statistics
Statistics package for easy and efficient data manipulation with builtin 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 precomputed 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(cx)');
print(answer1); // P(cx) > 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(cx)');
print(answer2); // P(cx) > 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(cx)');
print(answer1); // P(cx) > 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(cx)');
print(answer2); // P(cx) > 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(cd)');
print(answer3); // P(cd) > 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(cd)');
print(answer4); // P(cd) > 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(cd,x)');
print(answer5); // P(cd,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(cd,x)');
print(answer6); // P(cd,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(cancerexam)');
print(' Cancer probability with a positive Exam:');
print(' $answer2'); // P(cancerexam) > 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
HighPrecision Arithmetic
For highprecision arithmetics you can use DynamicInt
and Decimal
classes.
Both implements DynamicNumber
and are interchangeable in operations.

 An integer that internally uses a native or
BigInt
representation.  When a native
DynamicInt
operation will overflowDynamicInt.isSafeInteger
it will expand the internal representation using aBigInt
.
 An integer that internally uses a native or

 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
.
 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
The main motivation of this highPrecision 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:
 parseDouble
 parseInt
 parseNum
 parseDateTime
 All parses accepts a
dynamic
value as input and have a default value parameterdef
.
Formatters:
 formatDecimal
 DateTimeExtension.formatToYMD
 DateTimeExtension.formatToYMDHm
 DateTimeExtension.formatToYMDHms
 DateTimeExtension.formatToYMDHmZ
 DateTimeExtension.formatToYMDHmsZ
Extension:
 StringExtension.splitLines
 StringExtension.splitColumns
 StringExtension.containsAny
 IterableIterableExtension.toKeysMap
 IterableStringExtension.filterLines
 IterableStringExtension.toIntsList
 IterableStringExtension.toDoublesList
 IterableStringExtension.toNumsList
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 thestatistics
package.
Test Coverage
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 opensource 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
See Also
Take a look at SciDart, an experimental crossplatform scientific library for Dart by Angelo Polotto.
Libraries
 statistics
 Statistics library.