Probability Functions
| Name | Description | Example |
|---|---|---|
| averageDistribution(<variable>, <order>, <value>) | If <variable> has a normal distribution, the function evaluates the arithmetic mean of <order> copies of the distributions at <value>. Otherwise it evaluates to Undefined. | averageDistribution("Well Completion: Devonian A: Devonian P1: Initial Rate", 100, 40 [M bpd]) |
| distribution(<variable>, <value>) | If <variable> has a probability distribution, this function evaluates its cumulative distribution function at <value>. Otherwise it evaluates to Undefined. | distribution("Well Completion: Devonian A: Devonian P1: Initial Rate", 40 [M bpd]) |
| geometricMeanDistribution(<variable>, <order>, <value>) | If <variable> has a lognormal distribution, this function evaluates the geometric mean of <order> copies of the distribution at <value>. Otherwise it evaluates to Undefined. The Geometric Mean of n random variables X1, X2, ..., Xn is the random variable X = (X1 * ... * Xn)1/n. | geometricMeanDistribution("Well Completion: Devonian A: Devonian P1: Initial Rate", 100, 40 [M bpd]) |
| inverseDistribution(<variable>, <probability>) | If <variable> has a probability distribution, this function evaluates the inverse of its cumulative distribution function at <probability>. Otherwise it evaluates to Undefined. | inverseDistribution("Well Completion: Devonian A: Devonian P1: Initial Rate", 0.75) |
| inverseLognormal(<probability>, <mean>, <sd>) | Evaluates the inverse of the lognormal cumulative distribution in <probability>. | inverseLognormal(0.9, 100 [MM scf], 45 [M scf]) |
| inverseNormal(<probability>, <mean>, <sd>) | Evaluates the inverse of the normal cumulative distribution in <probability>. | inverseNormal(0.9, 100 [MM scf], 45 [M scf]) |
| inverseTriangular(<probability>, <min>, <mid> <max>) | Evaluates the inverse of the triangular distribution in <probability>. | inverseTriangular(0.9, 10 [M scf], 20 [M scf] 45 [M scf]) |
| lognormal(<value>, <mean>, <sd>, <cumulative>) | Evaluates the Log Normal Distribution in <value> when <cumulative> is true, or the Normal Density function when it is false. | lognormal("Well Completion: Proteus: Produce A1: Well Reserves", "Pvr: Mean", "Pvr: SD", true) |
| lognormalBayesianEvidence(<confidence>, <error>, <mu0>, <sd0>, <P90/P10>) | Returns the number of new experiments required to update the estimation of a Lognormal mean within the boundaries of the confidence interval given by <confidence> and <error>. The Lognormal distribution is assumed to have the percentile quotient <P90/P10> and a normally distributed mean with parameters <mu0> and <sd0>. The <error> is relative to the logarithmic width ln(P90) - ln(P10). | |
| lognormalMeanOfNormal(<mean>, <sd>) | Returns the mean value of the Lognormal distribution associated to the Normal distribution with mean <mean> and standard deviation <sd>. | |
| lognormalSdOfNormal(<mean>, <sd>) | Returns the standard deviation of the Lognormal distribution associated to the Normal distribution with mean <mean> and standard deviation <sd>. | |
| mean(<variable>) | If <variable> has a probability distribution, this function returns its mean value. Otherwise it evaluates to Undefined. The Arithmetic Mean of n random variables X1, X2, ..., Xn is the random variable X = (X1 + ... + Xn) / n. | mean("Well Completion: Proteus: Produce A1: Well Reserves") |
| normal(<value>, <mean>, <sd>, <cumulative>) | Evaluates the Normal Distribution in <value> when <cumulative> is true, or the Normal Density function when it is false. | normal("Well Completion: Proteus: Produce A1: Well Reserves", "Pvr: Mean", "Pvr: SD", true) |
| normalBayesianEvidence(<confidence>, <error>, <sd0>, <sd>) | Returns the number of new experiments required to update the estimation of a Normal mean within the boundaries of the confidence interval given by <confidence> and <error>. The Normal distribution is assumed to have a standard deviation <sd> and a normally distributed mean with standard deviation <sd0>. | |
normalMeanOfLognormal(<mean>, <sd>) | Returns the mean value of the Normal distribution associated to the Lognormal distribution with mean <mean> and standard deviation <sd>. | |
normalSdOfLognormal(<mean>, <sd>) | Returns the standard deviation of the Normal distribution associated to the Lognormal distribution with mean <mean> and standard deviation <sd>. | |
| sd(<variable>) | If <variable> has a probability distribution, this function returns its standard deviation. Otherwise it evaluates to Undefined. | sd("Well Completion: Proteus: Produce A1: Well Reserves") |
In PetroVR the mean and standard deviation parameters for lognormal and inverseLognormal correspond to the mean and standard deviation of the lognormal distributed variable, not the normal variable in its exponent. See further under Log Normal Distribution.
Probability functions that use a variable as argument only accept numeric and date variables (not Boolean or string).