Gaussian
A "normal" probability distribution function. CONSIDER making this a case class with a member corresponding to the l value of wiggle.
Attributes
Members list
Type members
Inherited types
The names of the product elements.
The names of the product elements.
Attributes
- Inherited from:
- Singleton
Attributes
- Inherited from:
- Singleton
The mirrored *-type.
The mirrored *-type.
Attributes
- Inherited from:
- Singleton
Attributes
- Inherited from:
- Singleton
Inherited and Abstract types
The name of the type.
The name of the type.
Attributes
- Inherited from:
- Mirror
Value members
Concrete methods
For the convolution of the product of two (independent) Gaussian distributions (see https://en.wikipedia.org/wiki/Variance). You must not use this expression when multiplying a fuzzy number by itself, for example, because then they are not independent.
For the convolution of the product of two (independent) Gaussian distributions (see https://en.wikipedia.org/wiki/Variance). You must not use this expression when multiplying a fuzzy number by itself, for example, because then they are not independent.
Var(X Y) = mux mux Var(Y) + muy muy Var(X) + Var(X) Var(Y)
Therefore, (sigma(x*y))**2 = (mux sigma(y))**2 + (muy sigma(x))**2 + (sigma(x) sigma(y))**2
Or, dividing by (mux muy)**2 (i.e., using relative variations)
sigma(x/mux 8 y/muy)**2 = sigma(x/mux)**2 + sigma(y/muy)**2 + (sigma(x/mux) sigma(y/muy))**2
Value parameters
- independent
-
whether the distributions are independent.
- sigma1
-
the first standard deviation.
- sigma2
-
the second standard deviation.
Attributes
Get the convolution of sum of two Gaussian distributions.
Get the convolution of sum of two Gaussian distributions.
This follows the fact that Var(X + Y) = Var(X) + Var(Y)
Value parameters
- sigma1
-
the first standard deviation.
- sigma2
-
the second standard deviation.
Attributes
- Returns
-
a double which is the root-mean-square of the sigmas.
Computes the effective magnitude of a Gaussian distribution based on the input parameter.
Computes the effective magnitude of a Gaussian distribution based on the input parameter.
Value parameters
- l
-
the scale parameter, typically representing the standard deviation of a Gaussian distribution.
Attributes
- Returns
-
a double representing the effective magnitude.
Computes the probability that random points will be found with the range -x to +x where l is the standard deviation of this Gaussian.
Computes the probability that random points will be found with the range -x to +x where l is the standard deviation of this Gaussian.
Value parameters
- l
-
the size or scale of the probability density function (e.g., standard deviation for a Gaussian distribution).
- x
-
the specific point that bounds the region we're interested in.
Attributes
- Returns
-
the calculated probability density at the given point.
wiggle(c) = l * erfinv(c) / sigma Inverting: c = erf(x * sigma / l)
wiggle(c) = l * erfinv(c) / sigma Inverting: c = erf(x * sigma / l)
Attributes
Adjusts the given value based on the specified confidence level, using the properties of a Gaussian distribution.
Adjusts the given value based on the specified confidence level, using the properties of a Gaussian distribution.
Value parameters
- confidence
-
the confidence level, a value between 0 and 1, representing the desired probability threshold.
- l
-
the scale or size parameter, typically representing the standard deviation of a Gaussian distribution.
Attributes
- Returns
-
a double representing the adjusted value based on the confidence level and scale.
Inherited methods
Creates a new instance of type T with elements taken from product p.
Creates a new instance of type T with elements taken from product p.
Attributes
- Inherited from:
- Singleton
An iterator over the names of all the elements of this product.
An iterator over the names of all the elements of this product.
Attributes
- Inherited from:
- Product
An iterator over all the elements of this product.
An iterator over all the elements of this product.
Attributes
- Returns
-
in the default implementation, an
Iterator[Any] - Inherited from:
- Product
Concrete fields
The standard deviation of a normal distribution whose variance is 1/2. This is the basis of the inverse error function.
The standard deviation of a normal distribution whose variance is 1/2. This is the basis of the inverse error function.