[][carthage] [][cocoadocs] [][cocoadocs] [][cocoadocs] [cocoadocs]: http://cocoadocs.org/docsets/SigmaSwiftStatistics [carthage]: https://github.com/Carthage/Carthage

This library is a collection of functions that perform statistical calculations in Swift. It can be used in Swift apps for Apple devices and in open source Swift programs on other platforms.

• average
• covariancePopulation
• covarianceSample
• max
• median
• medianHigh
• medianLow
• min
• normalDistribution
• normalDensity
• normalQuantile
• pearson
• percentile1
• standardDeviationPopulation
• standardDeviationSample
• sum
• variancePopulation
• varianceSample

There are four ways you can add Sigma to your project.

Add source (iOS 7+)

Simply add SigmaDistrib.swift file to your project.

Alternatively, add github "evgenyneu/SigmaSwiftStatistics" ~> 4.0 to your Cartfile and run carthage update.

If you are using CocoaPods add this text to your Podfile and run pod install.

use_frameworks!
target 'Your target name'
pod 'SigmaSwiftStatistics', '~> 4.0'

Add the following text to your Package.swift file and run swift build.

import PackageDescription

let package = Package(
    name: "YourPackageName",
    targets: [],
    dependencies: [
        .Package(url: "https://github.com/evgenyneu/SigmaSwiftStatistics.git",
                 versions: Version(4,0,0)..<Version(5,0,0))
    ]
)

Setup a previous version of the library if you use an older version of Swift.

Add import SigmaSwiftStatistics to your source code unless you used the file setup method.

Computes arithmetic mean of values in the array.

Note:

• Returns nil for an empty array.
• Same as AVERAGE in Microsoft Excel and Google Docs Sheets.

A = Σ(x) / n

Where:

• n is the number of values.

Sigma.average([1, 3, 8])
// Result: 4

Computes sample covariance between two variables: x and y.

Note:

• Returns nil if arrays x and y have different number of values.
• Returns nil for empty arrays or arrays containing a single element.
• Same as COVARIANCE.S function in Microsoft Excel.

cov(x,y) = Σ(x - mx)(y - my) / (n - 1)

Where:

• mx is the sample mean of the first variable.
• my is the sample mean of the second variable.
• n is the total number of values.

let x = [1, 2, 3.5, 3.7, 8, 12]
let y = [0.5, 1, 2.1, 3.4, 3.4, 4]
Sigma.covarianceSample(x: x, y: y)
// Result: 5.03

Computes covariance of the entire population between two variables: x and y.

Note:

• Returns nil if arrays x and y have different number of values.
• Returns nil for empty arrays.
• Same as COVAR and COVARIANCE.P functions in Microsoft Excel and COVAR in Google Docs Sheets.

cov(x,y) = Σ(x - mx)(y - my) / n

Where:

• mx is the population mean of the first variable.
• my is the population mean of the second variable.
• n is the total number of values.

let x = [1, 2, 3.5, 3.7, 8, 12]
let y = [0.5, 1, 2.1, 3.4, 3.4, 4]
Sigma.covariancePopulation(x: x, y: y)
// Result: 4.19166666666667

Returns the maximum value in the array.

Note: returns nil for an empty array.

Sigma.max([1, 8, 3])
// Result: 8

Returns the median value from the array.

Note:

• Returns nil when the array is empty.
• Returns the mean of the two middle values if there is an even number of items in the array.
• Same as MEDIAN in Microsoft Excel and Google Docs Sheets.

Sigma.median([1, 12, 19.5, 3, -5])
// Result: 3

Returns the median value from the array.

Note:

• Returns nil when the array is empty.
• Returns the higher of the two middle values if there is an even number of items in the array.

Sigma.medianHigh([1, 12, 19.5, 10, 3, -5])
// Result: 10

Returns the median value from the array.

Note:

• Returns nil when the array is empty.
• Returns the lower of the two middle values if there is an even number of items in the array.

Sigma.medianLow([1, 12, 19.5, 10, 3, -5])
// Result: 3

Returns the minimum value in the array.

Note: returns nil for an empty array.

Sigma.min([7, 2, 3])
// Result: 2

Returns the normal distribution for the given values of x, μ and σ. The returned value is the area under the normal curve to the left of the value x.

Note:

• Returns nil if σ is zero or negative.
• Defaults: μ = 0, σ = 1.
• Same as NORM.S.DIST, NORM.DIST and NORMDIST Excel functions and NORMDIST function in Google Docs sheet with cumulative argument equal to true.

