Statistics
If X is a vector, compute the mean of the elements of X
If X is a vector, compute the median value of the elements of X.
For a sample, X, calculate the quantiles, Q, corresponding to the
cumulative probability values in P.
Computes the value associated with the P-th percentile of X.
For vector arguments, return the mean square of the values.
If X is a vector, compute the standard deviation of the elements of X.
For vector arguments, return the (real) variance of the values.
Count the most frequently appearing value.
Compute covariance.
Compute correlation.
Compute correlation.
If X is a vector of length N, return the kurtosis
If X is a vector of length n, return the skewness
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, compute the P-th moment of 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).
If X is a vector, subtract its mean.
If X is a vector, subtract its mean and divide by its standard
deviation.
Compute the binomial coefficient or all combinations of N.
Generate all permutations of V, one row per permutation.
Return the different values in a column vector, arranged in ascending
order.
Create a contingency table T from data vectors.
Compute Spearman's rank correlation coefficient RHO for each of the
variables specified by the input arguments.
Count the upward runs along the first non-singleton dimension of X of
length 1, 2, .
Return the ranks of X along the first non-singleton dimension adjust
for ties.
If X is a vector, return the range, i.
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))
Return the complementary log-log function of X, defined as
Compute Kendall's TAU for each of the variables specified by the input
arguments.
If X is a vector, return the interquartile range, i.
Create categorical data out of numerical or continuous data by cutting
into intervals.
Perform a QQ-plot (quantile plot).
Perform a PP-plot (probability plot).
Perform a one-way analysis of variance (ANOVA).
Perform a Bartlett test for the homogeneity of variances in the data
vectors X1, X2, .
Given two samples X and Y, perform a chisquare test for homogeneity of
the null hypothesis that X and Y come from the same distribution, based
on the partition induced by the (strictly increasing) ent
Perform a chi-square test for independence based on the contingency
table X.
Test whether two samples X and Y come from uncorrelated populations.
Perform an F test for the null hypothesis rr * b = r in a classical
normal regression model y = X * b + e.
For a sample X from a multivariate normal distribution with unknown
mean and covariance matrix, test the null hypothesis that `mean (X) ==
M'.
For two samples X from multivariate normal distributions with the same
number of variables (columns), unknown means and unknown equal
covariance matrices, test the null hypothesis `mean (X) == mean (Y
Perform a Kolmogorov-Smirnov test of the null hypothesis that the
sample X comes from the (continuous) distribution dist.
Perform a 2-sample Kolmogorov-Smirnov test of the null hypothesis that
the samples X and Y come from the same (continuous) distribution.
Perform a Kruskal-Wallis one-factor "analysis of variance".
Perform a one-way multivariate analysis of variance (MANOVA).
For a square contingency table X of data cross-classified on the row
and column variables, McNemar's test can be used for testing the null
hypothesis of symmetry of the classification probabilities.
If X1 and N1 are the counts of successes and trials in one sample, and
X2 and N2 those in a second one, test the null hypothesis that the
success probabilities P1 and P2 are the same.
Perform a chi-square test with 6 degrees of freedom based on the upward
runs in the columns of X.
For two matched-pair samples X and Y, perform a sign test of the null
hypothesis PROB (X > Y) == PROB (X < Y) == 1/2.
For a sample X from a normal distribution with unknown mean and
variance, perform a t-test of the null hypothesis `mean (X) == M'.
For two samples x and y from normal distributions with unknown means
and unknown equal variances, perform a two-sample t-test of the null
hypothesis of equal means.
Perform an t test for the null hypothesis `RR * B = R' in a classical
normal regression model `Y = X * B + E'.
For two samples X and Y, perform a Mann-Whitney U-test of the null
hypothesis PROB (X > Y) == 1/2 == PROB (X < Y).
For two samples X and Y from normal distributions with unknown means
and unknown variances, perform an F-test of the null hypothesis of
equal variances.
For two samples X and Y from normal distributions with unknown means
and unknown and not necessarily equal variances, perform a Welch test
of the null hypothesis of equal means.
For two matched-pair sample vectors X and Y, perform a Wilcoxon
signed-rank test of the null hypothesis PROB (X > Y) == 1/2.
Perform a Z-test of the null hypothesis `mean (X) == M' for a sample X
from a normal distribution with unknown mean and known variance V.
For two samples X and Y from normal distributions with unknown means
and known variances V_X and V_Y, perform a Z-test of the hypothesis of
equal means.
Perform ordinal logistic regression.
For each element of X, returns the CDF at X of the beta distribution
with parameters A and B, i.
