Description Usage Arguments Details Author(s) References See Also Examples

compute kurtosis of a univariate distribution

1 2 |

`x` |
a numeric vector or object. |

`na.rm` |
a logical. Should missing values be removed? |

`method` |
a character string which specifies the method of computation.
These are either |

`...` |
arguments to be passed. |

This function was ported from the RMetrics package fUtilities to eliminate a
dependency on fUtilties being loaded every time. This function is identical
except for the addition of `checkData`

and additional labeling.

*kurtosis(moment) = sum((x-mean(x))^4/var(x)^2)/length(x)*

*kurtosis(excess) = sum((x-mean(x))^4/var(x)^2)/length(x) - 3*

*kurtosis(sample) = sum(((x-mean(x))/var(x))^4)*n*(n+1)/((n-1)*(n-2)*(n-3))*

*kurtosis (fisher) = ((n+1)*(n-1)*((sum(x^4)/n)/(sum(x^2)/n)^2 - (3*(n-1))/(n+1)))/((n-2)*(n-3))*

*kurtosis(sample excess) = sum(((x-mean(x))/var(x))^4)*n*(n+1)/((n-1)*(n-2)*(n-3)) - 3*(n-1)^2/((n-2)*(n-3))*

where *n* is the number of return, *\overline{r}* is the mean of the return
distribution, *σ_P* is its standard deviation and *σ_{S_P}* is its
sample standard deviation

Diethelm Wuertz, Matthieu Lestel

Carl Bacon, *Practical portfolio performance measurement
and attribution*, second edition 2008 p.84-85

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 | ```
## mean -
## var -
# Mean, Variance:
r = rnorm(100)
mean(r)
var(r)
## kurtosis -
kurtosis(r)
data(managers)
kurtosis(managers[,1:8])
data(portfolio_bacon)
print(kurtosis(portfolio_bacon[,1], method="sample")) #expected 3.03
print(kurtosis(portfolio_bacon[,1], method="sample_excess")) #expected -0.41
print(kurtosis(managers['1996'], method="sample"))
print(kurtosis(managers['1996',1], method="sample"))
``` |

PerformanceAnalytics documentation built on May 31, 2017, 3:16 a.m.

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