statistics

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Statistics package for easy and efficient data manipulation with built-in Bayesian Network (Bayes Net), many mathematical functions and tools.

API Documentation

See the API Documentation for a full list of functions, classes and extension.

Usage

Numeric extension:

import 'package:statistics/statistics.dart';

void main() {
  var ns = [10, 20.0, 30];
  print('ns: $ns');

  var mean = ns.mean;
  print('mean: $mean');

  var sdv = ns.standardDeviation;
  print('sdv: $sdv');

  var squares = ns.square;
  print('squares: $squares');
}

OUTPUT:

ns: [10, 20.0, 30]
mean: 20.0
sdv: 8.16496580927726
squares: [100.0, 400.0, 900.0]

Statistics

The class Statistics, that have many pre-computed statistics, can be generated from a numeric collection:

import 'package:statistics/statistics.dart';

void main() {
  var ns = [10, 20.0, 25, 30];
  var statistics = ns.statistics;

  print('Statistics.max: ${ statistics.max }');
  print('Statistics.min: ${ statistics.min }');
  print('Statistics.mean: ${ statistics.mean }');
  print('Statistics.standardDeviation: ${ statistics.standardDeviation }');
  print('Statistics.sum: ${ statistics.sum }');
  print('Statistics.center: ${ statistics.center }');
  print('Statistics.median: ${statistics.median} -> ${statistics.medianLow} , ${statistics.medianHigh}');
  print('Statistics.squaresSum: ${ statistics.squaresSum }');

  print('Statistics: $statistics');
}

OUTPUT:

Statistics.max: 30
Statistics.min: 10
Statistics.mean: 21.25
Statistics.standardDeviation: 7.39509972887452
Statistics.sum: 85.0
Statistics.center: 25
Statistics.median: 22.5 -> 20.0 , 25
Statistics.squaresSum: 2025.0
Statistics: {~21.25 +-7.3950 [10..(25)..30] #4}

Bayesian Network

Bayesian Network, also known as Bayes Network, is a very important tool in understanding the dependency among events and assigning probabilities to them.

Here's an example of how to build a BayesianNetwork.

import 'package:statistics/statistics.dart';

void main(){
  var bayesNet = BayesianNetwork('cancer');

  // C (cancer) = T (true) ; F (false)
  bayesNet.addVariable("C", [
    'F',
    'T',
  ], [], [
    "C = F: 0.99",
    "C = T: 0.01",
  ]);

  // X (exam) = P (positive) ; N (negative)
  bayesNet.addVariable("X", [
    '+P',
    '-N',
  ], [
    "C"
  ], [
    "X = N, C = F: 0.91",
    "X = P, C = F: 0.09",
    "X = N, C = T: 0.10",
    "X = P, C = T: 0.90",
  ]);

  // Show the network nodes and probabilities:
  print(bayesNet);

  var analyser = bayesNet.analyser;

  // Ask the probability to have cancer with a positive exame (X = P): 
  var answer1 = analyser.ask('P(c|x)');
  print(answer1); // P(c|x) -> C = T | X = P -> 0.09174311926605506 (0.009000000000000001) >> 917.43%

  // Ask the probability to have cancer with a negative exame (X = N):
  var answer2 = analyser.ask('P(c|-x)');
  print(answer2); // P(c|-x) -> C = T | X = N -> 0.0011087703736556158 (0.001) >> 11.09%
}

Variable Dependency

To support variables dependencies you can use the method addDependency:

import 'package:statistics/statistics.dart';

void main() {
  // ** Note that this example is NOT USING REAL probabilities for Cancer!
  
  var bayesNet = BayesianNetwork('cancer');

  // C (cancer) = T (true) ; F (false)
  bayesNet.addVariable("C", [
    'F',
    'T',
  ], [], [
    "C = F: 0.99",
    "C = T: 0.01",
  ]);

  // X (exam) = P (positive) ; N (negative)
  bayesNet.addVariable("X", [
    '+P',
    '-N',
  ], [
    "C"
  ], [
    "X = N, C = F: 0.91",
    "X = P, C = F: 0.09",
    "X = N, C = T: 0.10",
    "X = P, C = T: 0.90",
  ]);

