# Interface RandomVariable

All Superinterfaces:
Serializable
All Known Subinterfaces:
RandomVariableAccumulator, RandomVariableArray, RandomVariableDifferentiable
All Known Implementing Classes:
RandomVariableArrayImplementation, RandomVariableDifferentiableAAD, RandomVariableDifferentiableAD, RandomVariableFromDoubleArray, RandomVariableFromFloatArray, RandomVariableLazyEvaluation, Scalar

public interface RandomVariable extends Serializable
This interface describes the methods implemented by an immutable random variable. The random variable is immutable, i.e. method calls like add, sub, mult will return a new instance and leave the method receiver random variable unchanged (immutable). This is used to ensure that arguments or return values are not changed.
Version:
1.6
Author:
Christian Fries
• ## Method Summary

Modifier and Type
Method
Description
RandomVariable
abs()
Applies x → Math.abs(x), i.e.
RandomVariable
accrue(RandomVariable rate, double periodLength)
Applies x → x * (1.0 + rate * periodLength) to this random variable.
RandomVariable
add(double value)
Applies x → x + value to this random variable.
RandomVariable
add(RandomVariable randomVariable)
Applies x → x+randomVariable to this random variable.
RandomVariable
addProduct(RandomVariable factor1, double factor2)
Applies x → x + factor1 * factor2
RandomVariable
addProduct(RandomVariable factor1, RandomVariable factor2)
Applies x → x + factor1 * factor2
RandomVariable
addRatio(RandomVariable numerator, RandomVariable denominator)
Applies x → x + numerator / denominator
default RandomVariable
addSumProduct(List<RandomVariable> factor1, List<RandomVariable> factor2)
Applies \( x \mapsto x + \sum_{i=0}^{n-1} factor1_{i} * factor2_{i}
default RandomVariable
addSumProduct(RandomVariable[] factor1, RandomVariable[] factor2)
Applies \( x \mapsto x + \sum_{i=0}^{n-1} factor1_{i} * factor2_{i}
RandomVariable
apply(DoubleBinaryOperator operator, RandomVariable argument)
Applies x → operator(x,y) to this random variable, where x is this random variable and y is a given random variable.
RandomVariable
apply(DoubleUnaryOperator operator)
Applies x → operator(x) to this random variable.
RandomVariable
apply(DoubleTernaryOperator operator, RandomVariable argument1, RandomVariable argument2)
Applies x → operator(x,y,z) to this random variable, where x is this random variable and y and z are given random variable.
default RandomVariable
appy(RandomOperator operator)
Applies x → operator(x) to this random variable.
RandomVariable
average()
Returns a random variable which is deterministic and corresponds the expectation of this random variable.
default RandomVariable
bus(double value)
Applies x → value - x to this random variable.
RandomVariable
bus(RandomVariable randomVariable)
Applies x → randomVariable-x to this random variable.
RandomVariable
cache()
Return a cacheable version of this object (often a self-reference).
RandomVariable
cap(double cap)
Applies x → min(x,cap) to this random variable.
RandomVariable
cap(RandomVariable cap)
Applies x → min(x,cap) to this random variable.
RandomVariable
choose(RandomVariable valueIfTriggerNonNegative, RandomVariable valueIfTriggerNegative)
Applies x → (x ≥ 0 ? valueIfTriggerNonNegative : valueIfTriggerNegative)
RandomVariable
cos()
Applies x → cos(x) to this random variable.
default RandomVariable
covariance(RandomVariable value)
Returns a random variable which is deterministic and corresponds the covariance of this random variable and the argument.
RandomVariable
discount(RandomVariable rate, double periodLength)
Applies x → x / (1.0 + rate * periodLength) to this random variable.
RandomVariable
div(double value)
Applies x → x / value to this random variable.
RandomVariable
div(RandomVariable randomVariable)
Applies x → x/randomVariable to this random variable.
Double
doubleValue()
Returns the double value if isDeterministic() is true.
boolean
equals(RandomVariable randomVariable)
Compare this random variable with a given one
RandomVariable
exp()
Applies x → exp(x) to this random variable.
default RandomVariable
expectation()
Returns a random variable which is deterministic and corresponds the expectation of this random variable.
default RandomVariable
expm1()
Applies x → expm1(x) (that is x → exp(x)-1.0) to this random variable.
RandomVariable
floor(double floor)
Applies x → max(x,floor) to this random variable.
RandomVariable
floor(RandomVariable floor)
Applies x → max(x,floor) to this random variable.
double
get(int pathOrState)
Evaluate at a given path or state.
double
getAverage()
