getRangeStatCI: Confidence interval for range statistics

In dwoll/shotGroups: Analyze Shot Group Data

Confidence interval for range statistics

Description

Returns the confindence interval for given range statistics: extreme spread, figure of merit, bounding box diagonal. Calculations assume a circular bivariate normal shot distribution with 0 mean.

Usage

getRangeStatCI(x, stat="ES", n, nGroups, CIlevel=0.95,
               collapse=TRUE, dstTarget, conversion5)

Arguments

x	a numerical vector with values for extreme spread (ES), figure of merit (FoM), or the diagonal of the bounding box (D).
stat	a character vector with elements "ES" (extreme spread), "FoM" (figure of merit), or "D" (bounding box diagonal) indicating which range statistic is given in x. Elements correspond to those in x in the sense that the second element of stat indicates the statistic for the second element of x. If all elements of x are the same kind of statistic, stat only needs to indicate it once.
n	integer between 2 and 100. Number of shots in each group.
nGroups	integer between 1 and 10. Number of groups when x is the average of individually-measured range statistics from several groups.
CIlevel	confidence level (coverage probability) for the confidence interval. If one of 0.5, 0.9, 0.95, 0.99, the CI is based on the corresponding quantiles of the Monte Carlo distribution of the range statistic for given n and nGroups. If not, CI can only be calculated for extreme spread using a Patnaik chi^2 approximation to the conditional distribution as suggested by Taylor and Grubbs (1975).
collapse	logical: should the list with CIs be simplified if possible?
dstTarget	a numerical value giving the distance to the target - used in MOA calculation. See getMOA.
conversion	how to convert the measurement unit for distance to target to that of the (x,y)-coordinates in MOA calculation. Example 'm2cm'. See getMOA.

Details

Based on the lookup table DFdistr with results from a Monte Carlo simulation. If the value of n is not among those simulated (but is less than 100), a monotonic spline interpolation between the neighboring simulated values is used.

The CI is calculated based on implicit re-scaling by the Rayleigh sigma parameter. First, the tabulated CI boundaries are normalized to a range statistic with point estimate of 1 (via division by the tabulated mean). Then, the normalized CI boundaries are multiplied with the provided range statistic.

Value

A named list with first component range_stat. This is a matrix with columns ES (extreme spread), FoM (figure of merit), D (bounding box diagonal). The second component CI gives the corresponding confidence interval boundaries as a named list with components ES, FoM, D.

References

Grubbs, F. E. (1964b). Statistical measures of accuracy for riflemen and missile engineers. Ann Arbor, ML: Edwards Brothers.

See Also

getRangeStat, range2sigma

Examples

getRangeStatCI(c(1, 2, 3),
               stat=c("ES", "FoM", "D"),
               n=10,
               nGroups=1)

dwoll/shotGroups documentation built on Oct. 17, 2024, 3:23 a.m.