Estimate quantiles of a beta distribution.
eqbeta(x, p = 0.5, method = "mle", digits = 0)
a numeric vector of observations, or an object resulting from a call to an
estimating function that assumes a beta distribution
numeric vector of probabilities for which quantiles will be estimated.
All values of
character string specifying the method to use to estimate the shape and scale
parameters of the distribution. The possible values are
an integer indicating the number of decimal places to round to when printing out
the value of
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
ebeta, and then 2) calling the function
qbeta and using the estimated values for
shape1 and shape2.
x is a numeric vector,
eqbeta returns a
list of class
"estimate" containing the estimated quantile(s) and other
estimate.object for details.
x is the result of calling an estimation function,
returns a list whose class is the same as
x. The list
contains the same components as
x, as well as components called
The beta distribution takes real values between 0 and 1. Special cases of the
beta are the Uniform[0,1] when
shape2=1, and the arcsin distribution when
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
Steven P. Millard (EnvStats@ProbStatInfo.com)
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.
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# 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)
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