truncatedNormalToNormal function

Future<Map<String, num>> truncatedNormalToNormal(num xMin, num xMax, num meanTruncatedNormal, num stdDevTruncatedNormal, { num stdDevMin = 0.1, num stdDevMax = 5, })

Returns a Future<Map<String, num>> containing the mean and standard deviation of the parent distribution of a truncated normal distribution with:

• xMin: Left limit of the truncated normal distribution,
• xMax: Right limit of the truncated normal distribution. xMin < xMax,
• meanOfTruncatedNormal: mean of the truncated normal,
• stdDevOfTruncatedNormal: standard deviation of the truncated normal.

Important: The function uses a simulated annealing algorithm, and convergence is not strictly guaranteed.

Note: The distribution must have a maximum between xMin and xMax, that is the parent distribution must have xMin < mean < xMax.

Usage:

import 'package:sample_statistics/sample_statistics.dart';
void main(List<String> args) async {
  final xMin = 2.0;
  final xMax = 7.0;
  final meanTruncatedNormal = 4.0;
  final stdDevTruncatedNormal = 2.0;
  final Map<String, double> result = await truncatedNormalToNormal(
      xMin,
      xMax,
      meanTr,
      stdDevTr,
  );

  print('mean: ${result[0]}, stdDev: ${result[1]});
}

Implementation

Future<Map<String, num>> truncatedNormalToNormal(
  num xMin,
  num xMax,
  num meanTruncatedNormal,
  num stdDevTruncatedNormal, {
  num stdDevMin = 0.1,
  num stdDevMax = 5,
}) async {
  final mean = FixedInterval(
    xMin + stdDevMin,
    xMax - stdDevMin,
    name: 'mean',
  );
  final stdDev = FixedInterval(
    stdDevTruncatedNormal / 2,
    stdDevTruncatedNormal * 2,
    name: 'stdDev',
  );
  final space = SearchSpace.fixed(
    [mean, stdDev],
  );

  num logBase(num x, {num base = 10}) {
    return log(x) / log(base);
  }

  // This function will be minimized.
  num energy(List<num> x) {
    final result = (pow(
            meanTruncatedNormal - _meanTruncatedNormal(xMin, xMax, x[0], x[1]),
            2) +
        pow(
            stdDevTruncatedNormal -
                _stdDevTruncatedNormal(xMin, xMax, x[0], x[1]),
            2) +
        epsilon);
    // if (result.isNaN || result.isInfinite) {
    //   print('$x => energy: $result ');
    // }

    return logBase(result);
  }

  final field = EnergyField(energy, space);

  final sim = LoggingSimulator(
    field,
    gammaStart: 0.7,
    gammaEnd: 0.1,
    outerIterations: 150,
    innerIterationsStart: 3,
    innerIterationsEnd: 6,
    sampleSize: 350,
  )
    ..deltaPositionStart = [stdDevTruncatedNormal, meanTruncatedNormal]
    // ..deltaPositionEnd  = [1e-8, 1e-8]
    ..temperatureSequence = exponentialSequence
    ..startPosition = [meanTruncatedNormal, stdDevTruncatedNormal];

  final result = await sim.anneal(
    isRecursive: true,
    ratio: 0.7,
  );

  // await File('example/data/log.dat').writeAsString(sim.export());
  return {'mean': result[0], 'stdDev': result[1]};
}