Given a set of probabilities in the inputVector, this command computes the one-tailed "x" or "z" values for each and puts the results in resultVariable.

If the meanNumber and stdDevNumber are absent, then the elements of resultVariable will be computed based on a mean of zero and a standard deviation of 1.0. In other words, the elements of resultVariable will be "z" values.

If meanNumber and stDevNumber are present, then the elements of resultVariable will be computed using the given mean and standard deviation. In other words, the elements of resultVariable will be "x" values.

The relationship between x values and z values is given by the formula

z_i = Mean(X) – x _i / stdDev(X),

where X represents all x values and x_i represents any one of the values of the input vector.

See also: NORMALPROB

Implementation note: The implementation of this command is based upon an algorithm written by Peter J. Acklam that was coded into a Java class written by Sherali Keramov. Acklam claims the relative error for his algorithm for the normal cumulative distribution function has an absolute value less than 1.15·E-9 in the entire region.

Source: http://home.online.no/~pjacklam/notes/invnorm/

The following program illustrate the operations of the NORMALPROBINV as the inverse of the command.

NORMALPROB (-1 0 1) probabilities1
NORMALPROB (90 100 110) 100 10 probabilities2
NORMALPROBINV probabilities1 z
NORMALPROBINV probabilities2 100 10 x
PRINT probabilities1 probabilities2 z x

Here is the output of the above program:

probabilities1: (0.15865525393145702 0.5 0.841344746068543)
probabilities2: (0.15865525393145702 0.5 0.841344746068543)
z: (-1.0000000000000002 0.0 1.0000000000000004)
x: (90.0 100.0 110.0)