scipy.stats.Normal.

mode#

Normal.mode(*, method=None)[source]#

Mode (most likely value)

Informally, the mode is a value that a random variable has the highest probability (density) of assuming. That is, the mode is the element of the support \(\chi\) that maximizes the probability density function \(f(x)\):

\[\text{mode} = \arg\max_{x \in \chi} f(x)\]
Parameters:
method{None, ‘formula’, ‘optimization’}

The strategy used to evaluate the mode. By default (None), the infrastructure chooses between the following options, listed in order of precedence.

  • 'formula': use a formula for the median

  • 'optimization': numerically maximize the PDF

Not all method options are available for all distributions. If the selected method is not available, a NotImplementedError will be raised.

Returns:
outarray

The mode

See also

mean
median
pdf

Notes

For some distributions

  1. the mode is not unique (e.g. the uniform distribution);

  2. the PDF has one or more singularities, and it is debateable whether a singularity is considered to be in the domain and called the mode (e.g. the gamma distribution with shape parameter less than 1); and/or

  3. the probability density function may have one or more local maxima that are not a global maximum (e.g. mixture distributions).

In such cases, mode will

  1. return a single value,

  2. consider the mode to occur at a singularity, and/or

  3. return a local maximum which may or may not be a global maximum.

If a formula for the mode is not specifically implemented for the chosen distribution, SciPy will attempt to compute the mode numerically, which may not meet the user’s preferred definition of a mode. In such cases, the user is encouraged to subclass the distribution and override mode.

References

[1]

Mode (statistics), Wikipedia, https://en.wikipedia.org/wiki/Mode_(statistics)

Examples

Instantiate a distribution with the desired parameters:

>>> from scipy import stats
>>> X = stats.Normal(mu=1., sigma=2.)

Evaluate the mode:

>>> X.mode()
1.0

If the mode is not uniquely defined, mode nonetheless returns a single value.

>>> X = stats.Uniform(a=0., b=1.)
>>> X.mode()
0.5

If this choice does not satisfy your requirements, subclass the distribution and override mode:

>>> class BetterUniform(stats.Uniform):
...     def mode(self):
...         return self.b
>>> X = BetterUniform(a=0., b=1.)
>>> X.mode()
1.0
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