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BirnbaumSaundersDistribution Class |
Birnbaum-Saunders (Fatigue Life) distribution.
Inheritance HierarchySystemObject
Accord.Statistics.DistributionsDistributionBase
Accord.Statistics.Distributions.UnivariateUnivariateContinuousDistribution
Accord.Statistics.Distributions.UnivariateBirnbaumSaundersDistribution
Accord.Statistics.DistributionsDistributionBase
Accord.Statistics.Distributions.UnivariateUnivariateContinuousDistribution
Accord.Statistics.Distributions.UnivariateBirnbaumSaundersDistribution
Namespace: Accord.Statistics.Distributions.Univariate
Assembly: Accord.Statistics (in Accord.Statistics.dll) Version: 3.8.0
Syntax[SerializableAttribute] public class BirnbaumSaundersDistribution : UnivariateContinuousDistribution
The BirnbaumSaundersDistribution type exposes the following members.
Constructors| Name | Description | |
|---|---|---|
 | BirnbaumSaundersDistribution |
Constructs a Birnbaum-Saunders distribution
with location parameter 0, scale 1, and shape 1.
|
| BirnbaumSaundersDistribution(Double) |
Constructs a Birnbaum-Saunders distribution
with location parameter 0, scale 1, and the
given shape.
|
| BirnbaumSaundersDistribution(Double, Double, Double) |
Constructs a Birnbaum-Saunders distribution
with given location, shape and scale parameters.
|
Properties| Name | Description | |
|---|---|---|
 | Entropy |
This method is not supported.
(Overrides UnivariateContinuousDistributionEntropy.) |
| Location |
Gets the distribution's location parameter μ.
|
| Mean |
Gets the mean for this distribution.
(Overrides UnivariateContinuousDistributionMean.) |
| Median |
Gets the median for this distribution.
(Inherited from UnivariateContinuousDistribution.) |
| Mode |
This method is not supported.
(Overrides UnivariateContinuousDistributionMode.) |
| Quartiles |
Gets the Quartiles for this distribution.
(Inherited from UnivariateContinuousDistribution.) |
| Scale |
Gets the distribution's scale parameter β.
|
| Shape |
Gets the distribution's shape parameter γ.
|
| 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.) |
| 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.
(Overrides UnivariateContinuousDistributionInnerInverseDistributionFunction(Double).) |
| 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.) |
RemarksThe Birnbaum–Saunders distribution, also known as the fatigue life distribution, is a probability distribution used extensively in reliability applications to model failure times. There are several alternative formulations of this distribution in the literature. It is named after Z. W. Birnbaum and S. C. Saunders.
References:
- Wikipedia, The Free Encyclopedia. Birnbaum–Saunders distribution. Available from: http://en.wikipedia.org/wiki/Birnbaum%E2%80%93Saunders_distribution
- NIST/SEMATECH e-Handbook of Statistical Methods, Birnbaum-Saunders (Fatigue Life) Distribution Available from: http://www.itl.nist.gov/div898/handbook/eda/section3/eda366a.htm
ExamplesThis example shows how to create a Birnbaum-Saunders distribution and compute some of its properties.
// Creates a new Birnbaum-Saunders distribution var bs = new BirnbaumSaundersDistribution(shape: 0.42); double mean = bs.Mean; // 1.0882000000000001 double median = bs.Median; // 1.0 double var = bs.Variance; // 0.21529619999999997 double cdf = bs.DistributionFunction(x: 1.4); // 0.78956384911580346 double pdf = bs.ProbabilityDensityFunction(x: 1.4); // 1.3618433601225426 double lpdf = bs.LogProbabilityDensityFunction(x: 1.4); // 0.30883919386130815 double ccdf = bs.ComplementaryDistributionFunction(x: 1.4); // 0.21043615088419654 double icdf = bs.InverseDistributionFunction(p: cdf); // 2.0618330099769064 double hf = bs.HazardFunction(x: 1.4); // 6.4715276077824093 double chf = bs.CumulativeHazardFunction(x: 1.4); // 1.5585729930861034 string str = bs.ToString(CultureInfo.InvariantCulture); // BirnbaumSaunders(x; μ = 0, β = 1, γ = 0.42)
See Also