eqnbinom {EnvStats}  R Documentation 
Estimate Quantiles of a Negative Binomial Distribution
Description
Estimate quantiles of a negative binomial distribution.
Usage
eqnbinom(x, size = NULL, p = 0.5, method = "mle/mme", digits = 0)
Arguments
x 
vector of nonnegative integers indicating the number of trials that took place
before 
size 
vector of positive integers indicating the number of “successes” that
must be observed before the trials are stopped. Missing ( 
p 
numeric vector of probabilities for which quantiles will be estimated.
All values of 
method 
character string specifying the method of estimating the probability parameter.
Possible values are

digits 
an integer indicating the number of decimal places to round to when printing out
the value of 
Details
The function eqnbinom
returns estimated quantiles as well as
estimates of the prob
parameter.
Quantiles are estimated by 1) estimating the prob parameter by
calling enbinom
, and then 2) calling the function
qnbinom
and using the estimated value for
prob
.
Value
If x
is a numeric vector, eqnbinom
returns a
list of class "estimate"
containing the estimated quantile(s) and other
information. See estimate.object
for details.
If x
is the result of calling an estimation function, eqnbinom
returns a list whose class is the same as x
. The list
contains the same components as x
, as well as components called
quantiles
and quantile.method
.
Note
The negative binomial distribution has its roots in a gambling game where participants would bet on the number of tosses of a coin necessary to achieve a fixed number of heads. The negative binomial distribution has been applied in a wide variety of fields, including accident statistics, birthanddeath processes, and modeling spatial distributions of biological organisms.
The geometric distribution with parameter prob=
p
is a special case of the negative binomial distribution with parameters
size=1
and prob=
p
.
Author(s)
Steven P. Millard (EnvStats@ProbStatInfo.com)
References
Forbes, C., M. Evans, N. Hastings, and B. Peacock. (2011). Statistical Distributions. Fourth Edition. John Wiley and Sons, Hoboken, NJ.
Johnson, N. L., S. Kotz, and A. Kemp. (1992). Univariate Discrete Distributions. Second Edition. John Wiley and Sons, New York, Chapter 5.
See Also
enbinom
, NegBinomial, egeom
,
Geometric, estimate.object
.
Examples
# Generate an observation from a negative binomial distribution with
# parameters size=2 and prob=0.2, then estimate the parameter prob
# and the 90th percentile.
# Note: the call to set.seed simply allows you to reproduce this example.
# Also, the only parameter that is estimated is prob; the parameter
# size is supplied in the call to enbinom. The parameter size is printed in
# order to show all of the parameters associated with the distribution.
set.seed(250)
dat < rnbinom(1, size = 2, prob = 0.2)
dat
#[1] 5
eqnbinom(dat, size = 2, p = 0.9)
#Results of Distribution Parameter Estimation
#
#
#Assumed Distribution: Negative Binomial
#
#Estimated Parameter(s): size = 2.0000000
# prob = 0.2857143
#
#Estimation Method: mle/mme for 'prob'
#
#Estimated Quantile(s): 90'th %ile = 11
#
#Quantile Estimation Method: Quantile(s) Based on
# mle/mme for 'prob' Estimators
#
#Data: dat, 2
#
#Sample Size: 1
#
# Clean up
rm(dat)