y = skewness(X)
y = skewness(X,flag)
y = skewness(X,flag,dim)
y = skewness(X) returns the
sample skewness of
X. For vectors,
the skewness of the elements of
x. For matrices,
a row vector containing the sample skewness of each column. For N-dimensional
skewness operates along the first nonsingleton
y = skewness(X,flag) specifies
whether to correct for bias (
flag = 0)
or not (
flag = 1,
the default). When
X represents a sample from a
population, the skewness of
X is biased; that is,
it will tend to differ from the population skewness by a systematic
amount that depends on the size of the sample. You can set
flag = 0 to correct for this systematic
y = skewness(X,flag,dim) takes the skewness
missing values and removes them.
X = randn([5 4]) X = 1.1650 1.6961 -1.4462 -0.3600 0.6268 0.0591 -0.7012 -0.1356 0.0751 1.7971 1.2460 -1.3493 0.3516 0.2641 -0.6390 -1.2704 -0.6965 0.8717 0.5774 0.9846 y = skewness(X) y = -0.2933 0.0482 0.2735 0.4641
Skewness is a measure of the asymmetry of the data around the sample mean. If skewness is negative, the data are spread out more to the left of the mean than to the right. If skewness is positive, the data are spread out more to the right. The skewness of the normal distribution (or any perfectly symmetric distribution) is zero.
The skewness of a distribution is defined as
where µ is the mean of x, σ is
the standard deviation of x, and E(t)
represents the expected value of the quantity t.
a sample version of this population value.
When you set
flag to 1, the following equation
When you set
0, the following equation applies:
formula requires that
X contain at least three
This function fully supports tall arrays. For more information, see Tall Arrays (MATLAB).