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| WeibullDistribution (double scale, double shape) |
| Initializes a new Weibull 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 | 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 | 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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virtual double | Cumulant (int r) |
| Computes a cumulant of the distribution. More...
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Represents a Weibull distribution.
The Weibull distribution is a generalized form of the exponential distriubtion for which the decay probability is not constant, but instead increases with time (for shape parameters greater than one) or, less commonly, decreases with time (for shape parameters less than one). When the shape parameter is one, the Weibull distribution reduces to the exponential distribution.
The Weibull distribution is commonly used in engineering applications to model the time-to-failure of industrial componets.
static FitResult Meta.Numerics.Statistics.Distributions.WeibullDistribution.FitToSample |
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Sample |
sample | ) |
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inlinestatic |
Computes the Weibull distribution that best fits the given sample.
- Parameters
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- Returns
- The best fit parameters.
The returned fit parameters are the ShapeParameter and ScaleParameter, in that order. These are the same parameters, in the same order, that are required by the WeibullDistribution(double,double) constructor to specify a new Weibull distribution.
- Exceptions
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ArgumentNullException | sample is null. |
InvalidOperationException | sample contains non-positive values. |
InsufficientDataException | sample contains fewer than three values. |
References Meta.Numerics.Matrices.SymmetricMatrix.CholeskyDecomposition(), Meta.Numerics.Statistics.Sample.Count, Meta.Numerics.Analysis.FunctionMath.FindZero(), Meta.Numerics.Matrices.CholeskyDecomposition.Inverse(), Meta.Numerics.Statistics.Sample.InverseLeftProbability(), and Meta.Numerics.Statistics.Sample.Minimum.
Referenced by Test.BugTests.Bug7213(), Test.SampleTest.WeibullFit(), and Test.SampleTest.WeibullFitUncertainties().