equnif {EnvStats}

Estimate Quantiles of a Uniform Distribution

Description

Estimate quantiles of a uniform distribution.

Usage

  equnif(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 uniform distribution (e.g., eunif). 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 of estimating the distribution parameters. 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 eunif for more information on these estimation methods.

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 equnif returns estimated quantiles as well as estimates of the location and scale parameters.

Quantiles are estimated by 1) estimating the location and scale parameters by calling eunif, and then 2) calling the function qunif and using the estimated values for location and scale.

Value

If x is a numeric vector, equnif 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, equnif 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 uniform distribution (also called the rectangular distribution) with parameters min and max takes on values on the real line between min and max with equal probability. It has been used to represent the distribution of round-off errors in tabulated values. Another important application is that the distribution of the cumulative distribution function (cdf) of any kind of continuous random variable follows a uniform distribution with parameters min=0 and max=1.

Author(s)

Steven P. Millard ([e-mail])

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

eunif, Uniform, estimate.object.

Examples

  # Generate 20 observations from a uniform distribution with parameters 
  # min=-2 and max=3, then estimate the parameters via maximum likelihood
  # and estimate the 90th percentile. 
  # (Note: the call to set.seed simply allows you to reproduce this example.)

  set.seed(250) 
  dat <- runif(20, min = -2, max = 3) 
  equnif(dat, p = 0.9) 

  #Results of Distribution Parameter Estimation
  #--------------------------------------------
  #
  #Assumed Distribution:            Uniform
  #
  #Estimated Parameter(s):          min = -1.574529
  #                                 max =  2.837006
  #
  #Estimation Method:               mle
  #
  #Estimated Quantile(s):           90'th %ile = 2.395852
  #
  #Quantile Estimation Method:      Quantile(s) Based on
  #                                 mle Estimators
  #
  #Data:                            dat
  #
  #Sample Size:                     20

  #----------
  # Clean up

  rm(dat)