PHP Класс MathPHP\Statistics\Descriptive

IQR() публичный статический Метод

IQR - Interquartile range (midspread, middle fifty) Convenience wrapper function for interquartileRange.

public static IQR ( array $numbers, string $method = 'exclusive' ) : number
$numbers	array
$method	string	What quartile method to use (optional - default: exclusive)
Результат	number

coefficientOfVariation() публичный статический Метод

A standardized measure of dispersion of a probability distribution or frequency distribution. It is often expressed as a percentage. The ratio of the standard deviation to the mean. https://en.wikipedia.org/wiki/Coefficient_of_variation σ cᵥ = - μ

public static coefficientOfVariation ( array $numbers ) : number
$numbers	array
Результат	number

describe() публичный статический Метод

Get a report of all the descriptive statistics over a list of numbers Includes mean, median, mode, range, midrange, variance, standard deviation, quartiles, etc.

public static describe ( array $numbers, boolean $population = false ) : array
$numbers	array
$population	boolean
Результат	array	[ n, mean, median, mode, range, midrange, variance, sd, CV, mean_mad, median_mad, quartiles, skewness, kurtosis, sem, ci_95, ci_99 ]

fiveNumberSummary() публичный статический Метод

It consists of the five most important sample percentiles: 1) the sample minimum (smallest observation) 2) the lower quartile or first quartile 3) the median (middle value) 4) the upper quartile or third quartile 5) the sample maximum (largest observation) https://en.wikipedia.org/wiki/Five-number_summary

public static fiveNumberSummary ( array $numbers ) : array
$numbers	array
Результат	array	[min, Q1, median, Q3, max]

interquartileRange() публичный статический Метод

Difference between the upper and lower quartiles. https://en.wikipedia.org/wiki/Interquartile_range IQR = Q₃ - Q₁

public static interquartileRange ( array $numbers, string $method = 'exclusive' ) : number
$numbers	array
$method	string	What quartile method to use (optional - default: exclusive)
Результат	number

meanAbsoluteDeviation() публичный статический Метод

The average of the absolute deviations from a central point. It is a summary statistic of statistical dispersion or variability. (https://en.wikipedia.org/wiki/Average_absolute_deviation) ∑|xᵢ - x̄| MAD = --------- N x̄ is the mean N is the number of numbers in the population set

public static meanAbsoluteDeviation ( array $numbers ) : numeric
$numbers	array
Результат	numeric

medianAbsoluteDeviation() публичный статический Метод

The average of the absolute deviations from a central point. It is a summary statistic of statistical dispersion or variability. It is a robust measure of the variability of a univariate sample of quantitative data. (https://en.wikipedia.org/wiki/Median_absolute_deviation) MAD = median(|xᵢ - x̄|) x̄ is the median

public static medianAbsoluteDeviation ( array $numbers ) : numeric
$numbers	array
Результат	numeric

midhinge() публичный статический Метод

Equivalently, it is the 25% trimmed mid-range or 25% midsummary; it is an L-estimator. https://en.wikipedia.org/wiki/Midhinge Midhinge = (first quartile, third quartile) / 2

public static midhinge ( array $numbers ) : number
$numbers	array
Результат	number

midrange() публичный статический Метод

(https://en.wikipedia.org/wiki/Mid-range) max x + min x M = ------------- 2

public static midrange ( array $numbers ) : number
$numbers	array
Результат	number

percentile() публичный статический Метод

Nearest rank method P-th percentile (0 <= P <= 100) of a list of N ordered values (sorted from least to greatest) is the smallest value in the list such that P percent of the data is less than or equal to that value. This is obtained by first calculating the ordinal rank, and then taking the value from the ordered list that corresponds to that rank. https://en.wikipedia.org/wiki/Percentile ⌈ P ⌉ n = | --- × N | | 100 | n: ordinal rank P: percentile N: number of elements in list

public static percentile ( array $numbers, integer $P ) : number
$numbers	array
$P	integer	percentile to calculate
Результат	number	in list corresponding to P percentile

populationVariance() публичный статический Метод

If used with a subset of data (sample variance), it will be a biased variance. ∑⟮xᵢ - μ⟯² σ² = ---------- N μ is the population mean N is the number of numbers in the population set

public static populationVariance ( array $numbers ) : numeric
$numbers	array
Результат	numeric

quartiles() публичный статический Метод

https://en.wikipedia.org/wiki/Quartile There are multiple methods for computing quartiles: - Inclusive - Exclusive