Sigma.normalDistribution(x: -1, μ: 0, σ: 1)
// Result: 0.1586552539314570

Returns density of the normal function for the given values of x, μ and σ.

Note:

• Returns nil if σ is zero or negative.
• Defaults: μ = 0, σ = 1.
• Same as NORM.S.DIST, NORM.DIST and NORMDIST Excel functions and NORMDIST function in Google Docs sheet with cumulative argument equal to false.

Where:

• x is the input value of the normal density function.
• μ is the mean.
• σ is the standard deviation.

Sigma.normalDensity(x: 0, μ: 0, σ: 1)
// Result: 0.3989422804014327

Returns the quantile function for the normal distribution (the inverse of normal distribution). The p argument is the probability, or the area under the normal curve to the left of the returned value.

Note:

• Returns nil if σ is zero or negative.
• Returns nil if p is negative or greater than one.
• Returns -Double.infinity if p is zero, and Double.infinity if p is one.
• Defaults: μ = 0, σ = 1.
• Same as NORM.INV, NORM.S.INV and NORMINV Excel functions and NORMINV, NORMSINV Google Docs sheet functions.

Sigma.normalQuantile(p: 0.025, μ: 0, σ: 1)
// -1.9599639845400538

Calculates the Pearson product-moment correlation coefficient between two variables: x and y.

Note:

• Returns nil if arrays x and y have different number of values.
• Returns nil for empty arrays.
• Same as CORREL and PERSON functions in Microsoft Excel and Google Docs Sheets.

p(x,y) = cov(x,y) / (σx * σy)

Where:

• cov is the population covariance.
• σ is the population standard deviation.

let x = [1, 2, 3.5, 3.7, 8, 12]
let y = [0.5, 1, 2.1, 3.4, 3.4, 4]
Sigma.pearson(x: x, y: y)
// Result: 0.843760859352745

Calculates the Percentile value for the given dataset.

Note:

• Returns nil when the values array is empty.
• Returns nil when supplied percentile parameter is negative or greater than 1.
• Same as PERCENTILE or PERCENTILE.INC in Microsoft Excel and PERCENTILE in Google Docs Sheets.

See the Percentile 1 method documentation for more information.

// Calculate 40th percentile
Sigma.percentile1(values: [35, 20, 50, 40, 15], percentile: 0.4)
// Result: 29

Computes standard deviation based on a sample.

Note:

• Returns nil when the array is empty or contains a single value.
• Same as STDEV and STDEV.S in Microsoft Excel and STDEV in Google Docs Sheets.

s = sqrt( Σ( (x - m)^2 ) / (n - 1) )

Where:

• m is the sample mean.
• n is the sample size.

Sigma.standardDeviationSample([1, 12, 19.5, -5, 3, 8])
// Result: 8.674195447801869

Computes standard deviation of entire population.

Note:

• Returns nil for an empty array.
• Same as STDEVP and STDEV.P in Microsoft Excel and STDEVP in Google Docs Sheets.

σ = sqrt( Σ( (x - m)^2 ) / n )

Where:

• m is the population mean.
• n is the population size.

Sigma.standardDeviationPopulation([1, 12, 19.5, -5, 3, 8])
// Result: 7.918420858282849

Computes sum of values from the array.

Sigma.sum([1, 3, 8])
// Result: 12

Computes variance based on a sample.

Note:

• Returns nil when the array is empty or contains a single value.
• Same as VAR, VAR.S or VARA in Microsoft Excel and VAR or VARA in Google Docs Sheets.

s^2 = Σ( (x - m)^2 ) / (n - 1)

Where:

• m is the sample mean.
• n is the sample size.

Sigma.varianceSample([1, 12, 19.5, -5, 3, 8])
// Result: 75.24166667

Computes variance of entire population.

Note:

• Returns nil when the array is empty.
• Same as VAR.P or VARPA in Microsoft Excel and VARP or VARPA in Google Docs Sheets.

σ^2 = Σ( (x - m)^2 ) / n

Where:

• m is the population mean.
• n is the population size.

Sigma.variancePopulation([1, 12, 19.5, -5, 3, 8])
// Result: 62.70138889

If you need help or want to extend the library feel free to create an issue or submit a pull request.

• Thomas Fankhauser
• John Clema

Sigma is released under the MIT License.