Functions and Formulas

Statistical

comb

calculates the binomial coefficient (n choose k).

Object comb(Object n, Object k)

Parameters

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

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)

Parameters

x :

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

geoMeanE

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

Object geoMeanE(Collection x)

Parameters

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)

Parameters

x :

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

harMeanE

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

Object harMeanE(Collection x)

Parameters

x :

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

max

Returns the largest number in a container.

Object max(Collection x, Collection y=nothing)

Parameters

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

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)

Parameters

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)

Parameters

x :

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

meanE

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

Object meanE(Collection x)

Parameters

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)

Parameters

x :

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

medianE

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

Object medianE(Collection x)

Parameters

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, Collection y=nothing)

Parameters

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

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)

Parameters

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

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)

Parameters

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

norminv

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

float norminv(float x, float m, float s)

Parameters

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)

Parameters

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.

quartileE

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

Object quartileE(Collection x, Collection quartile)

Parameters

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.

rds

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

Object rds(Object a, Object b)

Parameters

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

rss

Calculates the square root of a²+b²

Object rss(Object a, Object b)

Parameters

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

sd

Calculates the standard deviation of a sample.

Object sd(Collection x)

Parameters

x :

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

sdE

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

Object sdE(Collection x)

Parameters

x :

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

sdp

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

Object sdp(Collection x)

Parameters

x :

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

sdpE

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 sdpE(Collection x)

Parameters

x :

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

seMean

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

Object seMean(Collection x)

Parameters

x :

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

seMeanE

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

Object seMeanE(Collection x)

Parameters

x :

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

size

returns the size (colums or rows) of an object

int size(Collection x, Object dim=nothing)

Parameters

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)

Parameters

z :

is the value for which you want the distribution

snorminv

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 snorminv(float p)

Parameters

p :

is the percentage of the propability.

trimmedMean

Calculates the trimmed mean of a sample or population.

Object trimmedMean(Collection x, Collection percent)

Parameters

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.

trimmedMeanE

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

Object trimmedMeanE(Collection x, Collection percent)

Parameters

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)

Parameters

x :

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

varE

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

Object varE(Collection x)

Parameters

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)

Parameters

x :

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

varpE

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

Object varpE(Collection x)

Parameters

x :

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

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