IGLib
1.7.2
The IGLib base library EXTENDED - with other lilbraries and applications.
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Represents a discrete distribution as a continous distribution. More...
Public Member Functions | |||
DiscreteAsContinuousDistribution (DiscreteDistribution distribution) | |||
Initializes a new shim that represents a discrete distribution as a continuous distribution. More... | |||
DiscreteAsContinuousDistribution (DiscreteDistribution distribution, Interval support) | |||
Initializes a new shim that represents a discrete distribution as a continuous distribution. More... | |||
override double | LeftProbability (double x) | ||
Returns the cumulative probability to the left of (below) the given point.
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override double | RightProbability (double x) | ||
Return the cumulative probability to the right of (above) the given point.
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override double | ProbabilityDensity (double x) | ||
Not valid for discrete distributions. More... | |||
override double | Moment (int n) | ||
Computes a raw moment of the distribution.
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override double | MomentAboutMean (int n) | ||
Computes a central moment of the distribution.
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override double | InverseLeftProbability (double P) | ||
Returns the point at which the cumulative distribution function attains a given value.
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virtual double | InverseRightProbability (double Q) | ||
Returns the point at which the right probability function attains the given value. More... | |||
override double | Moment (int r) | ||
Computes a raw moment of the distribution.
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override double | MomentAboutMean (int r) | ||
Computes a central moment of the distribution.
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virtual double | ExpectationValue (Func< double, double > f) | ||
Computes the expectation value of the given function. More... | |||
virtual double | GetRandomValue (Random rng) | ||
Returns a random value. More... | |||
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virtual double | Cumulant (int r) | ||
Computes a cumulant of the distribution. More... | |||
Properties | |
override double | Mean [get] |
override double | Variance [get] |
override double | Skewness [get] |
override Interval | Support [get] |
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virtual double | Median [get] |
Gets the median of the distribution. More... | |
virtual Interval | Support [get] |
Gets the interval over which the distribution is nonvanishing. More... | |
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virtual double | Mean [get] |
Gets the mean of the distribution. More... | |
virtual double | Variance [get] |
Gets the variance of the distribution. More... | |
virtual double | StandardDeviation [get] |
Gets the standard deviation of the distribution. More... | |
virtual double | Skewness [get] |
Gets the skewness of the distribution. More... | |
virtual double | ExcessKurtosis [get] |
Gets the excess kurtosis of the distribution. More... | |
Private Member Functions | |
void | ComputeEffectiveBin (double x, out int ki, out double kf) |
Private Attributes | |
DiscreteDistribution | d |
Interval | xSupport |
Represents a discrete distribution as a continous distribution.
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inline |
Initializes a new shim that represents a discrete distribution as a continuous distribution.
distribution | The discrete distiribution to represent. |
References Meta.Numerics.Interval.FromEndpoints().
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inline |
Initializes a new shim that represents a discrete distribution as a continuous distribution.
distribution | The discrete distiribution to represent. |
support | The continuous support interval into which the discrete support interval is to be mapped. |
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inlineprivate |
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inlinevirtual |
Returns the cumulative probability to the left of (below) the given point.
x | The reference point. |
Reimplemented from Meta.Numerics.Statistics.Distributions.Distribution.
References Meta.Numerics.Interval.LeftEndpoint, Meta.Numerics.Statistics.Distributions.DiscreteDistribution.LeftExclusiveProbability(), Meta.Numerics.Statistics.Distributions.DiscreteDistribution.ProbabilityMass(), and Meta.Numerics.Interval.RightEndpoint.
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inlinevirtual |
Return the cumulative probability to the right of (above) the given point.
x | The reference point. |
Reimplemented from Meta.Numerics.Statistics.Distributions.Distribution.
References Meta.Numerics.Interval.LeftEndpoint, Meta.Numerics.Statistics.Distributions.DiscreteDistribution.ProbabilityMass(), Meta.Numerics.Interval.RightEndpoint, and Meta.Numerics.Statistics.Distributions.DiscreteDistribution.RightExclusiveProbability().
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inlinevirtual |
Not valid for discrete distributions.
x | The argument. |
Technically, the PDF of a discrete probability distribution consists of delta functions at the integers, each with a weight equal to the PMF at that integer. Since this is not representable in floating point arithmetic, calling this method is an invalid operation.
Implements Meta.Numerics.Statistics.Distributions.Distribution.
References Meta.Numerics.Interval.LeftEndpoint, Meta.Numerics.Statistics.Distributions.DiscreteDistribution.Maximum, Meta.Numerics.Statistics.Distributions.DiscreteDistribution.Minimum, Meta.Numerics.Statistics.Distributions.DiscreteDistribution.ProbabilityMass(), Meta.Numerics.Interval.RightEndpoint, and Meta.Numerics.Interval.Width.
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inlinevirtual |
Computes a raw moment of the distribution.
r | The order of the moment to compute. |
Implements Meta.Numerics.Statistics.Distributions.UnivariateDistribution.
References Meta.Numerics.Statistics.Distributions.DiscreteDistribution.Moment().
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inlinevirtual |
Computes a central moment of the distribution.
r | The order of the moment to compute. |
Reimplemented from Meta.Numerics.Statistics.Distributions.UnivariateDistribution.
References Meta.Numerics.Statistics.Distributions.DiscreteDistribution.Maximum, Meta.Numerics.Statistics.Distributions.DiscreteDistribution.Minimum, Meta.Numerics.Statistics.Distributions.DiscreteDistribution.MomentAboutMean(), Meta.Numerics.MoreMath.Pow(), and Meta.Numerics.Interval.Width.
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inlinevirtual |
Returns the point at which the cumulative distribution function attains a given value.
P | The left cumulative probability P, which must lie between 0 and 1. |
Reimplemented from Meta.Numerics.Statistics.Distributions.Distribution.
References Meta.Numerics.Statistics.Distributions.DiscreteDistribution.InverseLeftProbability().
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