eqnbinom.Rd
Estimate quantiles of a negative binomial distribution.
eqnbinom(x, size = NULL, p = 0.5, method = "mle/mme", digits = 0)
vector of non-negative integers indicating the number of trials that took place
before size
“successes” occurred (the total number of
trials that took place is x+1
), or an object resulting
from a call to an estimating function that assumes a negative binomial distribution
(e.g., enbinom
). If x
is a vector of non-negative integers, then
missing (NA
), undefined (NaN
), and infinite (Inf
, -Inf
)
values are allowed but will be removed. If length(x)=n
and n
is
greater than 1, it is assumed that x
represents observations from n
separate negative binomial experiments that all had the same probability of
success (prob
), but possibly different values of size
.
vector of positive integers indicating the number of “successes” that
must be observed before the trials are stopped. Missing (NA
),
undefined (NaN
), and infinite (Inf
, -Inf
) values are allowed
but will be removed. The length of size
must be 1 or else the same
length as x
.
numeric vector of probabilities for which quantiles will be estimated.
All values of p
must be between 0 and 1. The default value is p=0.5
.
character string specifying the method of estimating the probability parameter.
Possible values are
"mle/mme"
(maximum likelihood and method of moments; the default) and
"mvue"
(minimum variance unbiased). You cannot use method="mvue"
if
the sum of the elements in size
is 1. See the DETAILS section of the help file
for enbinom
for more information on these estimation methods.
an integer indicating the number of decimal places to round to when printing out
the value of 100*p
. The default value is digits=0
.
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
.
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
.
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.
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, birth-and-death 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=
\(p\).
# 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
#[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
#>
#> Sample Size: 1
#>
#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)