- Function File: mean (X, OPT)
If X is a vector, compute the mean of the elements of X
mean (x) = SUM_i x(i) / N
If X is a matrix, compute the mean for each column and return them
in a row vector.
With the optional argument OPT, the kind of mean computed can be
selected. The following options are recognized:
`"a"'
Compute the (ordinary) arithmetic mean. This is the default.
`"g"'
Computer the geometric mean.
`"h"' Compute the harmonic mean.
- Function File: median (X)
If X is a vector, compute the median value of the elements of X.
x(ceil(N/2)), N odd
median(x) =
(x(N/2) + x((N/2)+1))/2, N even
If X is a matrix, compute the median value for each column
and return them in a row vector.
- Function File: std (X)
If X is a vector, compute the standard deviation of the elements
of X.
std (x) = sqrt (sumsq (x - mean (x)) / (n - 1))
If X is a matrix, compute the standard deviation for each
column and return them in a row vector.
- Function File: cov (X, Y)
If each row of X and Y is an observation and each column is a
variable, the (I,J)-th entry of `cov (X, Y)' is the covariance
between the I-th variable in X and the J-th variable in Y. If
called with one argument, compute `cov (X, X)'.
- Function File: corrcoef (X, Y)
If each row of X and Y is an observation and each column is a
variable, the (I,J)-th entry of `corrcoef (X, Y)' is the
correlation between the I-th variable in X and the J-th variable
in Y. If called with one argument, compute `corrcoef (X, X)'.
- Function File: kurtosis (X)
If X is a vector of length N, return the kurtosis
kurtosis (x) = N^(-1) std(x)^(-4) sum ((x - mean(x)).^4) - 3
of X. If X is a matrix, return the row vector containing the
kurtosis of each column.
- Function File: mahalanobis (X, Y)
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).
- Function File: skewness (X)
If X is a vector of length n, return the skewness
skewness (x) = N^(-1) std(x)^(-3) sum ((x - mean(x)).^3)
of X. If X is a matrix, return the row vector containing the
skewness of each column.
- Function File: values (X)
Return the different values in a column vector, arranged in
ascending order.
- Function File: var (X)
For vector arguments, return the (real) variance of the values.
For matrix arguments, return a row vector contaning the variance
for each column.
- Function File: [T, L_X] = table (X)
- Function File: [T, L_X, L_Y] = table (X, Y)
Create a contingency table T from data vectors. The L vectors are
the corresponding levels.
Currently, only 1- and 2-dimensional tables are supported.
- Function File: studentize (X)
If X is a vector, subtract its mean and divide by its standard
deviation.
If X is a matrix, do the above for each column.
- Function File: statistics (X)
If X is a matrix, return a matrix with the minimum, first
quartile, median, third quartile, maximum, mean, standard
deviation, skewness and kurtosis of the columns of X as its rows.
If X is a vector, treat it as a column vector.
- Function File: spearman (X, Y)
Compute Spearman's rank correlation coefficient RHO for each of
the variables specified by the input arguments.
For matrices, each row is an observation and each column a
variable; vectors are always observations and may be row or column
vectors.
`spearman (X)' is equivalent to `spearman (X, X)'.
For two data vectors X and Y, Spearman's RHO is the correlation of
the ranks of X and Y.
If X and Y are drawn from independent distributions, RHO has zero
mean and variance `1 / (n - 1)', and is asymptotically normally
distributed.
- Function File: run_count (X, N)
Count the upward runs in the columns of X of length 1, 2, ..., N-1
and greater than or equal to N.
- Function File: ranks (X)
If X is a vector, return the (column) vector of ranks of X
adjusted for ties.
If X is a matrix, do the above for each column of X.
- Function File: range (X)
If X is a vector, return the range, i.e., the difference between
the maximum and the minimum, of the input data.
If X is a matrix, do the above for each column of X.
- Function File: [Q, S] = qqplot (X, DIST, PARAMS)
Perform a QQ-plot (quantile plot).
