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MicroStrategy Functions Reference
Plug-In Package Functions
4
Statistical functions
337
• Cumulative is a logical value that determines the form of the function.

If Cumulative=0, it computes the Cumulative Binomial probability.

If Cumulative=1, it computes the Binomial probability.
Expression
For the binomial probability:
Where:
is Combine(n, x).
b(x ;n ,p
)
n
x
⎝ ⎠
⎛ ⎞
p
N
(1–p
)
n–N
=
n
x
⎝ ⎠
⎛ ⎞
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Plug-In Package Functions
MicroStrategy Functions Reference
4
338
Statistical functions
The cumulative binomial distribution is:
Usage notes
• If x or n is not an integer, it is truncated.
• The following are invalid conditions:

One of the arguments is nonnumeric.

x > n.

x< 0.

p < 0 or p > 1.
ChiSquareDistribution
Returns the cumulated chi-squared distribution of the degrees of freedom,
where the pdf is given by
Where:
is the degree of freedom
is the gamma function
The chi-squared distribution is associated with a chi-squared test. A
chi-squared test is used to compare observed values against expected ones. It
determines the validity of a hypothesis, such as the prediction that the next
generation of a certain plant hybrid will exhibit a specific combination of
colors.
Syntax
ChiSquareDistribution(x, df)
B(x ;n ,p
)
b(y ;n ,p
)
y
=0
N
=
f(x )
x
n
2
-–1
x
2
–-
⎝ ⎠
⎛ ⎞
exp
2
n
2
-
ϒ
n
2
-
⎝ ⎠
⎛ ⎞
------------------------
=
n
ϒ
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MicroStrategy Functions Reference
Plug-In Package Functions
4
Statistical functions
339
Where:
• x is a non-negative decimal value at which the distribution is evaluated.
• df is an integer greater than or equal to one (>=1) indicating the number
of degrees of freedom for the distribution.
Usage notes
• If df is not an integer, it is truncated
• The following are invalid conditions:

Either argument is nonnumeric

x < 0

df < 1
ChiSquareTest (chi-square test for goodness of fit)
Returns the result of a test for goodness of fit.
This function returns the
chi-squared distribution for a statistical value and its associated degrees of
freedom to determine, for example, to what extent an experiment verifies
hypothesized results.
Definition
P-value = Pr[Reject H
0
| H
is correct]
P-value is a probability of making a Type 2 error.
ChiSquareTest returns the p-value for the hypothesis test in the following
form:
• H
0
: Argument1 and argument2 come from the same distribution.
• H
1
: Argument1 and argument2 come from different distributions.
Decision
Reality:
H
0
is correct
Reality:
H
1
is correct
Accept H
0
No problem
Type 1 error
Reject H
0
Type 2 error
No problem
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Plug-In Package Functions
MicroStrategy Functions Reference
4
340
Statistical functions
Syntax
ChiSquareTest(Argument1, Argument2)
Where:
• Argument1 is a fact or metric representing a list of values that contains
observed values, which are to be tested against expected values.
• Argument2 is a fact or metric representing a list of expected values,
which are compared against the observed values provided by
Argument1.
Usage notes
• This function returns the probability for a chi-squared (x
2
) statistic and
its associated degrees of freedom (df).
• This function results in an invalid value if Argument1 and Argument2
have a different number of data points. Meaning, each observed value
must have an expected value to be compared to.
Confidence (confidence interval)
Returns the confidence interval for a population mean.
The confidence
interval is a range of values on either side of a mean. For example, if you
order a product through the mail, you can determine, within a given level of
confidence, the earliest and latest date of expected arrival.
Syntax
Confidence(Alpha, Stdev, Size)
Where:
• Alpha is the level of significance at which confidence is computed.
• Stdev is the standard deviation of the population for the given data
range.
• Size is a positive integer indicating the size of the sample.
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MicroStrategy Functions Reference
Plug-In Package Functions
4
Statistical functions
341
Expression
The confidence level is expressed as [100(1-alpha)%]. If alpha = 0.05, then:
• Confidence = 95%
• The area equivalent to 95% of the population = 1.96
• The confidence interval is
Usage notes
• If size is not an integer, it is truncated.
• The following are invalid conditions:

One of the arguments is nonnumeric.

alpha < 0 or alpha >1

stdev < 0

size < 1
Example
For an example of the Confidence function in use, see Confidence Level
example, page 72.
Correlation
Returns the correlation coefficient between two data sets. Correlation
indicates association between two quantitative variables and the degree to
which the values are related or associated.
This function is the same as the Pearson (Pearson product moment
correlation coefficient), page 371.
Syntax
Correlation <FactID> (Argument1, Argument2)
x 1.96
σ
n
----
⎝ ⎠
⎛ ⎞
±
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Plug-In Package Functions
MicroStrategy Functions Reference
4
342
Statistical functions
Where:
• FactID is a parameter that forces a calculation to take place on a fact
table that contains the selected fact.
• Argument1 and Argument2 are lists of values represented by facts or
metrics.
Usage notes
• The correlation coefficient is measured on a scale that varies from + 1
through 0 to - 1. So only a value between -1 and 1 is returned.
• Complete correlation between two variables is expressed by either + 1 or
-1. When one variable increases as the other increases, the correlation is
positive; when one decreases as the other increases, the correlation is
negative. Complete absence of correlation is represented by 0.
• If an array or reference argument contains text, logical values, or empty
cells, those values are ignored; however, cells with the value zero are
included.
• If Argument1 and Argument2 have a different number of data points,
Correlation returns an error.
• If either Argument1 or Argument2 is empty, or if the standard deviation
of their values equals zero, Correlation returns an error.
Covariance
Covariance is used to examine the relationship between two data sets. For
instance, the covariance could be used to examine whether an increase in
income is related to higher education levels. A covariance greater or less than
zero indicate a relationship, while a value of zero indicates no relationship.
Syntax
Covariance <FactID> (Argument1, Argument2)
Where:
• Argument1 and Argument2 are facts or metrics representing lists of
values.
• FactID is a parameter that forces a calculation to take place on a fact
table that contains the selected fact.
MicroStrategy Functions Reference
Plug-In Package Functions
4
Statistical functions
343
Expression
In the expression that follows:
• Argument1 = X
• Argument2
= Y
Where:
= average value of x
= average value of y
Usage notes
The following are invalid conditions:
• Argument1 and Argument2 do not contain the same number of data
points.
• Either value set is empty.
CritBinomial (criterion binomial)
Returns the smallest value for which the cumulative binomial distribution is
less than or equal to a criterion value. Use this function for quality control,
for example, to determine the maximum number of defective items that can
come off an assembly line run before rejecting an entire lot.
Syntax
CritBinomial(Trials, Probability_s, Alpha)
Where:
• Trials is the number of Bernoulli trials.
• Probability_s is the probability of a success on each trial.
• Alpha is the criterion value.
Cov (X ,Y
)
1
n–1
-------
x
i
μ
x
( –
) y
i
μ
y
( –
)
i
=1
n
=
μ
x
μ
y
Plug-In Package Functions
MicroStrategy Functions Reference
4
344
Statistical functions
Usage notes
The following are invalid conditions:
Where:
• Any argument is nonnumeric.
• Trials is not an integer.
• Trials < 0.
• Probability_s is < 0 or probability_s > 1.
• alpha < 0 or alpha > 1.
ExponentialDistribution
Returns either the probability density or the cumulative distribution of a
random variable. This function is used to model the time between events. For
example, it can be used to estimate the probability that an automatic-teller
machine will take no more than one minute to deliver requested cash.
Syntax
ExponentialDistribution <Cumulative> (x, lambda)
Where:
• Cumulative is a logical value that determines the form of the function:

If Cumulative=0 (default), it returns the cumulative distribution.

If Cumulative=1, it returns the probability density.
• x is the value of the function.
• lambda is the value of the parameter.
Expression
• For probability density:
• For cumulative distribution:
f(x ;λ
) λe
–λx
=
F(x ;λ
) 1 e
–λx
=