Returns the expectation of this random variable.
double
getAverage(RandomVariable probabilities)
Returns the expectation of this random variable for a given probability measure (weight).
default RandomVariable
getConditionalExpectation(ConditionalExpectationEstimator conditionalExpectationOperator)
Returns the conditional expectation using a given conditional expectation estimator.
double
getFiltrationTime()
Returns the filtration time.
double[]
getHistogram(double[] intervalPoints)
Generates a Histogram based on the realizations stored in this random variable.
double[][]
getHistogram(int numberOfPoints, double standardDeviations)
Generates a histogram based on the realizations stored in this random variable using interval points calculated from the arguments, see also getHistogram(double[]).
double
getMax()
Returns the maximum value attained by this random variable.
double
getMin()
Returns the minimum value attained by this random variable.
IntToDoubleFunction
getOperator()
Returns the operator path → this.get(path) corresponding to this random variable.
double
getQuantile(double quantile)
Returns the quantile value for this given random variable, i.e., the value x such that P(this < x) = quantile, where P denotes the probability measure.
double
getQuantile(double quantile, RandomVariable probabilities)
Returns the quantile value for this given random variable, i.e., the value x such that P(this < x) = quantile, where P denotes the probability measure.
double
getQuantileExpectation(double quantileStart, double quantileEnd)
Returns the expectation over a quantile for this given random variable.
double[]
getRealizations()
Returns a vector representing the realization of this random variable.
DoubleStream
getRealizationsStream()
Returns a stream of doubles corresponding to the realizations of this random variable.
double
getSampleVariance()
Returns the sample variance of this random variable, i.e., V * size()/(size()-1) where V = getVariance().
double
getStandardDeviation()
Returns the standard deviation of this random variable, i.e., sqrt(V) where V = ((X-m)^2).getAverage() and X = this and m = X.getAverage().
double
getStandardDeviation(RandomVariable probabilities)
Returns the standard deviation of this random variable, i.e., sqrt(V) where V = ((X-m)^2).getAverage(probabilities) and X = this and m = X.getAverage(probabilities).
double
getStandardError()
Returns the standard error (discretization error) of this random variable.
double
getStandardError(RandomVariable probabilities)
Returns the standard error (discretization error) of this random variable.
int
getTypePriority()
Returns the type priority.
default RandomVariable
getValues()
Returns the underlying values and a random variable.
double
getVariance()
Returns the variance of this random variable, i.e., V where V = ((X-m)^2).getAverage() and X = this and m = X.getAverage().
double
getVariance(RandomVariable probabilities)
Returns the variance of this random variable, i.e., V where V = ((X-m)^2).getAverage(probabilities) and X = this and m = X.getAverage(probabilities).
RandomVariable
invert()
Applies x → 1/x to this random variable.
boolean
isDeterministic()
Check if this random variable is deterministic in the sense that it is represented by a single double value.
RandomVariable
isNaN()
Applies x → (Double.isNaN(x) ? 1.0 : 0.0)
RandomVariable
log()
Applies x → log(x) to this random variable.
RandomVariable
mult(double value)
Applies x → x * value to this random variable.
RandomVariable
mult(RandomVariable randomVariable)
Applies x → x*randomVariable to this random variable.
RandomVariable
pow(double exponent)
Applies x → pow(x,exponent) to this random variable.
RandomVariable
sin()
Applies x → sin(x) to this random variable.
int
size()
Returns the number of paths or states.
RandomVariable
sqrt()
Applies x → sqrt(x) to this random variable.
RandomVariable
squared()
Applies x → x * x to this random variable.
RandomVariable
sub(double value)
Applies x → x - value to this random variable.
RandomVariable
sub(RandomVariable randomVariable)
Applies x → x-randomVariable to this random variable.
RandomVariable
subRatio(RandomVariable numerator, RandomVariable denominator)
Applies x → x - numerator / denominator
default RandomVariable
variance()
Returns a random variable which is deterministic and corresponds the variance of this random variable.
default RandomVariable
vid(double value)
Applies x → value / x to this random variable.
RandomVariable
vid(RandomVariable randomVariable)
Applies x → randomVariable/x to this random variable.
• ## Method Details