If F is the CDF of the distribution DIST with parameters PARAMS
and G its inverse, and X a sample vector of length N, the QQ-plot
graphs ordinate S(I) = I-th largest element of x versus abscissa
Q(If) = G((I - 0.5)/N).
If the sample comes from F except for a transformation of location
and scale, the pairs will approximately follow a straight line.
The default for DIST is the standard normal distribution. The
optional argument PARAMS contains a list of parameters of DIST.
For example, for a quantile plot of the uniform distribution on
[2,4] and X, use
qqplot (x, "uniform", 2, 4)
If no output arguments are given, the data are plotted directly.
- Function File: probit (P)
For each component of P, return the probit (the quantile of the
standard normal distribution) of P.
Function File: [P, Y] = ppplot (X, DIST, PARAMS)
Perform a PP-plot (probability plot).
If F is the CDF of the distribution DIST with parameters PARAMS
and X a sample vector of length N, the PP-plot graphs ordinate
Y(I) = F (I-th largest element of X) versus abscissa P(I) = (I -
0.5)/N. If the sample comes from F, the pairs will approximately
follow a straight line.
The default for DIST is the standard normal distribution. The
optional argument PARAMS contains a list of parameters of DIST.
For example, for a probability plot of the uniform distribution on
[2,4] and X, use
ppplot (x, "uniform", 2, 4)
If no output arguments are given, the data are plotted directly.
- Function File: moment (X, P, OPT)
If X is a vector, compute the P-th moment of X.
If X is a matrix, return the row vector containing the P-th moment
of each column.
With the optional string opt, the kind of moment to be computed can
be specified. If opt contains `"c"' or `"a"', central and/or
absolute moments are returned. For example,
moment (x, 3, "ac")
computes the third central absolute moment of X.
- Function File: meansq (X)
For vector arguments, return the mean square of the values. For
matrix arguments, return a row vector contaning the mean square of
each column.
- Function File: logit (P)
For each component of P, return the logit `log (P / (1-P))' of P.
- Function File: kendall (X, Y)
Compute Kendall's TAU for each of the variables specified by the
input arguments.
For matrices, each row is an observation and each column a
variable; vectors are always observations and may be row or column
vectors.
`kendall (X)' is equivalent to `kendall (X, X)'.
For two data vectors X, Y of common length N, Kendall's TAU is the
correlation of the signs of all rank differences of X and Y;
i.e., if both X and Y have distinct entries, then
1
tau = ------- SUM sign (q(i) - q(j)) * sign (r(i) - r(j))
n (n-1) i,j
in which the Q(I) and R(I) are the ranks of X and Y, respectively.
If X and Y are drawn from independent distributions, Kendall's TAU
is asymptotically normal with mean 0 and variance `(2 * (2N+5)) /
(9 * N * (N-1))'.
- Function File: iqr (X)
If X is a vector, return the interquartile range, i.e., the
difference between the upper and lower quartile, of the input data.
If X is a matrix, do the above for each column of X.
- Function File: cut (X, BREAKS)
Create categorical data out of numerical or continuous data by
cutting into intervals.
If BREAKS is a scalar, the data is cut into that many equal-width
intervals. If BREAKS is a vector of break points, the category
has `length (BREAKS) - 1' groups.
The returned value is a vector of the same size as X telling which
group each point in X belongs to. Groups are labelled from 1 to
the number of groups; points outside the range of BREAKS are
labelled by `NaN'.
- Function File: cor (X, Y)
The (I,J)-th entry of `cor (X, Y)' is the correlation between the
I-th variable in X and the J-th variable in Y.
For matrices, each row is an observation and each column a
variable; vectors are always observations and may be row or column
vectors.
`cor (X)' is equivalent to `cor (X, X)'.
- Function File: cloglog (X)
Return the complementary log-log function of X, defined as
- log (- log (X))
- Function File: center (X)
If X is a vector, subtract its mean. If X is a matrix, do the
above for each column.
&nbps