eqbeta {EnvStats}  R Documentation 
Estimate Quantiles of a Beta Distribution
Description
Estimate quantiles of a beta distribution.
Usage
eqbeta(x, p = 0.5, method = "mle", digits = 0)
Arguments
x 
a numeric vector of observations, or an object resulting from a call to an
estimating function that assumes a beta distribution
(e.g., 
p 
numeric vector of probabilities for which quantiles will be estimated.
All values of 
method 
character string specifying the method to use to estimate the shape and scale
parameters of the distribution. The possible values are

digits 
an integer indicating the number of decimal places to round to when printing out
the value of 
Details
The function eqbeta
returns estimated quantiles as well as
estimates of the shape1 and shape2 parameters.
Quantiles are estimated by 1) estimating the shape1 and shape2 parameters by
calling ebeta
, and then 2) calling the function
qbeta
and using the estimated values for
shape1 and shape2.
Value
If x
is a numeric vector, eqbeta
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, eqbeta
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 beta distribution takes real values between 0 and 1. Special cases of the
beta are the Uniform[0,1] when shape1=1
and
shape2=1
, and the arcsin distribution when shape1=0.5
and
shape2=0.5
. The arcsin distribution appears in the theory of random walks.
The beta distribution is used in Bayesian analyses as a conjugate to the binomial
distribution.
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 N. Balakrishnan. (1995). Continuous Univariate Distributions, Volume 2. Second Edition. John Wiley and Sons, New York.
See Also
Examples
# Generate 20 observations from a beta distribution with parameters
# shape1=2 and shape2=4, then estimate the parameters via
# maximum likelihood and estimate the 90'th percentile.
# (Note: the call to set.seed simply allows you to reproduce this example.)
set.seed(250)
dat < rbeta(20, shape1 = 2, shape2 = 4)
eqbeta(dat, p = 0.9)
#Results of Distribution Parameter Estimation
#
#
#Assumed Distribution: Beta
#
#Estimated Parameter(s): shape1 = 5.392221
# shape2 = 11.823233
#
#Estimation Method: mle
#
#Estimated Quantile(s): 90'th %ile = 0.4592796
#
#Quantile Estimation Method: Quantile(s) Based on
# mle Estimators
#
#Data: dat
#
#Sample Size: 20
#
# Clean up
rm(dat)