k6: The sixth central moment
In dangulod/ECTools: Economic Capital Tools
Description
Usage
Arguments
Value
References
Description
The sixth central moment
Usage
1
k6(x)
Arguments
loss
vector with input
scale
scale parameter
Value
High-order moments are moments beyond 4th-order moments. As with variance, skewness, and kurtosis, these are higher-order statistics,
involving non-linear combinations of the data, and can be used for description or estimation of further shape parameters. The higher the moment,
the harder it is to estimate, in the sense that larger samples are required in order to obtain estimates of similar quality. This is due to the
excess degrees of freedom consumed by the higher orders. Further, they can be subtle to interpret, often being most easily understood in terms
of lower order moments <e2><80><93> compare the higher derivatives of jerk and jounce in physics. For example, just as the 4th-order moment (kurtosis) can
be interpreted as "relative importance of tails versus shoulders in causing dispersion" (for a given dispersion, high kurtosis corresponds to
heavy tails, while low kurtosis corresponds to broad shoulders), the 5th-order moment can be interpreted as measuring "relative importance of
tails versus center (mode, shoulders) in causing skew" (for a given skew, high 5th moment corresponds to heavy tail and little movement of mode,
while low 5th moment corresponds to more change in shoulders).
References
https://en.wikipedia.org/wiki/Moment_(mathematics)
dangulod/ECTools documentation built on May 4, 2019, 3:19 p.m.
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Description Usage Arguments Value References
Description
The sixth central moment
Usage
1 | k6(x)
|
Arguments
loss |
vector with input |
scale |
scale parameter |
Value
High-order moments are moments beyond 4th-order moments. As with variance, skewness, and kurtosis, these are higher-order statistics, involving non-linear combinations of the data, and can be used for description or estimation of further shape parameters. The higher the moment, the harder it is to estimate, in the sense that larger samples are required in order to obtain estimates of similar quality. This is due to the excess degrees of freedom consumed by the higher orders. Further, they can be subtle to interpret, often being most easily understood in terms of lower order moments <e2><80><93> compare the higher derivatives of jerk and jounce in physics. For example, just as the 4th-order moment (kurtosis) can be interpreted as "relative importance of tails versus shoulders in causing dispersion" (for a given dispersion, high kurtosis corresponds to heavy tails, while low kurtosis corresponds to broad shoulders), the 5th-order moment can be interpreted as measuring "relative importance of tails versus center (mode, shoulders) in causing skew" (for a given skew, high 5th moment corresponds to heavy tail and little movement of mode, while low 5th moment corresponds to more change in shoulders).
References
https://en.wikipedia.org/wiki/Moment_(mathematics)
R Package Documentation
Browse R Packages
We want your feedback!
Note that we can't provide technical support on individual packages. You should contact the package authors for that.
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