  // D (Doctor diagnosis) = P (positive) ; N (negative)
  bayesNet.addVariable("D", [
    '+P',
    '-N',
  ], [
    "C"
  ], [
    "D = N, C = F: 0.99",
    "D = P, C = F: 0.01",
    "D = N, C = T: 0.75",
    "D = P, C = T: 0.25",
  ]);

  // Add dependency between D (Doctor diagnosis) and X (Exam),
  // where the probability of a correct diagnosis is improved:
  bayesNet.addDependency([
    'D',
    'X'
  ], [
    "D = N, X = N, C = F: 0.364",
    "D = P, X = N, C = F: 0.546",
    "D = N, X = P, C = F: 0.036",
    "D = P, X = P, C = F: 0.054",

    "D = N, X = N, C = T: 0.025",
    "D = N, X = P, C = T: 0.075",
    "D = P, X = N, C = T: 0.225",
    "D = P, X = P, C = T: 0.675",
  ]);

  // Show the network nodes and probabilities:
  print(bayesNet);

  var analyser = bayesNet.analyser;
  
  // Ask the probability to have cancer with a positive exame (X = P):
  var answer1 = analyser.ask('P(c|x)');
  print(answer1); // P(c|x) -> C = T | X = P -> 0.09174311926605506 (0.009000000000000001) >> 917.43%

  // Ask the probability to have cancer with a negative exame (X = N):
  var answer2 = analyser.ask('P(c|-x)');
  print(answer2); // P(c|-x) -> C = T | X = N -> 0.0011087703736556158 (0.001) >> 11.09%

  // Ask the probability to have cancer with a positive diagnosis from the Doctor (D = P):
  var answer3 = analyser.ask('P(c|d)');
  print(answer3); // P(c|d) -> C = T | D = P -> 0.20161290322580644 (0.0025) >> 2016.13%

  // Ask the probability to have cancer with a negative diagnosis from the Doctor (D = N):
  var answer4 = analyser.ask('P(c|-d)');
  print(answer4); // P(c|-d) -> C = T | D = N -> 0.007594167679222358 (0.0075) >> 75.94%

  // Ask the probability to have cancer with a positive diagnosis from the Doctor and a positive exame (D = P, X = P):
  var answer5 = analyser.ask('P(c|d,x)');
  print(answer5); // P(c|d,x) -> C = T | D = P, X = P -> 0.11210762331838567 (0.006750000000000001) >> 1121.08%

  // Ask the probability to have cancer with a negative diagnosis from the Doctor and a negative exame (D = N, X = N):
  var answer6 = analyser.ask('P(c|-d,-x)');
  print(answer6); // P(c|-d,-x) -> C = T | D = N, X = N -> 0.0006932697373894235 (0.00025) >> 6.93%
}

See a full example for Bayes Net with Variable Dependency at GitHub:

Event Monitoring

To help to generate the probabilities you can use the BayesEventMonitor class and then build the BayesianNetwork:

import 'package:statistics/statistics.dart';

void main() {
  // Monitor events to then build a Bayesian Network:
  // ** Note that this example is NOT USING REAL probabilities for Cancer!
  var eventMonitor = BayesEventMonitor('cancer');

  // The prevalence of Cancer in the population:
  // - 1% (10:990):

  for (var i = 0; i < 990; ++i) {
    eventMonitor.notifyEvent(['CANCER=false']);
  }

  for (var i = 0; i < 10; ++i) {
    eventMonitor.notifyEvent(['CANCER=true']);
  }

  // The Exam performance when the person have cancer:
  // - 90% Sensitivity.
  // - 10% false negative (1:9).

  for (var i = 0; i < 9; ++i) {
    eventMonitor.notifyEvent(['EXAM=positive', 'CANCER=true']);
  }

  for (var i = 0; i < 1; ++i) {
    eventMonitor.notifyEvent(['EXAM=negative', 'CANCER=true']);
  }

  // The Exam performance when the person doesn't have cancer:
  // - 91% Specificity
  // - 9% false positive (89:901).

