Accord.NET Framework

## FoldedNormalDistribution Class |

Folded Normal (Gaussian) distribution.

Inheritance Hierarchy

SystemObject

Accord.Statistics.DistributionsDistributionBase

Accord.Statistics.Distributions.UnivariateUnivariateContinuousDistribution

Accord.Statistics.Distributions.UnivariateFoldedNormalDistribution

Accord.Statistics.DistributionsDistributionBase

Accord.Statistics.Distributions.UnivariateUnivariateContinuousDistribution

Accord.Statistics.Distributions.UnivariateFoldedNormalDistribution

Syntax

[SerializableAttribute] public class FoldedNormalDistribution : UnivariateContinuousDistribution

The FoldedNormalDistribution type exposes the following members.

Constructors

Name | Description | |
---|---|---|

FoldedNormalDistribution |
Creates a new FoldedNormalDistribution
with zero mean and unit standard deviation.
| |

FoldedNormalDistribution(Double) |
Creates a new FoldedNormalDistribution with
the given mean and unit standard deviation.
| |

FoldedNormalDistribution(Double, Double) |
Creates a new FoldedNormalDistribution with
the given mean and stdDev |

Properties

Name | Description | |
---|---|---|

Entropy |
This method is not supported.
(Overrides UnivariateContinuousDistributionEntropy.) | |

Mean |
Gets the mean for this distribution.
(Overrides UnivariateContinuousDistributionMean.) | |

Median |
Gets the median for this distribution.
(Inherited from UnivariateContinuousDistribution.) | |

Mode |
Gets the mode for this distribution.
(Inherited from UnivariateContinuousDistribution.) | |

Quartiles |
Gets the Quartiles for this distribution.
(Inherited from UnivariateContinuousDistribution.) | |

StandardDeviation |
Gets the Standard Deviation (the square root of
the variance) for the current distribution.
(Inherited from UnivariateContinuousDistribution.) | |

Support |
Gets the support interval for this distribution.
(Overrides UnivariateContinuousDistributionSupport.) | |

Variance |
Gets the variance for this distribution.
(Overrides UnivariateContinuousDistributionVariance.) |

Methods

Name | Description | |
---|---|---|

Clone |
Creates a new object that is a copy of the current instance.
(Overrides DistributionBaseClone.) | |

ComplementaryDistributionFunction |
Gets the complementary cumulative distribution function
(ccdf) for this distribution evaluated at point x.
This function is also known as the Survival function.
(Inherited from UnivariateContinuousDistribution.) | |

CumulativeHazardFunction |
Gets the cumulative hazard function for this
distribution evaluated at point x.
(Inherited from UnivariateContinuousDistribution.) | |

DistributionFunction(Double) |
Gets the cumulative distribution function (cdf) for
this distribution evaluated at point x.
(Inherited from UnivariateContinuousDistribution.) | |

DistributionFunction(Double, Double) |
Gets the cumulative distribution function (cdf) for this
distribution in the semi-closed interval (a; b] given as
P(a < X ≤ b).
(Inherited from UnivariateContinuousDistribution.) | |

Equals | Determines whether the specified object is equal to the current object. (Inherited from Object.) | |

Finalize | Allows an object to try to free resources and perform other cleanup operations before it is reclaimed by garbage collection. (Inherited from Object.) | |

Fit(Double) |
Fits the underlying distribution to a given set of observations.
(Inherited from UnivariateContinuousDistribution.) | |

Fit(Double, IFittingOptions) |
Fits the underlying distribution to a given set of observations.
(Inherited from UnivariateContinuousDistribution.) | |

Fit(Double, Double) |
Fits the underlying distribution to a given set of observations.
(Inherited from UnivariateContinuousDistribution.) | |

Fit(Double, Int32) |
Fits the underlying distribution to a given set of observations.
(Inherited from UnivariateContinuousDistribution.) | |

Fit(Double, Double, IFittingOptions) |
Fits the underlying distribution to a given set of observations.
(Inherited from UnivariateContinuousDistribution.) | |

Fit(Double, Int32, IFittingOptions) |
Fits the underlying distribution to a given set of observations.
(Inherited from UnivariateContinuousDistribution.) | |

Generate |
Generates a random observation from the current distribution.
(Inherited from UnivariateContinuousDistribution.) | |

Generate(Int32) |
Generates a random vector of observations from the current distribution.
(Inherited from UnivariateContinuousDistribution.) | |

Generate(Random) |
Generates a random observation from the current distribution.
(Inherited from UnivariateContinuousDistribution.) | |

Generate(Int32, Double) |
Generates a random vector of observations from the current distribution.
(Inherited from UnivariateContinuousDistribution.) | |

Generate(Int32, Random) |
Generates a random vector of observations from the current distribution.
(Inherited from UnivariateContinuousDistribution.) | |

Generate(Int32, Double, Random) |
Generates a random vector of observations from the current distribution.
(Inherited from UnivariateContinuousDistribution.) | |

GetHashCode | Serves as the default hash function. (Inherited from Object.) | |

GetRange |
Gets the distribution range within a given percentile.
(Inherited from UnivariateContinuousDistribution.) | |