For each component of X, compute the quantile (the inverse of the CDF)
at X of the Beta distribution with parameters A and B.
For each element of X, returns the PDF at X of the beta distribution
with parameters A and B.
For each element of X, compute the CDF at X of the binomial
distribution with parameters N and P.
For each element of X, compute the quantile at X of the binomial
distribution with parameters N and P.
For each element of X, compute the probability density function (PDF)
at X of the binomial distribution with parameters N and P.
For each element of X, compute the cumulative distribution function
(CDF) at X of the Cauchy distribution with location parameter LAMBDA
and scale parameter SIGMA.
For each element of X, compute the quantile (the inverse of the CDF) at
X of the Cauchy distribution with location parameter LAMBDA and scale
parameter SIGMA.
For each element of X, compute the probability density function (PDF)
at X of the Cauchy distribution with location parameter LAMBDA and
scale parameter SIGMA > 0.
For each element of X, compute the cumulative distribution function
(CDF) at X of the chisquare distribution with N degrees of freedom.
For each element of X, compute the quantile (the inverse of the CDF) at
X of the chisquare distribution with N degrees of freedom.
For each element of X, compute the probability density function (PDF)
at X of the chisquare distribution with N degrees of freedom.
For each element of X, compute the cumulative distribution function
(CDF) at X of a univariate discrete distribution which assumes the
values in V with probabilities P.
For each component of X, compute the quantile (the inverse of the CDF)
at X of the univariate distribution which assumes the values in V with
probabilities P.
For each element of X, compute the probability density function (PDF)
at X of a univariate discrete distribution which assumes the values in
V with probabilities P.
For each element of X, compute the cumulative distribution function
(CDF) at X of the empirical distribution obtained from the univariate
sample DATA.
For each element of X, compute the quantile (the inverse of the CDF) at
X of the empirical distribution obtained from the univariate sample
DATA.
For each element of X, compute the probability density function (PDF)
at X of the empirical distribution obtained from the univariate sample
DATA.
For each element of X, compute the cumulative distribution function
(CDF) at X of the exponential distribution with mean LAMBDA.
For each element of X, compute the quantile (the inverse of the CDF) at
X of the exponential distribution with mean LAMBDA.
For each element of X, compute the probability density function (PDF)
of the exponential distribution with mean LAMBDA.
For each element of X, compute the CDF at X of the F distribution with
M and N degrees of freedom, i.
For each component of X, compute the quantile (the inverse of the CDF)
at X of the F distribution with parameters M and N.
For each element of X, compute the probability density function (PDF)
at X of the F distribution with M and N degrees of freedom.
For each element of X, compute the cumulative distribution function
(CDF) at X of the Gamma distribution with parameters A and B.
For each component of X, compute the quantile (the inverse of the CDF)
at X of the Gamma distribution with parameters A and B.
For each element of X, return the probability density function (PDF) at
X of the Gamma distribution with parameters A and B.
For each element of X, compute the CDF at X of the geometric
distribution with parameter P.
For each element of X, compute the quantile at X of the geometric
distribution with parameter P.
For each element of X, compute the probability density function (PDF)
at X of the geometric distribution with parameter P.
Compute the cumulative distribution function (CDF) at X of the
hypergeometric distribution with parameters T, M, and N.
For each element of X, compute the quantile at X of the hypergeometric
distribution with parameters T, M, and N.
Compute the probability density function (PDF) at X of the
hypergeometric distribution with parameters T, M, and N.
Return the CDF at X of the Kolmogorov-Smirnov distribution,
Inf
Q(x) = SUM (-1)^k exp(-2 k^2 x^2)
k = -Inf
For each element of X, compute the cumulative distribution function
(CDF) at X of the Laplace distribution.
For each element of X, compute the quantile (the inverse of the CDF) at
X of the Laplace distribution.
For each element of X, compute the probability density function (PDF)
at X of the Laplace distribution.
For each component of X, compute the CDF at X of the logistic
distribution.
For each component of X, compute the quantile (the inverse of the CDF)
at X of the logistic distribution.
For each component of X, compute the PDF at X of the logistic
distribution.
For each element of X, compute the cumulative distribution function
(CDF) at X of the lognormal distribution with parameters MU and SIGMA.
For each element of X, compute the quantile (the inverse of the CDF) at
X of the lognormal distribution with parameters MU and SIGMA.
For each element of X, compute the probability density function (PDF)
at X of the lognormal distribution with parameters MU and SIGMA.
For each element of X, compute the CDF at x of the Pascal (negative
binomial) distribution with parameters N and P.
