## Statistic

#### accumulateState

Accumulates the state flags of all cells in a tensor

Object accumulateState(Collection x)

• x: is the input tensor

#### DPMO

returns the defects per million opportunities (DPMO) for the given specification limits and distribution or the given number of trials and number of failures. The 7parameters are USL, LSL, trials, failures, distribution (0=normal), and up to 3 parameters describing the distribution.

Collection DPMO(Collection LSL, Collection USL, Collection trials, Collection failures, Collection dist, Collection param1, Collection param2, Collection param3)

• LSL: is the lower specification limit.
• USL: is the upper specification limit
• trials: is the number of trials. May be empty if a distribution is provided.
• failures: is the number of failures. May be empty if a distribution is provided. Must be >4 if no distribution is provided.
• dist: Describes the distribution. May be empty if no distribution is provided. Normal distribution = 1.
• param1: is the 1st parameter of the distribution (mean or shape)
• param2: is the 2nd parameter of the distribution (standard deviation or scale)
• param3: is the 3rd parameter of the distribution, if defined.

#### FisherTest

Performs the Fisher Test

Object FisherTest(Object a, Object b, Object c, Object d)

• a: a
• b: b
• c: c
• d: d

#### geoMean

Calculates the geometric mean of a sample or population. The geometric mean is the n-th root of the product of n values. In can be used e.g. to calculate a medium growth rate.

Object geoMean(Collection x)

• x: is the region with the sample or population for which the geometric mean is to be determined.

#### geoMeanExist

Calculates the geometric mean of a sample or population. Evaluates only existing relations in a matrix. Does not count empty cells.

Object geoMeanExist(Collection x)

• x: is the region with the sample or population for which the geometric mean is to be determined.

#### harMean

Calculates the harmonic mean of a sample or population. The harmonic mean is the inverse of the sum of inverses of the values.

Object harMean(Collection x)

• x: is the region with the sample or population for which the harmonic mean is to be determined.

#### harMeanExist

Calculates the harmonic mean of a sample or population. Evaluates only existing relations in a matrix. Does not count empty cells.

Object harMeanExist(Collection x)

• x: is the region with the sample or population for which the harmonic mean is to be determined.

#### identical

detects identical rows or columns in a matrix or tensor.

Object identical(Collection x)

• x: is the matrix or tensor to be checked

#### max

Returns the largest number in a container.

Object max(Collection x)

• x: is the container for which you want the largest number.

#### maxExist

Returns the largest existing number in a container. If the container or its respective row or column is empty, a default response is returned.

Object maxExist(Collection x, Collection alt=nothing)

• x: is the container for which you want the largest number.
• alt: is the default response

#### mean

Calculates the mean of a sample or population. The mean is the arithmetic average of a group of values.

Object mean(Collection x)

• x: is the region with the sample or population for which the mean is to be determined.

#### meanExist

Calculates the mean of a sample or population. Evaluates only existing relations in a matrix. Does not count empty cells.

Object meanExist(Collection x)

• x: is the region with the sample or population for which the mean is to be determined.

#### median

Calculates the median. Data from n samples is ordered from smallest to largest. For an odd sample size, median is the ordered value at (n+1)/2, for an even sample size median is the mean of the 2 middle ordered values.

Object median(Collection x)

• x: is the region with the sample data for which the median is to be determined

#### medianExist

Calculates the median. Evaluates only existing relations in a matrix. Does not count empty cells.

Object medianExist(Collection x)

• x: is the region with the sample data for which the median is to be determined

#### min

Returns the smallest number in a container.

Object min(Collection x)

• x: is the container for which you want the smallest number.

#### minExist

Returns the smallest existing number in a container. If the container or its respective row or column is empty, a default response is returned.

Object minExist(Collection x, Collection alt=nothing)

• x: is the container for which you want the smallest number.
• alt: is the default response

#### NChooseK

calculates the binomial coefficient (n choose k).

Object NChooseK(Object n, Object k)

• n: is the first index
• k: is the second index <= n

#### normdist

Returns the normal cumulative distribution for the specified mean and standard deviation. This function has a very wide range of applications in statistics, including hypothesis testing.

float normdist(float x, float m, float s)

• x: is a probability corresponding to the normal distribution
• m: is the arithmetic mean of the distribution.
• s: is the standard deviation of the distribution

#### normdistinv

Returns the inverse of the normal cumulative distribution (i.e. the z value) for the specified mean, standard deviation, and percentage.

float normdistinv(float x, float m, float s)

• x: is a probability corresponding to the normal distribution
• m: is the arithmetic mean of the distribution.
• s: is the standard deviation of the distribution

#### quartile

Calculates the quartiles. Data from n samples is ordered from smallest to largest. The first quartile is the value at n/4, the third quartile is the value at 3 n/4.

