# Maximum Likelihood¶

Maximum Likelihood algorithm decides whether a value is a value outside the region of interest based on that value’s distance from the estimated mean distribution. Generally, if

$|Y_i - \mu| > 3 \cdot \sigma \, \text{,}$

the data point is considered outside the region of interest. $$\mu$$ is the mean distribution, $$Y_i$$ is $$i$$th element of $$Y$$ and $$\sigma$$ denotes the standard deviation. Note that $$\mu \pm 3\sigma$$ contains $$99.7%$$ data under the assumption of normal distribution.

Input Parameters

Parameter Type Constraint Description Remarks
$$Y$$ $$Y \in \mathbb R^N$$ $$N \in \mathbb{N}$$ Input data sequence of length $$N$$
$$\mu$$ $$\mu \in \mathbb{R}$$   Mean distribution of $$Y$$
$$\sigma$$ $$\sigma\in \mathbb{R}$$   Standard deviation of $$Y$$

Output Parameters

Parameter Type Constraint Description Remarks
$$\hat{Y}$$ $$\hat{Y} \in \mathbb R^N$$   Values in the $$Y$$ list which are outside the region of interest are marked

Tool Support

• Matlab

For details refer to the online documentation of the function ‘mle’.

Single Steps using the Algorithm

References

• J. Han, M. Kamber and J. Pei, Data Mining - Concepts and Techniques, 3rd ed., Amsterdam: Morgan Kaufmann Publishers, 2012.