- 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.
 
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