eqhyper {EnvStats}  R Documentation 
Estimate Quantiles of a Hypergeometric Distribution
Description
Estimate quantiles of a hypergeometric distribution.
Usage
eqhyper(x, m = NULL, total = NULL, k = NULL, p = 0.5, method = "mle", digits = 0)
Arguments
x 
nonnegative integer indicating the number of white balls out of a sample of
size 
m 
nonnegative integer indicating the number of white balls in the urn.
You must supply 
total 
positive integer indicating the total number of balls in the urn (i.e.,

k 
positive integer indicating the number of balls drawn without replacement from the
urn. Missing values ( 
p 
numeric vector of probabilities for which quantiles will be estimated.
All values of 
method 
character string specifying the method of estimating the parameters of the
hypergeometric distribution. Possible values are

digits 
an integer indicating the number of decimal places to round to when printing out
the value of 
Details
The function eqhyper
returns estimated quantiles as well as
estimates of the hypergeometric distribution parameters.
Quantiles are estimated by 1) estimating the distribution parameters by
calling ehyper
, and then 2) calling the function
qhyper
and using the estimated values for
the distribution parameters.
Value
If x
is a numeric vector, eqhyper
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, eqhyper
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 hypergeometric distribution can be described by
an urn model with M
white balls and N
black balls. If K
balls
are drawn with replacement, then the number of white balls in the sample
of size K
follows a binomial distribution with
parameters size=
K
and prob=
M/(M+N)
. If K
balls are
drawn without replacement, then the number of white balls in the sample of
size K
follows a hypergeometric distribution
with parameters m=
M
, n=
N
, and k=
K
.
The name “hypergeometric” comes from the fact that the probabilities associated with this distribution can be written as successive terms in the expansion of a function of a Gaussian hypergeometric series.
The hypergeometric distribution is applied in a variety of fields, including quality control and estimation of animal population size. It is also the distribution used to compute probabilities for Fishers's exact test for a 2x2 contingency table.
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 6.
See Also
ehyper
, Hypergeometric, estimate.object
.
Examples
# Generate an observation from a hypergeometric distribution with
# parameters m=10, n=30, and k=5, then estimate the parameter m, and
# the 80'th percentile.
# Note: the call to set.seed simply allows you to reproduce this example.
# Also, the only parameter actually estimated is m; once m is estimated,
# n is computed by subtracting the estimated value of m (8 in this example)
# from the given of value of m+n (40 in this example). The parameters
# n and k are shown in the output in order to provide information on
# all of the parameters associated with the hypergeometric distribution.
set.seed(250)
dat < rhyper(nn = 1, m = 10, n = 30, k = 5)
dat
#[1] 1
eqhyper(dat, total = 40, k = 5, p = 0.8)
#Results of Distribution Parameter Estimation
#
#
#Assumed Distribution: Hypergeometric
#
#Estimated Parameter(s): m = 8
# n = 32
# k = 5
#
#Estimation Method: mle for 'm'
#
#Estimated Quantile(s): 80'th %ile = 2
#
#Quantile Estimation Method: Quantile(s) Based on
# mle for 'm' Estimators
#
#Data: dat
#
#Sample Size: 1
#
# Clean up
#
rm(dat)