finMath lib documentation
net.finmath.stochastic

## Interface RandomVariable

• All Superinterfaces:
Serializable
All Known Subinterfaces:
RandomVariableAccumulatorInterface, RandomVariableArray, RandomVariableDifferentiable
All Known Implementing Classes:

public interface RandomVariable
extends Serializable
This interface describes the methods implemented by an immutable random variable, i.e. methods that leave a random variable unchanged (immutable). This is used to ensure that arguments or return values are not changed. For C++ guys: In C++ you could achieve this by making a return value const.
IMPORTANT: As of version 1.3 / revision 487 the design of RandomVariableFromDoubleArray, RandomVariable has changed: All methods of RandomVariableFromDoubleArray leave the object immutable and the interface ImmutableRandomVariableInterface has been renamed to RandomVariable. Your code remains compatible if you perform the following changes:
• Change calls to RandomVariable objects value like value.mult(argument); to value = value.mult(argument);
• Remove calls to getMutableCopy() since they are no longer needed.
• Remove wrapping in RandomVariableMutableClone since they are no longer needed.
The change has some performance impact, however, the original performance may be achieved again via the use of Java 8 lambdas and the concept of the RandomVariableAccumulatorInterface.
Version:
1.5
Author:
Christian Fries
• ### Method Summary

All Methods
Modifier and Type Method and Description
RandomVariable abs()
Applies x → Math.abs(x), i.e. x → |x| to this random variable.
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(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.
RandomVariable apply(DoubleUnaryOperator 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.
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 ?
RandomVariable cos()
Applies x → cos(x) to this random variable.
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. otherwise throws an UnsupportedOperationException.
boolean equals(RandomVariable randomVariable)
Compare this random variable with a given one
RandomVariable exp()
Applies x → exp(x) 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) ?
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
RandomVariable vid(RandomVariable randomVariable)
Applies x → randomVariable/x to this random variable.
• ### Method Detail

• #### 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.
ssrn abstract 3246127
• #### 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.
• #### 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).
• #### 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.

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.
• #### 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.
• #### 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.
• #### 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.
• #### 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.

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.

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.

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.

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.

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.

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.