• ### equals

boolean equals(RandomVariable randomVariable)
Compare this random variable with a given one
Parameters:
randomVariable - Random variable to compare with.
Returns:
True if this random variable and the given one are equal, otherwise false
• ### getFiltrationTime

double getFiltrationTime()
Returns the filtration time.
Returns:
The filtration time.
• ### getTypePriority

int getTypePriority()
Returns the type priority.
Returns:
The type priority.
• ### get

double get(int pathOrState)
Evaluate at a given path or state.
Parameters:
pathOrState - Index of the path or state.
Returns:
Value of this random variable at the given path or state.
• ### size

int size()
Returns the number of paths or states.
Returns:
Number of paths or states.
• ### isDeterministic

boolean isDeterministic()
Check if this random variable is deterministic in the sense that it is represented by a single double value. Note that the methods returns false, if the random variable is represented by a vector where each element has the same value.
Returns:
True if this random variable is deterministic.
• ### getValues

default RandomVariable getValues()
Returns the underlying values and a random variable. If the implementation supports an "inner representation", returns the inner representation. Otherwise just returns this.
Returns:
The underling values.
• ### getRealizations

double[] getRealizations()
Returns a vector representing the realization of this random variable. This method is merely useful for analysis. Its interpretation depends on the context (Monte-Carlo or lattice). The method does not expose an internal data model.
Returns:
Vector of realizations of this random variable.
• ### doubleValue

Double doubleValue()
Returns the double value if isDeterministic() is true. otherwise throws an UnsupportedOperationException.
Returns:
The double value if isDeterministic() is true, otherwise throws an an UnsupportedOperationException.
• ### getOperator

IntToDoubleFunction getOperator()
Returns the operator path → this.get(path) corresponding to this random variable.
Returns:
The operator path → this.get(path) corresponding to this random variable.
• ### getRealizationsStream

DoubleStream getRealizationsStream()
Returns a stream of doubles corresponding to the realizations of this random variable.
Returns:
A stream of doubles corresponding to the realizations of this random variable.
• ### getMin

double getMin()
Returns the minimum value attained by this random variable.
Returns:
The minimum value.
• ### getMax

double getMax()
Returns the maximum value attained by this random variable.
Returns:
The maximum value.
• ### getAverage

double getAverage()
Returns the expectation of this random variable. The result of this method has to agrees with average().doubleValue().
Returns:
The average assuming equi-distribution.
• ### getAverage

double getAverage(RandomVariable probabilities)
Returns the expectation of this random variable for a given probability measure (weight). The result of this method is (mathematically) equivalent to
this.mult(probabilities).getAverage() / probabilities.getAverage()
while the internal implementation may differ, e.g. being more efficient by performing multiplication and summation in the same loop.
Parameters:
probabilities - The probability weights.
Returns:
The average assuming the given probability weights.
• ### getVariance

double getVariance()
Returns the variance of this random variable, i.e., V where V = ((X-m)^2).getAverage() and X = this and m = X.getAverage().
Returns:
The average assuming equi-distribution.
• ### getVariance

double getVariance(RandomVariable probabilities)
Returns the variance of this random variable, i.e., V where V = ((X-m)^2).getAverage(probabilities) and X = this and m = X.getAverage(probabilities).
Parameters:
probabilities - The probability weights.
Returns:
The average assuming the given probability weights.
• ### getSampleVariance

double getSampleVariance()
Returns the sample variance of this random variable, i.e., V * size()/(size()-1) where V = getVariance().
Returns:
The sample variance.
• ### getStandardDeviation

double getStandardDeviation()
Returns the standard deviation of this random variable, i.e., sqrt(V) where V = ((X-m)^2).getAverage() and X = this and m = X.getAverage().
Returns:
The standard deviation assuming equi-distribution.
• ### getStandardDeviation

double getStandardDeviation(RandomVariable probabilities)
Returns the standard deviation of this random variable, i.e., sqrt(V) where V = ((X-m)^2).getAverage(probabilities) and X = this and m = X.getAverage(probabilities).
Parameters:
probabilities - The probability weights.
Returns:
The standard error assuming the given probability weights.
• ### getStandardError

double getStandardError()
Returns the standard error (discretization error) of this random variable. For a Monte-Carlo simulation this is 1/Math.sqrt(n) * getStandardDeviation().
Returns:
The standard error assuming equi-distribution.
• ### getStandardError

double getStandardError(RandomVariable probabilities)
Returns the standard error (discretization error) of this random variable. For a Monte-Carlo simulation this is 1/Math.sqrt(n) * getStandardDeviation(RandomVariable).
Parameters:
probabilities - The probability weights.
Returns:
The standard error assuming the given probability weights.
• ### getQuantile

