Octave supports various helpful statistical functions. Many are useful as initial steps to prepare a data set for further analysis. Others provide different measures from those of the basic descriptive statistics.
If x is a vector, subtract its mean. If x is a matrix, do the above for each column. If the optional argument dim is given, operate along this dimension.
See also: zscore.
If x is a vector, subtract its mean and divide by its standard
deviation. If the standard deviation is zero, divide by 1 instead.
The optional parameter opt determines the normalization to use
when computing the standard deviation and is the same as the
corresponding parameter for
If x is a matrix, do the above along the first non-singleton dimension. If the third optional argument dim is given, operate along this dimension.
The mean and standard deviation along dim are given in mu and sigma respectively.
See also: mean, std, center.
Produce histogram counts.
When x is a vector, the function counts the number of elements of
x that fall in the histogram bins defined by edges. This must be
a vector of monotonically increasing values that define the edges of the
n(k) contains the number of elements in
x for which
edges(k) <= x < edges(k+1).
The final element of n contains the number of elements of x
exactly equal to the last element of edges.
When x is an N-dimensional array, the computation is carried out along dimension dim. If not specified dim defaults to the first non-singleton dimension.
When a second output argument is requested an index matrix is also returned. The idx matrix has the same size as x. Each element of idx contains the index of the histogram bin in which the corresponding element of x was counted.
See also: hist.
Compute the binomial coefficient or all combinations of a set of items.
If n is a scalar then calculate the binomial coefficient of n and k which is defined as
/ \ | n | n (n-1) (n-2) … (n-k+1) n! | | = ------------------------- = --------- | k | k! k! (n-k)! \ /
This is the number of combinations of n items taken in groups of size k.
If the first argument is a vector, set, then generate all
combinations of the elements of set, taken k at a time, with
one row per combination. The result c has k columns and
nchoosek (length (set), k) rows.
How many ways can three items be grouped into pairs?
nchoosek (3, 2) ⇒ 3
What are the possible pairs?
nchoosek (1:3, 2) ⇒ 1 2 1 3 2 3
nchoosek works only for non-negative, integer arguments. Use
bincoeff for non-integer and negative scalar arguments, or for
computing many binomial coefficients at once with vector inputs
for n or k.
See also: bincoeff, perms.
Generate all permutations of v, one row per permutation. The
result has size
factorial (n) * n, where n
is the length of v.
As an example,
perms ([1, 2, 3]) returns the matrix
1 2 3 2 1 3 1 3 2 2 3 1 3 1 2 3 2 1
Return the ranks of x along the first non-singleton dimension adjusted for ties. If the optional argument dim is given, operate along this dimension.
See also: spearman, kendall.
Count the upward runs along the first non-singleton dimension of x of length 1, 2, …, n-1 and greater than or equal to n.
If the optional argument dim is given then operate along this dimension.
Find the lengths of all sequences of common values. Return the vector of lengths and the value that was repeated.
runlength ([2, 2, 0, 4, 4, 4, 0, 1, 1, 1, 1]) ⇒ [2, 1, 3, 1, 4]
For each component of p, return the probit (the quantile of the standard normal distribution) of p.
For each component of p, return the logit of p defined as
logit (p) = log (p / (1-p))
See also: logistic_cdf.
Return the complementary log-log function of x, defined as
cloglog (x) = - log (- log (x))
Return the Mahalanobis’ D-square distance between the multivariate samples x and y, which must have the same number of components (columns), but may have a different number of observations (rows).
Create a contingency table t from data vectors. The l_x and l_y vectors are the corresponding levels.
Currently, only 1- and 2-dimensional tables are supported.