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NakagamiDistribution Class |
Nakagami distribution.
Inheritance HierarchySystemObject
Accord.Statistics.DistributionsDistributionBase
Accord.Statistics.Distributions.UnivariateUnivariateContinuousDistribution
Accord.Statistics.Distributions.UnivariateNakagamiDistribution
Accord.Statistics.DistributionsDistributionBase
Accord.Statistics.Distributions.UnivariateUnivariateContinuousDistribution
Accord.Statistics.Distributions.UnivariateNakagamiDistribution
Namespace: Accord.Statistics.Distributions.Univariate
Assembly: Accord.Statistics (in Accord.Statistics.dll) Version: 3.8.0
Syntax[SerializableAttribute] public class NakagamiDistribution : UnivariateContinuousDistribution, ISampleableDistribution<double>, IDistribution<double>, IDistribution, ICloneable, IRandomNumberGenerator<double>, IFormattable
The NakagamiDistribution type exposes the following members.
Constructors| Name | Description | |
|---|---|---|
 | NakagamiDistribution |
Initializes a new instance of the NakagamiDistribution class.
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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.
(Overrides UnivariateContinuousDistributionMode.) |
| Quartiles |
Gets the Quartiles for this distribution.
(Inherited from UnivariateContinuousDistribution.) |
| Shape |
Gets the distribution's shape parameter μ (mu).
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| Spread |
Gets the distribution's spread parameter ω (omega).
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| 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.) |
 | Estimate(Double) |
Estimates a new Nakagami distribution from a given set of observations.
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| Estimate(Double, Double) |
Estimates a new Nakagami distribution from a given set of observations.
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 | 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.
(Overrides UnivariateContinuousDistributionFit(Double, Double, IFittingOptions).) |
| 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(Random) |
Generates a random observation from the current distribution.
(Overrides UnivariateContinuousDistributionGenerate(Random).) |
| Generate(Int32) |
Generates a random vector of observations 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.
(Overrides UnivariateContinuousDistributionGenerate(Int32, Double, Random).) |
| 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.
(Inherited from UnivariateContinuousDistribution.) |
| InnerLogProbabilityDensityFunction |
Gets the log-probability density function (pdf) for
this distribution evaluated at point x.
(Overrides UnivariateContinuousDistributionInnerLogProbabilityDensityFunction(Double).) |
| 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.) |
| Random(Double, Double) |
Generates a random observation from the
Nakagami distribution with the given parameters.
|
| Random(Double, Double, Int32) |
Generates a random vector of observations from the
Nakagami distribution with the given parameters.
|
| Random(Double, Double, Random) |
Generates a random observation from the
Nakagami distribution with the given parameters.
|
| Random(Double, Double, Int32, Double) |
Generates a random vector of observations from the
Nakagami distribution with the given parameters.
|
| Random(Double, Double, Int32, Random) |
Generates a random vector of observations from the
Nakagami distribution with the given parameters.
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| Random(Double, Double, Int32, Double, Random) |
Generates a random vector of observations from the
Nakagami distribution with the given parameters.
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| 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 Nakagami distribution has been used in the modeling of wireless signal attenuation while traversing multiple paths.
References:
- Wikipedia, The Free Encyclopedia. Nakagami distribution. Available on: http://en.wikipedia.org/wiki/Nakagami_distribution
- Laurenson, Dave (1994). "Nakagami Distribution". Indoor Radio Channel Propagation Modeling by Ray Tracing Techniques.
- R. Kolar, R. Jirik, J. Jan (2004) "Estimator Comparison of the Nakagami-m Parameter and Its Application in Echocardiography", Radioengineering, 13 (1), 8–12
Examplesvar nakagami = new NakagamiDistribution(shape: 2.4, spread: 4.2); double mean = nakagami.Mean; // 1.946082119049118 double median = nakagami.Median; // 1.9061151110206338 double var = nakagami.Variance; // 0.41276438591729486 double cdf = nakagami.DistributionFunction(x: 1.4); // 0.20603416752368109 double pdf = nakagami.ProbabilityDensityFunction(x: 1.4); // 0.49253215371343023 double lpdf = nakagami.LogProbabilityDensityFunction(x: 1.4); // -0.708195533773302 double ccdf = nakagami.ComplementaryDistributionFunction(x: 1.4); // 0.79396583247631891 double icdf = nakagami.InverseDistributionFunction(p: cdf); // 1.400000000131993 double hf = nakagami.HazardFunction(x: 1.4); // 0.62034426869133652 double chf = nakagami.CumulativeHazardFunction(x: 1.4); // 0.23071485080660473 string str = nakagami.ToString(CultureInfo.InvariantCulture); // Nakagami(x; μ = 2,4, ω = 4,2)"
See Also