Object quartile(Collection x, Collection quartile)

• x: is the region with the sample or population for which the quartile is to be determined.
• quartile: is the quartile to be returned. This argument must be one of 0,1,2,3,4. If set to 1, the first quartile is returned. If set to 3, the third quartile is returned. 0,2 and 4 return the lowest value, the median and the highest value.

#### quartileExist

Calculates the quartiles. Evaluates only existing relations in a matrix. Does not count empty cells.

Object quartileExist(Collection x, Collection quartile)

• x: is the region with the sample or population for which the quartile is to be determined.
• quartile: is the quartile to be returned. This argument must be one of 0,1,2,3,4. If set to 1, the first quartile is returned. If set to 3, the third quartile is returned. 0,2 and 4 return the lowest value, the median and the highest value.

#### rootDiffSquares

Calculates the square root of a²-b². If (a²-b²) is negative, the function returns 0

Object rootDiffSquares(Object a, Object b)

• a: is the first value
• b: is the second value

#### rootSumSquares

Calculates the square root of a²+b²

Object rootSumSquares(Object a, Object b)

• a: is the first value
• b: is the second value

#### size

returns the size (colums or rows) of an object

int size(Collection x, Object dim=nothing)

• x: is the vector, matrix or tensor
• dim: is either the index of the dimension (0..n) or the tree of the dimension.

#### snormdist

Returns the standard normal cumulative distribution function, i.e. the area under the curve for a given value of z. The distribution has a mean of 0 (zero) and a standard deviation of one.

float snormdist(float z)

• z: is the value for which you want the distribution

#### snormdistinv

Returns the inverse of the standard normal cumulative distribution (i.e. the z value for a given percentage). The distribution has a mean of zero and a standard deviation of one.

float snormdistinv(float p)

• p: is the percentage of the propability.

#### stdDev

Calculates the standard deviation of a sample.

Object stdDev(Collection x)

• x: is the region with the sample data for which the standard deviation is to be determined

#### stdDevExist

Calculates the standard deviation of a sample. Evaluates only existing relations in a matrix. Does not count empty cells.

Object stdDevExist(Collection x)

• x: is the region with the sample data for which the standard deviation is to be determined

#### stdDevP

Calculates the standard deviation of a population, when all data is available.

Object stdDevP(Collection x)

• x: is the region with the population data for which the standard deviation is to be determined.

#### stdDevPExist

Calculates the standard deviation of a population, when all data is available. Evaluates only existing relations in a matrix. Does not count empty cells.

Object stdDevPExist(Collection x)

• x: is the region with the population data for which the standard deviation is to be determined.

#### stdErrorMean

Calculates the standard error of mean, defined as the standard deviation of the sample divided through the square root of the sample size.

Object stdErrorMean(Collection x)

• x: is the region with the sample data for which the standard error of mean is to be determined

#### stdErrorMeanExist

Calculates the standard error of mean. Evaluates only existing relations in a matrix. Does not count empty cells.

Object stdErrorMeanExist(Collection x)

• x: is the region with the sample data for which the standard error of mean is to be determined

#### trimmedMean

Calculates the trimmed mean of a sample or population.

Object trimmedMean(Collection x, Collection percent)

• x: is the region with the sample or population for which the trimmed mean is to be determined.
• percent: is the percentage of both largest and smallest values to be removed before calculating the mean. For the trimmed mean, this value should be set to 5%. When set to 0, the normal mena is returned.

#### trimmedMeanExist

Calculates the trimmed mean of a sample or population. Evaluates only existing relations in a matrix. Does not count empty cells.

Object trimmedMeanExist(Collection x, Collection percent)

• x: is the region with the sample or population for which the trimmed mean is to be determined.
• percent: is the percentage of both largest and smallest values to be removed before calculating the mean. For the trimmed mean, this value should be set to 5%. When set to 0, the normal mena is returned.

#### var

Calculates the variance of a sample.

Object var(Collection x)

• x: is the region with the sample data for which the variance is to be determined

#### varExist

Calculates the variance of a sample. Evaluates only existing relations in a matrix. Does not count empty cells.

Object varExist(Collection x)

• x: is the region with the sample data for which the variance is to be determined

#### varP

Calculates the variance of a population, when all data is available.

Object varP(Collection x)

• x: is the region with the population data for which the variance is to be determined

#### varPExist

Calculates the variance of a population, when all data is available. Evaluates only existing relations in a matrix. Does not count empty cells.

Object varPExist(Collection x)

• x: is the region with the population data for which the variance is to be determined

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