Module net.finmath.lib
Package net.finmath.stochastic

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 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.
      See Also:

    • 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

      RandomVariable 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

      RandomVariable apply(DoubleUnaryOperator 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 double to double.
      Returns:
      New random variable with the result of the function.

    • apply

      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. 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.

    • add

      RandomVariable add(double value)
      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

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

    • exp

      RandomVariable 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

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

    • sin

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

    • cos

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

    • add

      RandomVariable add(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.

    • 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

      RandomVariable cap(RandomVariable 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

      RandomVariable floor(RandomVariable 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

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

    • addProduct

      RandomVariable addProduct(RandomVariable factor1, double factor2)
      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.

    • addProduct

      RandomVariable addProduct(RandomVariable factor1, RandomVariable factor2)
      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.

    • addRatio

      RandomVariable addRatio(RandomVariable numerator, RandomVariable denominator)
      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.

    • addSumProduct

      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.

    • addSumProduct

      default RandomVariable addSumProduct(List<RandomVariable> factor1, List<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.

    • isNaN

      RandomVariable isNaN()
      Applies x → (Double.isNaN(x) ? 1.0 : 0.0)
      Returns:
      A random variable which is 1.0 for all states that are NaN, otherwise 0.0.