getNegBinFromCI {bootComb} R Documentation

## Find the best-fit negative binomial distribution for a given confidence interval.

### Description

Finds the best-fit negative binomial distribution for a given confidence interval; returns the corresponding probability mass, distribution, quantile and sampling functions. The use of this function within the bootComb package is limited: this is a discrete distribution but since users provide confidence intervals, the corresponding parameters will be best approximated by continuous distributions.

### Usage

getNegBinFromCI(
qLow,
qUpp,
alpha = 0.05,
initPars = c(10, 0.5),
maxiter = 1000
)


### Arguments

 qLow The observed lower quantile. qUpp The observed upper quantile. alpha The confidence level; i.e. the desired coverage is 1-alpha. Defaults to 0.05. initPars A vector of length 2 giving the initial parameter values (size & prob) to start the optimisation; defaults to c(10,0.5). maxiter Maximum number of iterations for optim. Defaults to 1e3. Set to higher values if convergence problems are reported.

### Value

A list with 5 elements:

 r The sampling function. d The probability mass function. p The distribution function. q The quantile function. pars A vector of length 2 giving the mean and standard deviation for the best-fit negatove binomial distribution (size and prob as in rnbinom, dnbinom, pnbinom, qnbinom).

identifyNegBinPars, optim, dnbinom

### Examples

n<-getNegBinFromCI(qLow=1.96,qUpp=19.12)
print(n$pars) # the fitted parameter values (size & prob) n$r(10) # 10 random values from the fitted negative binomial distribution
n$d(8) # the probability mass at x=8 for the negative binomial distribution n$p(12) # the cumulative probability at x=12 for the fitted negative binomial distribution
n$q(c(0.25,0.5,0.75)) # the 25th, 50th (median) and 75th percentiles of the fitted distribution x<-0:30 y<-n$d(x)
barplot(height=y,names.arg=x,xlab="",ylab="probability mass") # bar plot of the fitted neg. bin. pmf



[Package bootComb version 1.1.2 Index]