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| BetaDistribution (double alpha, double beta) |
| Initializes a new β distribution. More...
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override double | ProbabilityDensity (double x) |
| Returns the probability density at the given point. - Parameters
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- Returns
- The probability density p(x).
The probability density function (PDF) gives the relative probability of obtaining different values. More...
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override double | LeftProbability (double x) |
| Returns the cumulative probability to the left of (below) the given point. - Parameters
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- Returns
- The integrated probability to obtain a result below the reference point.
The left probability function is commonly called the cumulative distribution function (CDF). More...
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override double | RightProbability (double x) |
| Return the cumulative probability to the right of (above) the given point. - Parameters
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- Returns
- The integrated probability 1-P(x1) to obtain a result above the reference point.
In survival analysis, the right probability function is commonly called the survival function, because it gives the fraction of the population remaining after the given time. More...
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override double | Moment (int r) |
| Computes a raw moment of the distribution. - Parameters
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r | The order of the moment to compute. |
- Returns
- The rth raw moment of the distribution.
- See also
- Moment
More...
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override double | MomentAboutMean (int r) |
| Computes a central moment of the distribution. - Parameters
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r | The order of the moment to compute. |
- Returns
- The rth central moment of the distribution.
- See also
- Moment
More...
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override double | InverseLeftProbability (double P) |
| Returns the point at which the cumulative distribution function attains a given value. - Parameters
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P | The left cumulative probability P, which must lie between 0 and 1. |
- Returns
- The value x at which LeftProbability equals P.
The inverse left probability is commonly called the quantile function. Given a quantile, it tells which variable value is the lower border of that quantile. More...
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override double | InverseRightProbability (double Q) |
| Returns the point at which the right probability function attains the given value. - Parameters
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Q | The right cumulative probability, which must lie between 0 and 1. |
- Returns
- The value x for which RightProbability equals Q.
More...
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override double | GetRandomValue (Random rng) |
| Returns a random value. - Parameters
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rng | A random number generator. |
- Returns
- A number distributed according to the distribution.
Note that the random number generator rng will be advanced by this method. The next call to its generator methods will not give the same value as it would had it not been passed to this method. More...
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override double | Moment (int r) |
| Computes a raw moment of the distribution. - Parameters
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r | The order of the moment to compute. |
- Returns
- The rth raw moment of the distribution.
- See also
- Moment
More...
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override double | MomentAboutMean (int r) |
| Computes a central moment of the distribution. - Parameters
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r | The order of the moment to compute. |
- Returns
- The rth central moment of the distribution.
- See also
- Moment
More...
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virtual double | ExpectationValue (Func< double, double > f) |
| Computes the expectation value of the given function. More...
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virtual double | Cumulant (int r) |
| Computes a cumulant of the distribution. More...
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Represents a beta distribution.
The beta distribution is defined on the interval [0,1]. Depending on its two shape parameters, it can take on a wide variety of forms on this interval.
If the two shape parameters are equal, the distribution is symmetric. If the first shape parameter is less than one, the distribution has a singularity at its left endpoint. If the first shape parameter is greater than one, the distribution goes to zero at its left endpoint. The second shape parameter similarly governs the distribution's behavior at its right endpoint.
When both shape parameters are one, the beta distribution reduces to a standard uniform distribution.
Beta distributions describe the maximum and minimum values obtained from multiple, independent draws from a standard uniform distribution. For n draws, the maximum value is distributed as B(n,1).
Similiarly, the minimum value is distributed as B(1,n).
Because of the wide variety of shapes it can take, the beta distribution is sometimes used as an ad hoc model to describe any distribution observed on a finite interval.