RustQuant::math

Struct Gamma

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pub struct Gamma { /* private fields */ }
Expand description

Gamma distribution

There are two common parametrizations for the Gamma distribution.

  1. X ~ Gamma(alpha, beta) = Gamma(shape, rate)
  2. X ~ Gamma(k, theta) = Gamma(shape, scale)

This implementation uses the first parametrization (shape, rate).

Note that scale = 1 / rate <=> rate = 1 / scale.

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impl Gamma

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pub fn new(alpha: f64, beta: f64) -> Gamma

New instance of a Gamma distribution.

§Panics

Panics if alpha and beta are not positive.

Trait Implementations§

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impl Distribution for Gamma

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fn cf(&self, t: f64) -> Complex<f64>

Characteristic function of the distribution. Returns the value of the characteristic function at t. The characteristic function is defined as:
cf(t) = E[e^{itX}]
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fn pdf(&self, x: f64) -> f64

Probability density function of the distribution. Returns the probability that a random variable is equal to x. NOTE: Panics if the distribution is discrete.
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fn pmf(&self, x: f64) -> f64

Probability mass function of the distribution. Returns the probability that a random variable is equal to x. NOTE: Panics if the distribution is continuous.
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fn cdf(&self, x: f64) -> f64

Distribution function of the distribution. Returns the probability that a random variable is less than or equal to x.
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fn inv_cdf(&self, _p: f64) -> f64

Inverse distribution function of the distribution. Returns the value of x such that cdf(x) = p.
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fn mean(&self) -> f64

Returns the mean of the distribution. Mean is the average value of the distribution. https://en.wikipedia.org/wiki/Mean
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fn median(&self) -> f64

Returns the median of the distribution. Median is the value that splits the distribution into two equal parts. https://en.wikipedia.org/wiki/Median
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fn mode(&self) -> f64

Returns the mode of the distribution. Mode is the value that maximizes the probability density function. https://en.wikipedia.org/wiki/Mode_(statistics)
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fn variance(&self) -> f64

Returns the variance of the distribution. Variance is a measure of the spread of the distribution. https://en.wikipedia.org/wiki/Variance
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fn skewness(&self) -> f64

Returns the skewness of the distribution. Skewness is a measure of the asymmetry of the distribution. https://en.wikipedia.org/wiki/Skewness
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fn kurtosis(&self) -> f64

Returns the kurtosis of the distribution. Kurtosis is a measure of the “tailedness” of the distribution. https://en.wikipedia.org/wiki/Kurtosis
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fn entropy(&self) -> f64

Returns the entropy of the distribution. Entropy is a measure of the uncertainty of the distribution.
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fn mgf(&self, t: f64) -> f64

Moment generating function of the distribution. M = E[e^{tX}] https://en.wikipedia.org/wiki/Moment-generating_function
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fn sample(&self, n: usize) -> Result<Vec<f64>, RustQuantError>

Generates a random sample from the distribution.

Auto Trait Implementations§

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impl Freeze for Gamma

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impl RefUnwindSafe for Gamma

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impl Send for Gamma

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impl Sync for Gamma

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impl Unpin for Gamma

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impl UnwindSafe for Gamma

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