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| ChiSquaredDistribution (int nu) |
| Initializes a new χ2 distribution. More...
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override double | ProbabilityDensity (double x) |
| Returns the probability density at the given point. - Parameters
-
- 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 | 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 | 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 | Cumulant (int r) |
| Computes a cumulant of the distribution. More...
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virtual double | InverseRightProbability (double Q) |
| Returns the point at which the right probability function attains the given value. 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 | GetRandomValue (Random rng) |
| Returns a random value. More...
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Represents a χ2 distribution.
A chi squared distribution is an asymmetrical distribution ranging from zero to infinity with a peak near its number of degrees of freedom ν. It is a one-parameter distribution determined entirely by the parameter nu.
The figure above shows the χ2 distribution for ν = 6, as well as the normal distribution with equal mean and variance for reference.
The sum of the squares of ν independent standard-normal distributed variables is distributed as χ2 with ν degrees of freedom.
The χ2 distribution appears in least-squares fitting as the distribution of the sum-of-squared-deviations under the null hypothesis that the model explains the data. For example, the goodness-of-fit statistic returned by the model our model fitting methods (UncertainMeasurementSample{T}.FitToFunction, UncertainMeasurementSample{T}.FitToLinearFunction, UncertainMeasurementSample.FitToLine, and others) follows a χ2 distribution.
- See also
- ContingencyTable.PearsonChiSquaredTest