stats::obliquity
-- obliquity
(skewness)stats::obliquity
(data)
returns the
obliquity (skewness) of the data.
stats::obliquity(x1, x2, ..)
stats::obliquity([x1, x2, ..])
stats::obliquity(s <, c>)
x1, x2, .. |
- | the statistical data: arithmetical expressions. |
s |
- | a sample of domain type stats::sample . |
c |
- | an integer representing a column index of the sample
s . This column provides the data x1 ,
x2 etc. |
an arithmetical expression. FAIL
is returned, if the
obliquity does not exist.
(1/n*((x[1] - X)^3 + .. +(x[n] - X)^3)) / (1/n*((x[1] - X)^2 + .. +(x[n] - X)^2))^(3/2) ,where X is the mean value of the x[i]. The obliquity is a measure for the symmetry of a distribution. It is zero, if the distribution of the data is symmetric around the mean. Positive values indicate that the distribution function has a ``longer tail'' to the right of the mean than to the left. Negative values indicate a ``longer tail'' to the left.
c
is optional, if the data are given
by a stats::sample
object containing only one non-string column. Cf. example 3.We calculate the obliquity of a data sequence:
>> float(stats::obliquity(0, 7, 7, 6, 6, 6, 5, 5, 4, 1))
-1.041368312
Alternatively, the data may be passed as a list:
>> stats::obliquity([2, 2, 4, 6, 8, 10, 10])
0
We create a sample:
>> stats::sample([[a, 5, 8], [b, 3, 7], [c, d, 0]])
a 5 8 b 3 7 c d 0
The obliquity of the second column is:
>> stats::obliquity(%, 2)
1/2 / / d \3 / d \3 / 2 d \3 \ 3 | | 1/3 - - | + | 7/3 - - | + | --- - 8/3 | | \ \ 3 / \ 3 / \ 3 / / ----------------------------------------------------- / / d \2 / d \2 / 2 d \2 \3/2 | | 1/3 - - | + | 7/3 - - | + | --- - 8/3 | | \ \ 3 / \ 3 / \ 3 / /
We create a sample consisting of one string column and one non-string column:
>> stats::sample([["1996", 1242], ["1997", 1353], ["1998", 1142]])
"1996" 1242 "1997" 1353 "1998" 1142
We compute the obliquity of the second column. In this case this column does not have to be specified, since it is the only non-string column:
>> float(stats::obliquity(%))
0.06374333648