  for (var i = 0; i < 901; ++i) {
    eventMonitor.notifyEvent(['EXAM=negative', 'CANCER=false']);
  }
  for (var i = 0; i < 89; ++i) {
    eventMonitor.notifyEvent(['EXAM=positive', 'CANCER=false']);
  }

  var bayesNet = eventMonitor.buildBayesianNetwork();

  var analyser = bayesNet.analyser;

  var answer1 = analyser.ask('P(cancer)');
  print('- Cancer probability without an Exam:');
  print('  $answer1'); // P(cancer) -> CANCER = TRUE |  -> 0.01 >> 100.00%

  var answer2 = analyser.ask('P(cancer|exam)');
  print('- Cancer probability with a positive Exam:');
  print('  $answer2'); // P(cancer|exam) -> CANCER = TRUE | EXAM = POSITIVE -> 0.09183673469387756 (0.009000000000000001) >> 918.37%
}

See a full example for Bayes Net at GitHub:

CSV

To generate a CSV document, just use the extension generateCSV in your data collection. You can pass the parameter separator to change the value separator (default: ,).

import 'package:statistics/statistics.dart';

void main() {
  var categories = <String, List<double?>>{
    'a': [10.0, 20.0, null],
    'b': [100.0, 200.0, 300.0]
  };

  var csv = categories.generateCSV();
  print(csv);
}

OUTPUT:

#,a,b
1,10.0,100.0
2,20.0,200.0
3,0.0,300.0

High-Precision Arithmetic

For high-precision arithmetics you can use DynamicInt and Decimal classes. Both implements DynamicNumber and are interchangeable in operations.

  • DynamicInt:

    • An integer that internally uses a native or BigInt representation.
    • When a native DynamicInt operation will overflow DynamicInt.isSafeInteger it will expand the internal representation using a BigInt.
  • Decimal:

    • A decimal number with variable decimal precision. The precision can be defined in the constructor or is identified automatically while parsing or converting a number to Decimal.
    • If an operation needs more precision to correctly represent a Decimal the precision will be expanded.
    • The internal representation uses a DynamicInt.

The main motivation of this high-Precision Arithmetic implementation is to have an internal representation that avoid the use of BigInt unless is really needed, avoiding slow BigInt operations and extra memory. Also, this implementation allows power with high precision and power with decimal exponents, what is not present int many libraries.

Example:

import 'package:statistics/statistics.dart';

void main(){
  var n1 = DynamicInt.fromInt(123) + Decimal.parse('0.456');
  print(n1); // 123.456

  var n2 = Decimal.parse('0.1') + Decimal.parse('0.2');
  print(n2); // 0.3

  // Using `toDecimal` extension to convert an `int` to `Decimal`:
  var n3 = 123.toDecimal().powerInt(41); // power with an integer exponent. 
  print(n3); // 48541095000524544750127162673405880068636916264012200797813591925035550682238127143323.0

  var n4 = 2.toDecimal().powerDouble(2.2); // power with a double exponent.
  print(n4); // 4.594793419988

  // Using `toDynamicInt` extension to convert an `int` to `DynamicInt`:
  var n5 = 2.toDynamicInt().powerInt(-1); // power with a negative exponent.
  print(n5); // 0.5
}

See the API Documentation for a full documentation of DynamicInt and Decimal.

Tools

Parsers:

Formatters:

Extension:

See the API Documentation for a full list of functions, extension and classes.

data_serializer

The statistics package exports the package data_serializer to help the handling of primitives, data, bytes and files.

  • Some extension in data_serializer were originally in the statistics package.

Test Coverage

Codecov

This package aims to always have a high test coverage percentage, over 95%. With that the package can be a reliable tool to support your important projects.

Source

The official source code is hosted @ GitHub:

Features and bugs

Please file feature requests and bugs at the issue tracker.

Contribution

Any help from the open-source community is always welcome and needed:

  • Found an issue?
    • Please fill a bug report with details.
    • Wish a feature?
      • Open a feature request with use cases.
    • Are you using and liking the project?
      • Promote the project: create an article, do a post or make a donation.
    • Are you a developer?
      • Fix a bug and send a pull request.
      • Implement a new feature.
      • Improve the Unit Tests.
    • Have you already helped in any way?
      • Many thanks from me, the contributors and everybody that uses this project!

If you donate 1 hour of your time, you can contribute a lot, because others will do the same, just be part and start with your 1 hour.

Author

Graciliano M. Passos: gmpassos@GitHub.

License

Apache License - Version 2.0

See Also

Take a look at SciDart, an experimental cross-platform scientific library for Dart by Angelo Polotto.

Libraries

statistics
Statistics library.