean
and variance , the mode is
- For a Poisson distribution with integral sample space and mean
, if is non-integral, then the mode is the largest integer less than or equal to ; if is an integer, then both and are modes.
- For a normal distribution with mean
and standard deviation , the mode is .
- For a gamma distribution with the shape parameter
, location parameter , and scale parameter , the mode is if .
- Both the Pareto and the exponential distributions have mode = 0.
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"mode" is owned by CWoo.
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Cross-references: exponential distributions, location parameter, parameter, gamma distribution, standard deviation, normal distribution, integer, integral, Poisson distribution, variance, mean, binomial distribution, distribution function, contains, real number, random variable, function, density, distribution
There are 18 references to this entry.
This is version 1 of mode, born on 2004-06-04.
Object id is 5889, canonical name is Mode.
Accessed 5004 times total.
Classification:
| AMS MSC: | 60A99 (Probability theory and stochastic processes :: Foundations of probability theory :: Miscellaneous) |
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Pending Errata and Addenda
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