GetType | Gets the Type of the current instance. (Inherited from Object.) | |

HalfNormal |
Creates a new Half-normal distribution with the givenstdDev. The half-normal distribution is a special case
of the FoldedNormalDistribution when location is zero.
| |

HazardFunction |
Gets the hazard function, also known as the failure rate or
the conditional failure density function for this distribution
evaluated at point x.
(Inherited from UnivariateContinuousDistribution.) | |

InnerComplementaryDistributionFunction |
Gets the complementary cumulative distribution function
(ccdf) for this distribution evaluated at point x.
This function is also known as the Survival function.
(Inherited from UnivariateContinuousDistribution.) | |

InnerDistributionFunction |
Gets the cumulative distribution function (cdf) for
this distribution evaluated at point x.
(Overrides UnivariateContinuousDistributionInnerDistributionFunction(Double).) | |

InnerInverseDistributionFunction |
Gets the inverse of the cumulative distribution function (icdf) for
this distribution evaluated at probability p. This function
is also known as the Quantile function.
(Inherited from UnivariateContinuousDistribution.) | |

InnerLogProbabilityDensityFunction |
Gets the log-probability density function (pdf) for
this distribution evaluated at point x.
(Inherited from UnivariateContinuousDistribution.) | |

InnerProbabilityDensityFunction |
Gets the probability density function (pdf) for
this distribution evaluated at point x.
(Overrides UnivariateContinuousDistributionInnerProbabilityDensityFunction(Double).) | |

InverseDistributionFunction |
Gets the inverse of the cumulative distribution function (icdf) for
this distribution evaluated at probability p. This function
is also known as the Quantile function.
(Inherited from UnivariateContinuousDistribution.) | |

LogCumulativeHazardFunction |
Gets the log of the cumulative hazard function for this
distribution evaluated at point x.
(Inherited from UnivariateContinuousDistribution.) | |

LogProbabilityDensityFunction |
Gets the log-probability density function (pdf) for
this distribution evaluated at point x.
(Inherited from UnivariateContinuousDistribution.) | |

MemberwiseClone | Creates a shallow copy of the current Object. (Inherited from Object.) | |

ProbabilityDensityFunction |
Gets the probability density function (pdf) for
this distribution evaluated at point x.
(Inherited from UnivariateContinuousDistribution.) | |

QuantileDensityFunction |
Gets the first derivative of the
inverse distribution function (icdf) for this distribution evaluated
at probability p.
(Inherited from UnivariateContinuousDistribution.) | |

ToString |
Returns a String that represents this instance.
(Inherited from DistributionBase.) | |

ToString(IFormatProvider) |
Returns a String that represents this instance.
(Inherited from DistributionBase.) | |

ToString(String) |
Returns a String that represents this instance.
(Inherited from DistributionBase.) | |

ToString(String, IFormatProvider) |
Returns a String that represents this instance.
(Overrides DistributionBaseToString(String, IFormatProvider).) |

Extension Methods

Name | Description | |
---|---|---|

HasMethod |
Checks whether an object implements a method with the given name.
(Defined by ExtensionMethods.) | |

IsEqual |
Compares two objects for equality, performing an elementwise
comparison if the elements are vectors or matrices.
(Defined by Matrix.) | |

To(Type) | Overloaded.
Converts an object into another type, irrespective of whether
the conversion can be done at compile time or not. This can be
used to convert generic types to numeric types during runtime.
(Defined by ExtensionMethods.) | |

ToT | Overloaded.
Converts an object into another type, irrespective of whether
the conversion can be done at compile time or not. This can be
used to convert generic types to numeric types during runtime.
(Defined by ExtensionMethods.) |

Remarks

The folded normal distribution is a probability distribution related to the normal distribution. Given a normally distributed random variable X with mean μ and variance σ², the random variable Y = |X| has a folded normal distribution. Such a case may be encountered if only the magnitude of some variable is recorded, but not its sign. The distribution is called Folded because probability mass to the left of the x = 0 is "folded" over by taking the absolute value.

The Half-Normal (Gaussian) distribution is a special case of this distribution and can be created using a named constructor.

References:

Examples

This examples shows how to create a Folded Normal distribution and how to compute some of its properties and measures.

// Creates a new Folded Normal distribution based on a Normal // distribution with mean value 4 and standard deviation 4.2: // var fn = new FoldedNormalDistribution(mean: 4, stdDev: 4.2); double mean = fn.Mean; // 4.765653108337438 double median = fn.Median; // 4.2593565881862734 double mode = fn.Mode; // 2.0806531871308014 double var = fn.Variance; // 10.928550450993715 double cdf = fn.DistributionFunction(x: 1.4); // 0.16867109769018807 double pdf = fn.ProbabilityDensityFunction(x: 1.4); // 0.11998602818182187 double lpdf = fn.LogProbabilityDensityFunction(x: 1.4); // -2.1203799747969523 double ccdf = fn.ComplementaryDistributionFunction(x: 1.4); // 0.83132890230981193 double icdf = fn.InverseDistributionFunction(p: cdf); // 1.4 double hf = fn.HazardFunction(x: 1.4); // 0.14433039420191671 double chf = fn.CumulativeHazardFunction(x: 1.4); // 0.18472977144474392 string str = fn.ToString(CultureInfo.InvariantCulture); // FN(x; μ = 4, σ² = 17.64)

See Also