This is meant to perform in the same way as quantile() so it can be a drop in replacement for code using quantile() but using distributional assumptions.

## Usage

binomProbs(x, ...)

# S3 method for default
binomProbs(
x,
probs = c(0.025, 0.05, 0.5, 0.95, 0.975),
na.rm = FALSE,
names = TRUE,
onlyProbs = TRUE,
n = 0L,
m = 0L,
pred = FALSE,
piMethod = c("lim"),
M = 5e+05,
tol = .Machine\$double.eps^0.25,
ciMethod = c("wilson", "wilsonCorrect", "agrestiCoull", "wald", "wc", "ac"),
...
)

## Arguments

x

numeric vector whose mean and probability based confidence values are wanted, NA and NaN values are not allowed in numeric vectors unless na.rm is TRUE.

...

Arguments passed to default method, allows many different methods to be applied.

probs

numeric vector of probabilities with values in the interval 0 to 1, inclusive. When 0, it represents the maximum observed, when 1, it represents the maximum observed. When 0.5 it represents the expected probability (mean).

na.rm

logical; if true, any NA and NaN's are removed from x before the quantiles are computed.

names

logical; if true, the result has a names attribute.

onlyProbs

logical; if true, only return the probability based confidence interval/prediction interval estimates, otherwise return extra statistics.

n

integer/integerish; this is the n used to calculate the prediction or confidence interval. When n=0 (default) use the number of non-NA observations. When calculating the prediction interval, this represents the number of observations used in the input ("true") distribution.

m

integer. When using the prediction interval this represents the number of samples that will be observed in the future for the prediction interval.

pred

Use a prediction interval instead of a confidence interval. By default this is FALSE.

piMethod

gives the prediction interval method (currently only lim) from Lu 2020

M

number of simulations to run for the LIM PI.

tol

tolerance of root finding in the LIM prediction interval

ciMethod

gives the method for calculating the confidence interval.

Can be:

• "argestiCoull" or "ac" -- Agresti-Coull method. For a 95\ interval, this method does not use the concept of "adding 2 successes and 2 failures," but rather uses the formulas explicitly described in the following link:

https://en.wikipedia.org/wiki/Binomial_proportion_confidence_interval#Agresti-Coull_Interval.

• "wilson" -- Wilson Method

• "wilsonCorrect" or "wc" -- Wilson method with continuity correction

• "wald" -- Wald confidence interval or standard z approximation.

## Value

By default the return has the probabilities as names (if named) with the points where the expected distribution are located given the sampling mean and standard deviation. If onlyProbs=FALSE then it would prepend mean, variance, standard deviation, minimum, maximum and number of non-NA observations.

## Details

It is used for confidence intervals with rxode2 solved objects using confint(mean="binom")

## References

• Newcombe, R. G. (1998). "Two-sided confidence intervals for the single proportion: comparison of seven methods". Statistics in Medicine. 17 (8): 857–872. doi:10.1002/(SICI)1097-0258(19980430)17:8<857::AID-SIM777>3.0.CO;2-E. PMID 9595616.

• Hezhi Lu, Hua Jin, A new prediction interval for binomial random variable based on inferential models, Journal of Statistical Planning and Inference, Volume 205, 2020, Pages 156-174, ISSN 0378-3758, https://doi.org/10.1016/j.jspi.2019.07.001.

## Author

Matthew L. Fidler

## Examples


x<- rbinom(7001, p=0.375, size=1)
binomProbs(x)
#>      2.5%        5%       50%       95%     97.5%
#> 0.3716257 0.3734362 0.3829453 0.3925448 0.3943933

# you can also use the prediction interval
# \donttest{
binomProbs(x, pred=TRUE)
#>      2.5%        5%       50%       95%     97.5%
#> 0.3668047 0.3695186 0.3829453 0.3965148 0.3990858
# }

# Can get some extra statistics if you request onlyProbs=FALSE
binomProbs(x, onlyProbs=FALSE)
#>         mean          var           sd            n         2.5%           5%
#>    0.3829453    0.2362982    0.4861051 7001.0000000    0.3716257    0.3734362
#>          50%          95%        97.5%
#>    0.3829453    0.3925448    0.3943933

x[2] <- NA_real_

binomProbs(x, onlyProbs=FALSE)
#>  mean   var    sd     n  2.5%    5%   50%   95% 97.5%
#>    NA    NA    NA    NA    NA    NA    NA    NA    NA

binomProbs(x, na.rm=TRUE)
#>      2.5%        5%       50%       95%     97.5%
#> 0.3715373 0.3733478 0.3828571 0.3924570 0.3943055