DFdistr: Lookup table for distribution of range statistics and...
In dwoll/shotGroups: Analyze Shot Group Data

DFdistr

R Documentation

Lookup table for distribution of range statistics and Rayleigh sigma

Description

Lookup table for the distribution of range statistics and Rayleigh sigma from a Monte Carlo simulation of circular bivariate normal shot groups with 0 mean and variance 1 in both directions. Includes the first four moments and several quantiles of the distribution of extreme spread, figure of merit, bounding box diagonal, and Rayleigh sigma for each combination of number of shots per group and number of groups, repeated 10 million times.

Usage

data(DFdistr)

Format

A data frame with 590 observations on the following 77 variables.

n: number of shots in each group. One of 2, 3, ..., 49, 50, 45, ..., 95, 100.
nGroups: number of groups with individual simulated range statistics that were averaged over to yield the final value. One of 1, 2, ..., 9, 10.
nShots: total number of shots, i.e., n*nGroups.
ES_M: Extreme spread mean over all Monte Carlo simulations
ES_V: Extreme spread variance over all Monte Carlo simulations
ES_SD: Extreme spread standard deviation over all Monte Carlo simulations
ES_CV: Extreme spread coefficient of variation over all Monte Carlo simulations
ESSQ_M: Squard extreme spread mean over all Monte Carlo simulations
ESSQ_V: Squared extreme spread variance over all Monte Carlo simulations
ES_SKEW: Extreme spread skewness over all Monte Carlo simulations (smoothed)
ES_KURT: Extreme spread kurtosis over all Monte Carlo simulations (smoothed)
ES_MED: Extreme spread median (50% quantile) over all Monte Carlo simulations
ES_Q005: Extreme spread 0.5% quantile over all Monte Carlo simulations
ES_Q025: Extreme spread 2.5% quantile over all Monte Carlo simulations
ES_Q050: Extreme spread 5% quantile over all Monte Carlo simulations
ES_Q100: Extreme spread 10% quantile over all Monte Carlo simulations
ES_Q250: Extreme spread 25% quantile over all Monte Carlo simulations
ES_Q500: Extreme spread 50% quantile (median) over all Monte Carlo simulations
ES_Q750: Extreme spread 75% quantile over all Monte Carlo simulations
ES_Q900: Extreme spread 90% quantile over all Monte Carlo simulations
ES_Q950: Extreme spread 95% quantile over all Monte Carlo simulations
ES_Q975: Extreme spread 97.5% quantile over all Monte Carlo simulations
ES_Q995: Extreme spread 99.5% quantile over all Monte Carlo simulations
FoM_M: Figure of merit mean over all Monte Carlo simulations
FoM_V: Figure of merit variance over all Monte Carlo simulations
FoM_SD: Figure of merit standard deviation over all Monte Carlo simulations
FoM_CV: Figure of merit coefficient of variation over all Monte Carlo simulations
FoM_SKEW: Figure of merit skewness over all Monte Carlo simulations (smoothed)
FoM_KURT: Figure of merit kurtosis over all Monte Carlo simulations (smoothed)
FoM_MED: Figure of merit median (50% quantile) over all Monte Carlo simulations
FoM_Q005: Figure of merit 0.5% quantile over all Monte Carlo simulations
FoM_Q025: Figure of merit 2.5% quantile over all Monte Carlo simulations
FoM_Q050: Figure of merit 0.25% quantile over all Monte Carlo simulations
FoM_Q100: Figure of merit 10% quantile over all Monte Carlo simulations
FoM_Q250: Figure of merit 25% quantile over all Monte Carlo simulations
FoM_Q500: Figure of merit 50% quantile (median) over all Monte Carlo simulations
FoM_Q750: Figure of merit 75% quantile over all Monte Carlo simulations
FoM_Q900: Figure of merit 90% quantile over all Monte Carlo simulations
FoM_Q950: Figure of merit 95% quantile over all Monte Carlo simulations
FoM_Q975: Figure of merit 97.5% quantile over all Monte Carlo simulations
FoM_Q995: Figure of merit 99.5% quantile over all Monte Carlo simulations
D_M: Bounding box diagonal mean over all Monte Carlo simulations
