## GSLIB Help Page: POSTIK

Description:

- The output from `ik3d` requires additional processing before being used. The program `postik` performs order relations corrections, change of support calculations, and computes various statistics according to the following options:

- Compute the ``E-type'' estimate, i.e., the mean value of the conditional distribution
- Compute the variance the conditional distribution.
- Compute the probability of exceeding a fixed threshold, the average value above that threshold, and the average value below that threshold.
- Compute the value where a fixed conditional cumulative distribution function (cdf) value p is reached, i.e., the conditional p-quantile value.

Parameters:

- distfl: the output IK file (from program `ik3d`) which is considered as input.
- outfl: the output file (output differs depending on output option, see below).
- iout and outpar: iout=1 computes the E-type estimate and the conditional variance, iout=2 computes the probability and means above and below the value outpar, iout=3 computes the z value (p-quantile) corresponding to the cdf value outpar=p, iout=4 computes the conditional variance
- ncut: the number of thresholds.
- cut(i),i=1,ncut: the threshold values used in `ik3d`.
- ivol, ivoltyp, and varred: if ivol = 1 then volume support correction is attempted with the affine correction (ivoltyp=1) or the indirect correction through permanence of a lognormal distribution (ivoltyp=2). The variance reduction factor (between 0 and 1) is specified as varred.
- datafl: the data file containing z-data that provides the details between the IK thresholds. This file is used only if table look-up values are called for in one of the interpolation/extrapolation options.
- icolvr and icolwt: when either ltail, middle or utail is 3 then these variables identify the column for the values and the column for the (declustering) weight in datafl that will be used for the global distribution.
- tmin and tmax: all values strictly less than tmin and strictly greater than tmax are ignored.
- zmin and zmax: minimum and maximum data values allowed. Even when not using linear interpolation it is safe to control the minimum and maximum values entered. The lognormal or hyperbolic upper tail is constrained by zmax.
- ltail and ltpar specify the extrapolation in the lower tail: ltail=1 implements linear interpolation to the lower limit zmin; ltail=2 implements power model interpolation, with w=ltpar, to the lower limit zmin; and ltail=3 implements linear interpolation between tabulated quantiles.
- middle and midpar specify the interpolation within the middle of the distribution: middle=1 implements linear interpolation to the lower limit zmin; middle=2 implements power model interpolation, with w=midpar, to the lower limit zmin; and middle=3 allows for linear interpolation between tabulated quantile values.
- utail and utpar specify the extrapolation in the upper tail of the distribution: utail=1 implements linear interpolation to the upper limit zmax, utail=2 implements power model interpolation, with w=utpar, to the upper limit zmax; utail=3 implements linear interpolation between tabulated quantiles; and, utail=4 implements hyperbolic model extrapolation with w=utpar.
- maxdis: a maximum discretization parameter. The default value of 50 is typically fine; greater accuracy is obtained with a larger number and quicker execution time is obtained with a lower number. A short description of the program

Application notes:

- Although order relations are corrected by `ik3d` they are checked again in `postik`.
- A facility for volume support correction has been provided although we strongly suggest that volume support correction be approached through small-scale simulations. Either the affine correction or the indirect lognormal correction is available.
- There are a number of consequential decisions that must be made about how to interpolate between and extrapolate beyond known values of the cumulative distribution function.
- Both the conditional (E-type) mean and the mean above a specified threshold are calculated by summing the z values at regularly spaced ccdf increments. A parameter maxdis specifies how many such cdf values to calculate. This can be increased depending on the precision required.