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| LogisticDistribution () |
| Initializes a new standard logistic distribution. More...
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| LogisticDistribution (double m, double s) |
| Initializes a new logistic distribution with the given mean and width parameters. 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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override double | Cumulant (int r) |
| Computes a cumulant of the distribution. - Parameters
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r | The index of the cumulant to compute. |
- Returns
- The rth cumulant of the distribution.
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 logistic distribution.
Like the normal distribution, the logistic distribution is a symmetric, unimodal distribution distribution with exponentially supressed tails.
A logistic distribution with mean zero and standard deviation one is called a standard logistic distribution. Any logistic distribution can be converted to a standard logistic distribution by reparameterzing into z = (x-m)/s.