# eqbeta: Estimate Quantiles of a Beta Distribution

### Description

Estimate quantiles of a beta distribution.

### Usage

 `1` ``` 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., `ebeta`). If `x` is a numeric vector, missing (`NA`), undefined (`NaN`), and infinite (`Inf`, `-Inf`) values are allowed but will be removed. `p` 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`. `method` character string specifying the method to use to estimate the shape and scale parameters of the distribution. The possible values are `"mle"` (maximum likelihood; the default), `"mme"` (method of moments), and `"mmue"` (method of moments based on the unbiased estimator of variance). See the DETAILS section of the help file for `ebeta` for more information. `digits` 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`.

### 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.

`ebeta`, `Beta`, `estimate.object`.

### Examples

 ``` 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32``` ``` # 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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