EXSTAT

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Calculation of statistical moments.

[SPU EXSTAT X PX NORM OUT M1 M2 M3 M4 N]

input description data type value type default value
X data vector number, vector variable 0,1,..
PX probability vector number, vector variable 1, 1, ...
NORM normalization flag number (int.), string constant 0 (= NO)
output description data type value type comment
M1 1st moment (mean) number variable
M2 2nd moment (variance or spread) number variable
M2 3rd moment (skewness) number variable
M4 4th moment (kurtosis) number variable
N number of data samples number constant

Note:

  • At least one of the data vectors X and PX must be supplied!
  • The number of data points N is set to the length of the vector X or PX.
  • If X is a not connected, the x-data are initialized with xi = i.
  • If X is a number, the x-data are initialized with xi = X+i.
  • If PX is not a vector, the probabilies pxi are set to 1.
Description

{\displaystyle {\begin{matrix}\mu ={\frac {\sum _{i=0}^{N-1}x_{i}px_{i}}{\sum _{i=0}^{N-1}px_{i}}}&\sigma ^{2}={\frac {\sum _{i=0}^{N-1}(x_{i}-\mu )^{2}px_{i}}{\sum _{i=0}^{N-1}px_{i}}}\\K={\frac {\sum _{i=0}^{N-1}(x_{i}-\mu )^{3}px_{i}}{\sum _{i=0}^{N-1}px_{i}}}&S={\frac {\sum _{i=0}^{N-1}(x_{i}-\mu )^{4}px_{i}}{\sum _{i=0}^{N-1}px_{i}}}\end{matrix}}}

output NORM=0 NORM=1
M1 {\displaystyle \mu \!} {\displaystyle \mu \!}
M2 {\displaystyle \sigma ^{2}\!} {\displaystyle {\frac {\sigma ^{2}}{\mu }}}
See also

<SP-atoms>

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