module

statistics

Source: statdoc.js:8

Statistics module.

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

Methods

getZScore(x, mu, sigma)
mean(input)
std(X[, flag][, dim])
zscore(mat[, flag][, dim])

Methods

static

getZScore(x, mu, sigma) → number

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.

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

Parameters

Name Type Optional Description

x

Number

 

The sampled point.

mu

Number

 

Mean of the distribution.

sigma

Number

 

Variance of the distribution.
Returns

numberB The z-score of the sampled point.

static

mean(input) → (number or module:la.Vector)

Calculates the mean value(s).

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);

Parameter

Name Type Optional Description

input

(module:la.Vector or module:la.Matrix)

 

The input the method is used on.
Returns

(number or module:la.Vector)B
1. If input is module:la.Vector, returns the mean of the vector.
2. If input is module:la.Matrix, returns a vector of where the i-th value is the mean of i-th column.

static

std(X[, flag][, dim]) → (number or module:la.Vector)

Calculates the standard deviation(s).

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);

Parameters

Name Type Optional Description

X

(module:la.Vector or module:la.Matrix)

 

The input the method is used on.

flag

number

Yes

If set to to 0, it normalizes X by n-1; If set to 1 to, it normalizes by n.

Defaults to 0.

dim

number

Yes

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.

Defaults to 1.
Returns

(number or module:la.Vector)B
1. If X is module:la.Vector, returns standard deviation of the vector.
2. If X is module:la.Matrix, returns a vector where the i-th value is the standard deviation of the i-th column(row).

static

zscore(mat[, flag][, dim]) → Object

Returns an object containing the standard deviation of each column of matrix, mean vector and z-score matrix.

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);

Parameters

Name Type Optional Description

mat

module:la.Matrix

 

The matrix.

flag

number

Yes

If set to 0, it normalizes mat by n-1; if set to 1, it normalizes by n.

Defaults to 0.

dim

number

Yes

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.

Defaults to 1.
Returns

ObjectB The object zscoreResult containing:
zscoreResult.sigma - module:la.Vector of standard deviations of mat used to compute the z-scores.
zscoreResult.mu - module:la.Vector of mean values of mat used to compute the z-scores.
zscoreResult.Z - module:la.Matrix of z-scores that has mean 0 and variance 1.