octave: Basic Statistical Functions
26.2 Basic Statistical Functions
================================
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.
-- : center (X)
-- : center (X, DIM)
Center data by subtracting its mean.
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.
Programming Note: ‘center’ has obvious application for normalizing
statistical data. It is also useful for improving the precision of
general numerical calculations. Whenever there is a large value
that is common to a batch of data, the mean can be subtracted off,
the calculation performed, and then the mean added back to obtain
the final answer.
See also: 
zscore XREFzscore.
-- : Z = zscore (X)
-- : Z = zscore (X, OPT)
-- : Z = zscore (X, OPT, DIM)
-- : [Z, MU, SIGMA] = zscore (...)
Compute the Z score of X
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 has the same definition as the
corresponding parameter for ‘std’.
If X is a matrix, calculate along the first non-singleton
dimension. If the third optional argument DIM is given, operate
along this dimension.
The optional outputs MU and SIGMA contain the mean and standard
deviation.
DONTPRINTYET See also: mean XREFmean, std XREFstd, *notecenter:
DONTPRINTYET See also: mean XREFmean, std XREFstd, center
XREFcenter.
-- : N = histc (X, EDGES)
-- : N = histc (X, EDGES, DIM)
-- : [N, IDX] = histc (...)
Compute 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 histogram bins. ‘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 XREFhist.
‘unique’ function documented at unique XREFunique. is often
useful for statistics.
-- : C = nchoosek (N, K)
-- : C = nchoosek (SET, K)
Compute the binomial coefficient of N or list all possible
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.
For example:
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
Programming Note: When calculating the binomial coefficient
‘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 XREFbincoeff, perms XREFperms.
-- : perms (V)
Generate all permutations of V with one row per permutation.
The result has size ‘factorial (N) * N’, where N is the length of
V.
Example
perms ([1, 2, 3])
⇒
1 2 3
2 1 3
1 3 2
2 3 1
3 1 2
3 2 1
Programming Note: The maximum length of V should be less than or
equal to 10 to limit memory consumption.
See also: permute XREFpermute, randperm XREFrandperm,
nchoosek XREFnchoosek.
-- : ranks (X, DIM)
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 XREFspearman, kendall XREFkendall.
-- : run_count (X, N)
-- : run_count (X, N, DIM)
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.
See also: runlength XREFrunlength.
-- : count = runlength (X)
-- : [count, value] = runlength (X)
Find the lengths of all sequences of common values.
COUNT is a vector with the lengths of each repeated value.
The optional output VALUE contains the value that was repeated in
the sequence.
runlength ([2, 2, 0, 4, 4, 4, 0, 1, 1, 1, 1])
⇒ [2, 1, 3, 1, 4]
See also: run_count XREFrun_count.
-- : probit (P)
Return the probit (the quantile of the standard normal
distribution) for each element of P.
See also: logit XREFlogit.
-- : logit (P)
Compute the logit for each value of P
The logit is defined as
logit (P) = log (P / (1-P))
DONTPRINTYET See also: probit XREFprobit, *notelogistic_cdf:
DONTPRINTYET See also: probit XREFprobit, logistic_cdf
XREFlogistic_cdf.
-- : cloglog (X)
Return the complementary log-log function of X.
The complementary log-log function is defined as
cloglog (x) = - log (- log (X))
-- : [T, L_X] = table (X)
-- : [T, L_X, L_Y] = table (X, Y)
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.
Info Catalog
octave: Descriptive Statistics
octave: Statistics
octave: Statistical Plots