public static quartiles ( array $numbers, string $method = 'exclusive' ) : array
$numbers	array
$method	string	What quartile method to use (optional - default: exclusive)
Результат	array	[ 0%, Q1, Q2, Q3, 100%, IQR ]

quartilesExclusive() публичный статический Метод

https://en.wikipedia.org/wiki/Quartile 0% is smallest number Q1 (25%) is first quartile (lower quartile, 25th percentile) Q2 (50%) is second quartile (median, 50th percentile) Q3 (75%) is third quartile (upper quartile, 75th percentile) 100% is largest number interquartile_range is the difference between the upper and lower quartiles. (IQR = Q₃ - Q₁) Method used - Use the median to divide the ordered data set into two halves. - If there are an odd number of data points in the original ordered data set, do not include the median (the central value in the ordered list) in either half. - If there are an even number of data points in the original ordered data set, split this data set exactly in half. - The lower quartile value is the median of the lower half of the data. The upper quartile value is the median of the upper half of the data. This rule is employed by the TI-83 calculator boxplot and "1-Var Stats" functions. This is the most basic method that is commonly taught in math textbooks.

public static quartilesExclusive ( array $numbers ) : array
$numbers	array
Результат	array	[ 0%, Q1, Q2, Q3, 100%, IQR ]

quartilesInclusive() публичный статический Метод

https://en.wikipedia.org/wiki/Quartile 0% is smallest number Q1 (25%) is first quartile (lower quartile, 25th percentile) Q2 (50%) is second quartile (median, 50th percentile) Q3 (75%) is third quartile (upper quartile, 75th percentile) 100% is largest number interquartile_range is the difference between the upper and lower quartiles. (IQR = Q₃ - Q₁) Method used - Use the median to divide the ordered data set into two halves. - If there are an odd number of data points in the original ordered data set, include the median (the central value in the ordered list) in both halves. - If there are an even number of data points in the original ordered data set, split this data set exactly in half. - The lower quartile value is the median of the lower half of the data. The upper quartile value is the median of the upper half of the data. The values found by this method are also known as "Tukey's hinges". This is the method that the programming language R uses by default.

public static quartilesInclusive ( array $numbers ) : array
$numbers	array
Результат	array	[ 0%, Q1, Q2, Q3, 100%, IQR ]

range() публичный статический Метод

It provides an indication of statistical dispersion. (https://en.wikipedia.org/wiki/Range_(statistics)) R = max x - min x

public static range ( array $numbers ) : number
$numbers	array
Результат	number

sampleVariance() публичный статический Метод

∑⟮xᵢ - x̄⟯² S² = ---------- n - 1 x̄ is the sample mean n is the number of numbers in the sample set

public static sampleVariance ( array $numbers ) : numeric
$numbers	array
Результат	numeric

sd() публичный статический Метод

sd - Standard deviation - convenience method

public static sd ( array $numbers, boolean $SD＋ = false ) : numeric
$numbers	array
$SD＋	boolean
Результат	numeric

standardDeviation() публичный статический Метод

A low standard deviation indicates that the data points tend to be close to the mean (also called the expected value) of the set. A high standard deviation indicates that the data points are spread out over a wider range of values. (https://en.wikipedia.org/wiki/Standard_deviation) σ = √⟮σ²⟯ = √⟮variance⟯ SD+ = √⟮σ²⟯ = √⟮sample variance⟯

public static standardDeviation ( array $numbers, boolean $SD＋ = false ) : numeric
$numbers	array
$SD＋	boolean
Результат	numeric

variance() публичный статический Метод

Variance measures how far a set of numbers are spread out. A variance of zero indicates that all the values are identical. Variance is always non-negative: a small variance indicates that the data points tend to be very close to the mean (expected value) and hence to each other. A high variance indicates that the data points are very spread out around the mean and from each other. (https://en.wikipedia.org/wiki/Variance) ∑⟮xᵢ - μ⟯² σ² = ---------- ν Generalized method that allows setting the degrees of freedom. For population variance, set d.f. (ν) to n For sample variance, set d.f (ν) to n - 1 Or use popluationVariance or sampleVaraince covenience methods. μ is the population mean ν is the degrees of freedom, which usually is the number of numbers in the population set or n - 1 for sample set.

public static variance ( array $numbers, integer $ν ) : numeric
$numbers	array
$ν	integer	degrees of freedom
Результат	numeric