## McSimulation Extra Data

List of valid values:
Data
Refers to the output of QuantLib's data function.
Returns the array of sample final values and their respective weights in the context of a monte carlo algorithm.

Error Estimate
Refers to the output of QuantLib's errorEstimate function.
Returns the error estimate on the mean value in the context of a monte carlo algorithm, defined as σ/n, where σ is the standard deviation and n² = N with N being the number of samples.

Gaussian Downside Deviation
Refers to the output of QuantLib's gaussianDownsideDeviation function.
Returns the downside deviation in the context of a monte carlo algorithm, defined as the quare root of the downside variance.

Gaussian Downside Variance
Refers to the output of QuantLib's gaussianDownsideVariance function.
Returns the downside variance in the context of a monte carlo algorithm, defined as N/(N-1)<θ(x-<x>)²>, where N is the number of samples, <x> is the mean of the sample values xi, θ equals 1 if x-<x> is negative and otherwise equals 0, which means that <θ(x-<x>)²> is the mean of the squared negative distances from the mean (xi-<x>)², such that xi-<x> < 0.

Kurtosis
Refers to the output of QuantLib's kurtosis function.
of the 4th power of the distances from the mean (xi-<x>)^4 and σ is the standard deviation.
The above evaluates to 0 for a Gaussian distribution.

Max
Refers to the output of QuantLib's max function.
Returns the maximum sample value in the context of a monte carlo algorithm.

Mean
Refers to the output of QuantLib's mean function.
Returns the mean in the context of a monte carlo algorithm, defined as Sum{ wi*xi } / Sum{ wi }, where wi are the weights and xi the sample values.

Min
Refers to the output of QuantLib's min function.
Returns the minimum sample value in the context of a monte carlo algorithm.

Samples
Refers to the output of QuantLib's samples function.
Returns the number of samples in the context of a monte carlo algorithm.

Skewness
Refers to the output of QuantLib's skewness function.
Returns the skewness in the context of a monte carlo algorithm, defined as N²/[(N-1)(N-2)] n<(x-<x>)³>/σ³, where n = N²/[(N-1)(N-2)], N is the number of samples, <x> is the mean of the sample values xi and <(x-<x>)³> is the mean of the cubed distances from the mean (xi-<x>)³ and σ is the standard deviation.
The above evaluates to 0 for a Gaussian distribution.

Standard Deviation
Refers to the output of QuantLib's standardDeviation function.
Returns the standard deviation in the context of a monte carlo algorithm, defined as the square root of the variance.

Variance
Refers to the output of QuantLib's variance function.
Returns the variance in the context of a monte carlo algorithm, defined as N/(N-1)<(x-<x>)²>, where N is the number of samples, <x> is the mean of the sample values xi and <(x-<x>)²> is the mean of the squared distances from the mean (xi-<x>)².

Weight Sum
Refers to the output of QuantLib's weightSum function.
Returns the sum of the weights in the context of a monte carlo algorithm.