double getQuantile(double quantile)
Returns the quantile value for this given random variable, i.e., the value x such that P(this < x) = quantile, where P denotes the probability measure. The method will consider picewise constant values (with constant extrapolation) in the random variable. That is getQuantile(0) wiil return the smallest value and getQuantile(1) will return the largest value.
Parameters:
quantile - The quantile level.
Returns:
The quantile value assuming equi-distribution.
• ### getQuantile

double getQuantile(double quantile, RandomVariable probabilities)
Returns the quantile value for this given random variable, i.e., the value x such that P(this < x) = quantile, where P denotes the probability measure.
Parameters:
quantile - The quantile level.
probabilities - The probability weights.
Returns:
The quantile value assuming the given probability weights.
• ### getQuantileExpectation

double getQuantileExpectation(double quantileStart, double quantileEnd)
Returns the expectation over a quantile for this given random variable. The method will consider picewise constant values (with constant extrapolation) in the random variable. For a ≤ b the method returns (Σa ≤ i ≤ b x[i]) / (b-a+1), where
• a = min(max((n+1) * quantileStart - 1, 0, 1);
• b = min(max((n+1) * quantileEnd - 1, 0, 1);
• n = this.size();
For quantileStart > quantileEnd the method returns getQuantileExpectation(quantileEnd, quantileStart).
Parameters:
quantileStart - Lower bound of the integral.
quantileEnd - Upper bound of the integral.
Returns:
The (conditional) expectation of the values between two quantile levels assuming equi-distribution.
• ### getHistogram

double[] getHistogram(double[] intervalPoints)
Generates a Histogram based on the realizations stored in this random variable. The returned result array's length is intervalPoints.length+1.
• The value result[0] equals the relative frequency of values observed in the interval ( -infinity, intervalPoints[0] ].
• The value result[i] equals the relative frequency of values observed in the interval ( intervalPoints[i-1], intervalPoints[i] ].
• The value result[n] equals the relative frequency of values observed in the interval ( intervalPoints[n-1], infinity ).
where n = intervalPoints.length. Note that the intervals are open on the left, closed on the right, i.e., result[i] contains the number of elements x with intervalPoints[i-1] < x ≤ intervalPoints[i]. Thus, is you have a random variable which only takes values contained in the (sorted) array possibleValues, then result = getHistogram(possibleValues) returns an array where result[i] is the relative frequency of occurrence of possibleValues[i]. The sum of result[i] over all i is equal to 1, except for uninitialized random variables where all values are 0.
Parameters:
intervalPoints - Array of ascending values defining the interval boundaries.
Returns:
A histogram with respect to a provided interval.
• ### getHistogram

double[][] getHistogram(int numberOfPoints, double standardDeviations)
Generates a histogram based on the realizations stored in this random variable using interval points calculated from the arguments, see also getHistogram(double[]). The interval points are set with equal distance over an the interval of the specified standard deviation. The interval points used are x[i] = mean + alpha[i] * standardDeviations * sigma where The methods result is an array of two vectors, where result[0] are the intervals center points ('anchor points') and result[1] contains the relative frequency for the interval. The 'anchor point' for the interval (-infinity, x[0]) is x[0] - 1/2 (x[1]-x[0]) and the 'anchor point' for the interval (x[n], infinity) is x[n] + 1/2 (x[n]-x[n-1]). Here n = numberOfPoints is the number of interval points.
Parameters:
numberOfPoints - The number of interval points.
standardDeviations - The number of standard deviations defining the discretization radius.
Returns:
A histogram, given as double[2][], where result[0] are the center point of the intervals and result[1] is the value of getHistogram(double[]) for the given the interval points. The length of result[0] and result[1] is numberOfPoints+1.
• ### cache

Return a cacheable version of this object (often a self-reference). This method should be called when you store the object for later use, i.e., assign it, or when the object is consumed in a function, but later used also in another function.
Returns:
A cacheable version of this object (often a self-reference).
• ### appy

default RandomVariable appy(RandomOperator operator)
Applies x → operator(x) to this random variable. It returns a new random variable with the result.
Parameters:
operator - An unary operator/function, mapping RandomVariable to RandomVariable.
Returns:
New random variable with the result of the function.
• ### apply

Applies x → operator(x) to this random variable. It returns a new random variable with the result.
Parameters:
operator - An unary operator/function, mapping double to double.
Returns:
New random variable with the result of the function.
• ### apply

