IGLib
1.7.2
The IGLib base library EXTENDED - with other lilbraries and applications.
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Represents a discrete binomial distribution. More...
Public Member Functions | |||
BinomialDistribution (double p, int n) | |||
Initializes a new binomial distribution. More... | |||
override double | ProbabilityMass (int k) | ||
Returns the probability of the obtaining the given value.
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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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override double | LeftExclusiveProbability (int k) | ||
Computes the probability of obtaining a value less than the given value.
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override double | RightExclusiveProbability (int k) | ||
Computes the probability of obtaining a value greater than the given value.
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override int | InverseLeftProbability (double P) | ||
Computes the value corresponding to the given percentile.
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virtual double | LeftInclusiveProbability (int k) | ||
Computes the probability of obtaining a value less than or equal to the given value. More... | |||
virtual double | ExpectationValue (Func< int, double > f) | ||
Computes the expectation value of an artibrary function. More... | |||
override double | Moment (int r) | ||
Gets a raw moment of the distribution. More... | |||
override double | MomentAboutMean (int r) | ||
Gets a central moment of the distribution. More... | |||
virtual int | GetRandomValue (Random rng) | ||
Produces a random integer drawn from the distribution. More... | |||
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virtual double | Cumulant (int r) | ||
Computes a cumulant of the distribution. More... | |||
Properties | |
override int | Minimum [get] |
override int | Maximum [get] |
override double | Mean [get] |
override double | Variance [get] |
override double | Skewness [get] |
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abstract int | Minimum [get] |
Gets the smallest value in the distribution. More... | |
abstract int | Maximum [get] |
Gets the largest value in the distribution. More... | |
override double | Mean [get] |
Gets the mean of the distribution. 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 Attributes | |
readonly int | n |
readonly double | p |
readonly double | q |
Represents a discrete binomial distribution.
The binomial distribution gives the probability of obtaining k successes in n independent Bernoulli trials in which the probability of success in each trial is p.
For a single trial, the binomial distribution reduces to a Bernoulli distribution (BernoulliDistribution).
The test statistic for a sign test (Sample.SignTest) is distributed according to the Bernoulli distribution.
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inline |
Initializes a new binomial distribution.
p | The probability of the success in a single trial, which must lie between zero and one. |
n | The number of trials, which must be positive. |
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inlinevirtual |
Returns the probability of the obtaining the given value.
k | The value. |
Implements Meta.Numerics.Statistics.Distributions.DiscreteDistribution.
References Meta.Numerics.Functions.AdvancedIntegerMath.BinomialCoefficient(), and Meta.Numerics.MoreMath.Pow().
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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.MoreMath.Pow().
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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.Functions.AdvancedIntegerMath.BinomialCoefficient().
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inlinevirtual |
Computes the probability of obtaining a value less than the given value.
k | The value. |
Reimplemented from Meta.Numerics.Statistics.Distributions.DiscreteDistribution.
References Meta.Numerics.Functions.AdvancedMath.LeftRegularizedBeta().
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inlinevirtual |
Computes the probability of obtaining a value greater than the given value.
k | The value. |
Reimplemented from Meta.Numerics.Statistics.Distributions.DiscreteDistribution.
References Meta.Numerics.Functions.AdvancedMath.Beta().
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inlinevirtual |
Computes the value corresponding to the given percentile.
P | The percentile. |
Reimplemented from Meta.Numerics.Statistics.Distributions.DiscreteDistribution.
References Meta.Numerics.Functions.AdvancedIntegerMath.BinomialCoefficients(), and Meta.Numerics.MoreMath.Pow().
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