binomProbs function

Calculate expected confidence bands with binomial sampling distribution

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.

binomProbs(x, ...)

## Default S3 method:
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.

Returns

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")

Examples

x<- rbinom(7001, p=0.375, size=1)
binomProbs(x)

# you can also use the prediction interval

binomProbs(x, pred=TRUE)

# Can get some extra statistics if you request onlyProbs=FALSE
binomProbs(x, onlyProbs=FALSE)

x[2] <- NA_real_

binomProbs(x, onlyProbs=FALSE)

binomProbs(x, na.rm=TRUE)

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(s)

Matthew L. Fidler