Applies x → operator(x,y) to this random variable, where x is this random variable and y is a given random variable. It returns a new random variable with the result.
Parameters:
operator - A binary operator/function, mapping (double,double) to double.
argument - A random variable.
Returns:
New random variable with the result of the function.
• ### apply

RandomVariable apply(DoubleTernaryOperator operator, RandomVariable argument1, RandomVariable argument2)
Applies x → operator(x,y,z) to this random variable, where x is this random variable and y and z are given random variable. It returns a new random variable with the result.
Parameters:
operator - A ternary operator/function, mapping (double,double,double) to double.
argument1 - A random variable representing y.
argument2 - A random variable representing z.
Returns:
New random variable with the result of the function.
• ### cap

RandomVariable cap(double cap)
Applies x → min(x,cap) to this random variable. It returns a new random variable with the result.
Parameters:
cap - The cap.
Returns:
New random variable with the result of the function.
• ### floor

RandomVariable floor(double floor)
Applies x → max(x,floor) to this random variable. It returns a new random variable with the result.
Parameters:
floor - The floor.
Returns:
New random variable with the result of the function.

Applies x → x + value to this random variable. It returns a new random variable with the result.
Parameters:
value - The value to add.
Returns:
New random variable with the result of the function.
• ### sub

RandomVariable sub(double value)
Applies x → x - value to this random variable.
Parameters:
value - The value to subtract.
Returns:
New random variable with the result of the function.
• ### bus

default RandomVariable bus(double value)
Applies x → value - x to this random variable.
Parameters:
value - The value from which this is subtracted.
Returns:
New random variable with the result of the function.
• ### mult

RandomVariable mult(double value)
Applies x → x * value to this random variable.
Parameters:
value - The value to multiply.
Returns:
New random variable with the result of the function.
• ### div

RandomVariable div(double value)
Applies x → x / value to this random variable.
Parameters:
value - The value to divide.
Returns:
New random variable with the result of the function.
• ### vid

default RandomVariable vid(double value)
Applies x → value / x to this random variable.
Parameters:
value - The numerator of the ratio where this is the denominator.
Returns:
New random variable with the result of the function.
• ### pow

RandomVariable pow(double exponent)
Applies x → pow(x,exponent) to this random variable.
Parameters:
exponent - The exponent.
Returns:
New random variable with the result of the function.
• ### average

RandomVariable average()
Returns a random variable which is deterministic and corresponds the expectation of this random variable.
Returns:
New random variable being the expectation of this random variable.
• ### expectation

default RandomVariable expectation()
Returns a random variable which is deterministic and corresponds the expectation of this random variable.
Returns:
New random variable being the expectation of this random variable.
• ### variance

default RandomVariable variance()
Returns a random variable which is deterministic and corresponds the variance of this random variable. Note: The default implementation is a biased estimator. Use the factor n/(n-1) to convert to an unbiased estimator.
Returns:
New random variable being the variance of this random variable and the argument.
• ### covariance

default RandomVariable covariance(RandomVariable value)
Returns a random variable which is deterministic and corresponds the covariance of this random variable and the argument. Note: The default implementation is a biased estimator. Use the factor n/(n-1) to convert to an unbiased estimator.
Parameters:
value - The random variable Y to be used in Cov(X,Y) with X being this.
Returns:
New random variable being the covariance of this random variable and the argument.
• ### getConditionalExpectation

default RandomVariable getConditionalExpectation(ConditionalExpectationEstimator conditionalExpectationOperator)
Returns the conditional expectation using a given conditional expectation estimator.
Parameters:
conditionalExpectationOperator - A given conditional expectation estimator.
Returns:
The conditional expectation of this random variable (as a random variable)
• ### squared

RandomVariable squared()
Applies x → x * x to this random variable.
Returns:
New random variable with the result of the function.
• ### sqrt

Applies x → sqrt(x) to this random variable.
Returns:
New random variable with the result of the function.
• ### exp

Applies x → exp(x) to this random variable.
Returns:
New random variable with the result of the function.
• ### expm1

default RandomVariable expm1()
Applies x → expm1(x) (that is x → exp(x)-1.0) to this random variable.
Returns:
New random variable with the result of the function.
• ### log

Applies x → log(x) to this random variable.
Returns:
New random variable with the result of the function.
• ### sin

Applies x → sin(x) to this random variable.
Returns:
New random variable with the result of the function.
• ### cos

Applies x → cos(x) to this random variable.
Returns:
New random variable with the result of the function.

