Sample Statistics

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Introduction

The package sample_statistics provides helpers for calculating statistics of numerical samples and generating/exporting histograms. It includes common probability distribution functions and simple random sample generators.

Usage

To use this package include sample_statistics as a dependency in your pubspec.yaml file. The package uses null-safety features and requires Dart SDK version >=2.10.0.

Random Sample Statistics

To access basis sample statistics use the class SampleStats. It calculates most sample statistics in a lazy fashion and caches results to avoid expensive calculations if the same quantity is accessed repeatedly.

 import 'package:sample_statistics/sample_statistics.dart'

 void main() {

   final sample = <num>[-10, 0, 1, 2, 3, 4, 5, 6, 20]
   final stats = SampleStats(sample)

   print('\nRunning statistic_example.dart ...')
   print('Sample: $sample')
   print('min: ${stats.min}')
   print('max:  ${stats.max}')
   print('mean: ${stats.mean}')
   print('median: ${stats.median}')
   print('first quartile:  ${stats.quartile1}')
   print('third quartile:  ${stats.quartile3}')
   print('standard deviation:  ${stats.stdDev}')

   final outliers = sample.removeOutliers();
   print('outliers: $outliers')
   print('sample with outliers removed:  $sample');
 }
Click to show console output.
  $ dart --enable-experiment=non-nullable sample_statistics_example.dart

  Running sample_statistic_example.dart ...
  Sample: [-10, 0, 1, 2, 3, 4, 5, 6, 20]
  min: -10
  max: 20
  mean: 3.4444444444444446
  median: 3
  first quartile: 1
  third quartile: 5
  standard deviation: 7.779960011322538
  outliers:[-10, 20]
  sample with outliers removed: [0, 1, 2, 3, 4, 5, 6]

Random Sample Generators

This package sample_statistics includes functions that can be used to generate random samples.

The function samplePdf is based on the rejection sampling method. It expects a callback of type ProbabilityDensity and can be used to generate random samples that follow an arbitrary probability distribution function. Additinally, the package includes random sample generators based on the following probability distribution functions:

  • normal distribution,
  • truncated normal distribution,
  • exponential distribution,
  • uniform distribution,
  • triangular distribution.
 import 'package:sample_statistics/sample_statistics.dart';

 void main(List<String> args) {
   final min = 1.0;
   final max = 9.0;
   final mean = 5.0;
   final stdDev = 2.0;

   // Generating the random sample with 1000 entries.
   final sample = sampleTruncatedNormalPdf(1000, min, max, mean, stdDev);

   final stats = SampleStats(sample);
   print(stats.mean);
   print(stats.stdDev);
   print(stats.min);

   // Exporting a histogram.
   sample.exportHistogram(
     '../plots/truncated_normal.hist',
     pdf: (x) =>
         truncatedNormalPdf(x, stats.min, stats.max, stats.mean, stats.stdDev),
   );
 }

Histograms

To generate a histogram the first step is to divide the random sample range max - min into a suitable number of intervals. The second step consists of counting how many sample entries fall into each interval.

The method histogram provided by the class SampleStats returns an object of type List<List<num>> (each list entry is a numerical list). The first entry contains the left margins of the histogram intervals or bins. The second entry contains a count of how many sample values fall into each interval. By default, the count is normalized such that the total area under the histogram is equal to 1.0. This is useful when comparing a histogram to a probability density function.

The method histogram accepts the optional parameter probabilityDensity, a function of type ProbabilityDensity. If this function is specified it is used to generate the values in the third list entry by evaluating the probability density function for each interval.

The figure below shows the histograms obtained from two random samples following a truncated normal distribution with min = 1.5, max = 6.0 and parent distribution with mean = 3.0, and stdDev = 1.0. The samples were generated using the function sampleTruncatedNormalPdf.


Histogram


The figure on the left shows the histogram of a sample with size 1000. The figure on the right shows the histogram of a sample with size 6750. Increasing the random sample size leads to an increasingly closer match between the shape of the histogram and the underlying probability distribution.

Using the distribution parameters mentioned above with the function meanTruncatedNormal, one can determine a theoretical mean of 3.134. It can be seen that in the limit of a large sample size the sample mean approaches the mean of the underlying probability distribution.

Examples

For further examples on how to generate random samples, export histograms, and access sample statistics see folder example.

Features and bugs

Please file feature requests and bugs at the issue tracker.

Libraries

sample_statistics
Utilities and functions for calculating sample statistics and generating random samples.