Standard Deviation (st_dev)
Contents
Standard Deviation of Linear Loss scenarios calculated with Matrix of Scenarios or Covariance Matrix.
Syntax
st_dev(matrix) |
short call for case of matrix of scenarios; |
sqrt_quadratic(matrix_cov) |
short call for case of covariance matrix; |
st_dev_name(matrix) |
call with optional name; |
sqrt_quadratic_name(matrix_cov) |
call with optional name. |
Parameters
matrix is a Matrix of Scenarios:
where the header row contains names of variables (except scenario_probability, and scenario_benchmark). Other rows contain numerical data. The scenario_probability, and scenario_benchmark columns are optional.
matrix_cov is a PSG matrix:
where the header row contains names of variables. Other rows contain numerical data.
,
,
, 
.
Mathematical Definition
Standard Deviation function is calculated on the matrix of scenarios matrix as follows:
,
where
, 
.
random vector 
has components 
and J vector scenarios, 
,
random value 
, which is the i-th component of the random vector, 
, has J discrete scenarios 
,
is probability of the scenario 
.
is Loss Function (See section Loss and Gain Functions).
Standard Deviation is calculated on the covariance matrix matrix_cov as follows:
,
is a Square Root Quadratic function.
is an argument of Standard Deviation function.
Example
Case Studies with Standard Deviation
See also
Root Mean Squared Error, Root Mean Squared Error Normal Independent, Root Mean Squared Error Normal Dependent, Standard Risk, Standard Gain, Standard Risk Normal Independent, Standard Gain Normal Independent, Standard Risk Normal Dependent, Standard Gain Normal Dependent, Mean Square Error, Mean Square Error Normal Independent, Mean Square Error Normal Dependent, Variance