Applies x → x+randomVariable to this random variable.
Parameters:
randomVariable - A random variable (compatible with this random variable).
Returns:
New random variable with the result of the function.
• ### sub

RandomVariable sub(RandomVariable randomVariable)
Applies x → x-randomVariable to this random variable.
Parameters:
randomVariable - A random variable (compatible with this random variable).
Returns:
New random variable with the result of the function.
• ### bus

RandomVariable bus(RandomVariable randomVariable)
Applies x → randomVariable-x to this random variable.
Parameters:
randomVariable - A random variable (compatible with this random variable).
Returns:
New random variable with the result of the function.
• ### mult

RandomVariable mult(RandomVariable randomVariable)
Applies x → x*randomVariable to this random variable.
Parameters:
randomVariable - A random variable (compatible with this random variable).
Returns:
New random variable with the result of the function.
• ### div

RandomVariable div(RandomVariable randomVariable)
Applies x → x/randomVariable to this random variable.
Parameters:
randomVariable - A random variable (compatible with this random variable).
Returns:
New random variable with the result of the function.
• ### vid

RandomVariable vid(RandomVariable randomVariable)
Applies x → randomVariable/x to this random variable.
Parameters:
randomVariable - A random variable (compatible with this random variable).
Returns:
New random variable with the result of the function.
• ### cap

Applies x → min(x,cap) to this random variable.
Parameters:
cap - The cap. A random variable (compatible with this random variable).
Returns:
New random variable with the result of the function.
• ### floor

Applies x → max(x,floor) to this random variable.
Parameters:
floor - The floor. A random variable (compatible with this random variable).
Returns:
New random variable with the result of the function.
• ### accrue

RandomVariable accrue(RandomVariable rate, double periodLength)
Applies x → x * (1.0 + rate * periodLength) to this random variable.
Parameters:
rate - The accruing rate. A random variable (compatible with this random variable).
periodLength - The period length
Returns:
New random variable with the result of the function.
• ### discount

RandomVariable discount(RandomVariable rate, double periodLength)
Applies x → x / (1.0 + rate * periodLength) to this random variable.
Parameters:
rate - The discounting rate. A random variable (compatible with this random variable).
periodLength - The period length
Returns:
New random variable with the result of the function.
• ### choose

RandomVariable choose(RandomVariable valueIfTriggerNonNegative, RandomVariable valueIfTriggerNegative)
Applies x → (x ≥ 0 ? valueIfTriggerNonNegative : valueIfTriggerNegative)
Parameters:
valueIfTriggerNonNegative - The value used if this is greater or equal 0
valueIfTriggerNegative - The value used if the this is less than 0
Returns:
New random variable with the result of the function.
• ### invert

RandomVariable invert()
Applies x → 1/x to this random variable.
Returns:
New random variable with the result of the function.
• ### abs

Applies x → Math.abs(x), i.e. x → |x| to this random variable.
Returns:
New random variable with the result of the function.

Applies x → x + factor1 * factor2
Parameters:
factor1 - The factor 1. A random variable (compatible with this random variable).
factor2 - The factor 2.
Returns:
New random variable with the result of the function.

Applies x → x + factor1 * factor2
Parameters:
factor1 - The factor 1. A random variable (compatible with this random variable).
factor2 - The factor 2. A random variable (compatible with this random variable).
Returns:
New random variable with the result of the function.

Applies x → x + numerator / denominator
Parameters:
numerator - The numerator of the ratio to add. A random variable (compatible with this random variable).
denominator - The denominator of the ratio to add. A random variable (compatible with this random variable).
Returns:
New random variable with the result of the function.
• ### subRatio

RandomVariable subRatio(RandomVariable numerator, RandomVariable denominator)
Applies x → x - numerator / denominator
Parameters:
numerator - The numerator of the ratio to sub. A random variable (compatible with this random variable).
denominator - The denominator of the ratio to sub. A random variable (compatible with this random variable).
Returns:
New random variable with the result of the function.

default RandomVariable addSumProduct(RandomVariable[] factor1, RandomVariable[] factor2)
Applies \( x \mapsto x + \sum_{i=0}^{n-1} factor1_{i} * factor2_{i}
Parameters:
factor1 - The factor 1. A list of random variables (compatible with this random variable).
factor2 - The factor 2. A list of random variables (compatible with this random variable).
Returns:
New random variable with the result of the function.
factor1 - The factor 1. A list of random variables (compatible with this random variable).
factor2 - The factor 2. A list of random variables (compatible with this random variable).