``````/**
* Copyright (c) 2015, Jozef Stefan Institute, Quintelligence d.o.o. and contributors
*
* LICENSE file in the root directory of this source tree.
*/
/**
* Statistics module.
* @module statistics
* @example
* // import the modules
* var qm = require('qminer');
* var statistics = qm.statistics;
* // create a vector
* var vec = new qm.la.Vector([0, 1, 2, -1, -2]);
* // calculate the mean value of the vector
* var mean = statistics.mean(vec); // returns 0
*/
/**
* Calculates the mean value(s).
* @param {(module:la.Vector | module:la.Matrix)} input - The input the method is used on.
* @returns {(number | module:la.Vector)}
* &lt;br>1. If input is {@link module:la.Vector}, returns the mean of the vector.
* &lt;br>2. If input is {@link module:la.Matrix}, returns a vector of where the i-th value is the mean of i-th column.
* @example
* // import modules
* var qm = require('qminer');
* var la = qm.la;
* var statistics = qm.statistics;
* // create a matrix
* var mat = new la.Matrix([[1, 2, 1], [-1, 2, -1], [3, 2, 3]]);
* // calculate the mean of the matrix columns
* // vector contains the elements [1, 2, 1]
* var mean = statistics.mean(mat);
*/
exports.mean = function (input) { return input instanceof Object.create(require('qminer').la.Vector) ? 0.0 : Object.create(require('qminer').la.Vector.prototype); }
/**
* Calculates the standard deviation(s).
* @param {(module:la.Vector | module:la.Matrix)} X - The input the method is used on.
* @param {number} [flag=0] - If set to to 0, it normalizes X by n-1; If set to 1 to, it normalizes by n.
* @param {number} [dim=1] - Computes the standard deviations along the dimension of X specified by parameter `dim`.
* If set to 1, calculates the column standard deviation. If set to 2, calculates the row standard deviation.
* @returns {(number | module:la.Vector)}
* &lt;br>1. If X is {@link module:la.Vector}, returns standard deviation of the vector.
* &lt;br>2. If X is {@link module:la.Matrix}, returns a vector where the i-th value is the standard deviation of the i-th column(row).
* @example
* // import modules
* var qm = require('qminer');
* var la = qm.la;
* var statistics = qm.statistics;
* // create a matrix
* var mat = new la.Matrix([[1, 2, 1], [-1, 2, -1], [3, 2, 3]]);
* // calculate the standard deviation of the matrix columns
* var mean = statistics.std(mat);
*/
exports.std = function (X, flag, dim) { return input instanceof Object.create(require('qminer').la.Vector) ? 0.0 : Object.create(require('qminer').la.Vector.prototype); }
/**
* Returns an object containing the standard deviation of each column of matrix, mean vector and z-score matrix.
* @param {module:la.Matrix} mat - The matrix.
* @param {number} [flag=0] - If set to 0, it normalizes mat by n-1; if set to 1, it normalizes by n.
* @param {number} [dim=1] - Computes the standard deviations along the dimension of mat specified by parameter `dim`.
* If set to 1, calculates the column standard deviation. If set to 2, calculates the row standard deviation.
* @returns {Object} The object `zscoreResult` containing:
* &lt;br>`zscoreResult.sigma` - {@link module:la.Vector} of standard deviations of mat used to compute the z-scores.
* &lt;br>`zscoreResult.mu` - {@link module:la.Vector} of mean values of mat used to compute the z-scores.
* &lt;br>`zscoreResult.Z` - {@link module:la.Matrix} of z-scores that has mean 0 and variance 1.
* @example
* // import modules
* var qm = require('qminer');
* var la = qm.la;
* var statistics = qm.statistics;
* // create a matrix
* var mat = new la.Matrix([[1, 2, 1], [-1, 2, -1], [3, 2, 3]]);
* // calculate the standard deviation of the matrix columns
* var mean = statistics.zscore(mat);
*/
exports.zscore = function (mat, flag, dim) { return {sigma: Object.create(require('qminer').la.Vector.prototype), mu: Object.create(require('qminer').la.Vector.prototype), Z: Object.create(require('qminer').la.Matrix.prototype)}; }
/**
* function studentCdf calculates Student's t cumulative distribution function (PDF integral from -inf to t)
* function studentCdf returns 'Alpha' as in the p-value of a Student t-test
* If you already have a t-value than the studentCdf function has 2 inputs: t-value and degrees of freedom
* @param {number} val - The t-value value of the sample you want to calculate the p-value for
* @param {number} df - Degrees of freedom for the sample (if your sample is big n than degrees of freedom in n-1)
* If you don't have the t-value than studentCdf function has 4 inputs: Value, Mean, Standard deviation and degrees of freedom
* @param {number} val - The average value of the sample you want to calculate the p-value for
* @param {number} mean - The mean value of the sample you want to calculate the p-value for
* @param {number} std - The sample standard deviation of the sample you want to calculate the p-value for
* @param {number} df - Degrees of freedom for the sample (if your sample is n big then degrees of freedom is n-1)
* @returns {Alpha}
*/

/**
* Calculates the z-score for a point sampled from a Gaussian distribution. The z-score indicates
* how many standard deviations an element is from the meam and can be calculated using
* the following formula: `z = (x - mu) / sigma`.
* @param {Number} x - The sampled point.
* @param {Number} mu - Mean of the distribution.
* @param {Number} sigma - Variance of the distribution.
* @returns {number} The z-score of the sampled point.
* @example
* // import modules
* var stat = require('qminer').statistics;
* // calculate the z-score of the sampled point
* var point = 10;
* var mu    = 5;
* var sigma = 5;
* var zScore = stat.getZScore(point, mu, sigma); // returns 1
*/
exports.getZScore = function (x, mu, sigma) {
return (x - mu) / sigma;
}

``````