D_V: Bounding box diagonal variance over all Monte Carlo simulations
D_SD: Bounding box diagonal standard deviation over all Monte Carlo simulations
D_CV: Bounding box diagonal coefficient of variation over all Monte Carlo simulations
D_SKEW: Bounding box diagonal skewness over all Monte Carlo simulations (smoothed)
D_KURT: Bounding box diagonal kurtosis over all Monte Carlo simulations (smoothed)
D_MED: Bounding box diagonal median (50% quantile) over all Monte Carlo simulations
D_Q005: Bounding box diagonal 0.5% quantile over all Monte Carlo simulations
D_Q025: Bounding box diagonal 2.5% quantile over all Monte Carlo simulations
D_Q050: Bounding box diagonal 5% quantile over all Monte Carlo simulations
D_Q100: Bounding box diagonal 10% quantile over all Monte Carlo simulations
D_Q250: Bounding box diagonal 25% quantile over all Monte Carlo simulations
D_Q500: Bounding box diagonal 50% quantile (median) over all Monte Carlo simulations
D_Q750: Bounding box diagonal 75% quantile over all Monte Carlo simulations
D_Q900: Bounding box diagonal 90% quantile over all Monte Carlo simulations
D_Q950: Bounding box diagonal 95% quantile over all Monte Carlo simulations
D_Q975: Bounding box diagonal 97.5% quantile over all Monte Carlo simulations
D_Q995: Bounding box diagonal 99.5% quantile over all Monte Carlo simulations
RS_M: Rayleigh sigma mean over all Monte Carlo simulations
RS_V: Rayleigh sigma variance over all Monte Carlo simulations
RS_SD: Rayleigh sigma standard deviation over all Monte Carlo simulations
RS_CV: Rayleigh sigma coefficient of variation over all Monte Carlo simulations
RS_SKEW: Rayleigh sigma skewness over all Monte Carlo simulations (smoothed)
RS_KURT: Rayleigh sigma kurtosis over all Monte Carlo simulations (smoothed)
RS_MED: Rayleigh sigma median (50% quantile) over all Monte Carlo simulations
RS_Q005: Rayleigh sigma 0.5% quantile over all Monte Carlo simulations
RS_Q025: Rayleigh sigma 2.5% quantile over all Monte Carlo simulations
RS_Q050: Rayleigh sigma 5% quantile over all Monte Carlo simulations
RS_Q100: Rayleigh sigma 10% quantile over all Monte Carlo simulations
RS_Q250: Rayleigh sigma 25% quantile over all Monte Carlo simulations
RS_Q500: Rayleigh sigma 50% quantile (median) over all Monte Carlo simulations
RS_Q750: Rayleigh sigma 75% quantile over all Monte Carlo simulations
RS_Q900: Rayleigh sigma 90% quantile over all Monte Carlo simulations
RS_Q950: Rayleigh sigma 95% quantile over all Monte Carlo simulations
RS_Q975: Rayleigh sigma 97.5% quantile over all Monte Carlo simulations
RS_Q995: Rayleigh sigma 99.5% quantile over all Monte Carlo simulations

Details

The Monte Carlo distribution used 10 million repetitions in each scenario. One scenario was a combination of the n shots in each group, and the nGroups groups over which individual range statistics were averaged. Values for n were 2, 3, ..., 49, 50, 45, ..., 95, 100. Values for nGroups were 1, 2, ... 9, 10.

Skewness and kurtosis were smoothed using separate linear spline fits for each number of groups except for kurtosis of Rayleigh sigma which was fitted using the density of the gamma distribution.

Used in range2sigma to estimate Rayleigh parameter sigma from range statistics, and in efficiency to estimate the number of groups and total shots required to estimate the confidence interval (CI) for Rayleigh sigma with a given coverage probability (CI level) and width.

See the following source for an independent simulation, and for the rationale behind using it to estimate Rayleigh sigma:

http://ballistipedia.com/index.php?title=Range_Statistics

An older eqivalent simulation with less repetitions was done by Taylor and Grubbs (1975).

References

Taylor, M. S., & Grubbs, F. E. (1975). Approximate Probability Distributions for the Extreme Spread (BRL-MR-2438). Aberdeen Proving Ground, MD: U.S. Ballistic Research Laboratory.