For each element of X, compute the quantile at X of the Pascal
(negative binomial) distribution with parameters N and P.
For each element of X, compute the probability density function (PDF)
at X of the Pascal (negative binomial) distribution with parameters N
and P.
For each element of X, compute the cumulative distribution function
(CDF) at X of the normal distribution with mean M and standard
deviation S.
For each element of X, compute the quantile (the inverse of the CDF) at
X of the normal distribution with mean M and standard deviation S.
For each element of X, compute the probability density function (PDF)
at X of the normal distribution with mean M and standard deviation S.
For each element of X, compute the cumulative distribution function
(CDF) at X of the Poisson distribution with parameter lambda.
For each component of X, compute the quantile (the inverse of the CDF)
at X of the Poisson distribution with parameter LAMBDA.
For each element of X, compute the probability density function (PDF)
at X of the poisson distribution with parameter LAMBDA.
For each element of X, compute the cumulative distribution function
(CDF) at X of the t (Student) distribution with N degrees of freedom,
i.
For each probability value X, compute the the inverse of the cumulative
distribution function (CDF) of the t (Student) distribution with
degrees of freedom N.
For each element of X, compute the probability density function (PDF)
at X of the T (Student) distribution with N degrees of freedom.
For each element of X, compute the cumulative distribution function
(CDF) at X of a univariate discrete distribution which assumes the
values in V with equal probability.
For each component of X, compute the quantile (the inverse of the CDF)
at X of the univariate discrete distribution which assumes the values
in V with equal probability
For each element of X, compute the probability density function (PDF)
at X of a univariate discrete distribution which assumes the values in
V with equal probability.
Return the CDF at X of the uniform distribution on [A, B], i.
For each element of X, compute the quantile (the inverse of the CDF) at
X of the uniform distribution on [A, B].
For each element of X, compute the PDF at X of the uniform distribution
on [A, B].
Compute the cumulative distribution function (CDF) at X of the Weibull
distribution with shape parameter SCALE and scale parameter SHAPE,
which is
Compute the quantile (the inverse of the CDF) at X of the Weibull
distribution with shape parameter SCALE and scale parameter SHAPE.
Compute the probability density function (PDF) at X of the Weibull
distribution with shape parameter SCALE and scale parameter SHAPE which
is given by
Return an R by C or `size (SZ)' matrix of random samples from the Beta
distribution with parameters A and B.
Return an R by C or a `size (SZ)' matrix of random samples from the
binomial distribution with parameters N and P.
Return an R by C or a `size (SZ)' matrix of random samples from the
Cauchy distribution with parameters LAMBDA and SIGMA which must both be
scalar or of size R by C.
Return an R by C or a `size (SZ)' matrix of random samples from the
chisquare distribution with N degrees of freedom.
Generate a row vector containing a random sample of size N from the
univariate distribution which assumes the values in V with
probabilities P.
Generate a bootstrap sample of size N from the empirical distribution
obtained from the univariate sample DATA.
Return an R by C matrix of random samples from the exponential
distribution with mean LAMBDA, which must be a scalar or of size R by
C.
Return an R by C matrix of random samples from the F distribution with
M and N degrees of freedom.
Return an R by C or a `size (SZ)' matrix of random samples from the
Gamma distribution with parameters A and B.
Return an R by C matrix of random samples from the geometric
distribution with parameter P, which must be a scalar or of size R by C.
Return an R by C matrix of random samples from the hypergeometric
distribution with parameters T, M, and N.
Return an R by C matrix of random numbers from the Laplace
distribution.
Return an R by C matrix of random numbers from the logistic
distribution.
Return an R by C matrix of random samples from the lognormal
distribution with parameters MU and SIGMA.
Return an R by C matrix of random samples from the Pascal (negative
binomial) distribution with parameters N and P.
Return an R by C or `size (SZ)' matrix of random samples from the
normal distribution with parameters mean M and standard deviation S.
Return an R by C matrix of random samples from the Poisson distribution
with parameter LAMBDA, which must be a scalar or of size R by C.
Return an R by C matrix of random samples from the t (Student)
distribution with N degrees of freedom.
Return random values from discrete uniform distribution, with maximum
value(s) given by the integer MX, which may be a scalar or
multidimensional array.
Return an R by C or a `size (SZ)' matrix of random samples from the
uniform distribution on [A, B].
Return an R by C matrix of random samples from the Weibull distribution
with parameters SCALE and SHAPE which must be scalar or of size R by C.
Return a simulated realization of the D-dimensional Wiener Process on
the interval [0, T].