EnvStats (version 2.1.0)

eqpareto: Estimate Quantiles of a Pareto Distribution

Description

Estimate quantiles of a Pareto distribution.

Usage

eqpareto(x, p = 0.5, method = "mle", plot.pos.con = 0.375, digits = 0)

Arguments

x

a numeric vector of observations, or an object resulting from a call to an estimating function that assumes a Pareto distribution (e.g., epareto). If x is a numeric vector, missing

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. Possible values are "mle" (maximum likelihood; the default), and "lse" (least-squares). See the DETAILS section of the help file for

plot.pos.con

numeric scalar between 0 and 1 containing the value of the plotting position constant used to construct the values of the empirical cdf. The default value is plot.pos.con=0.375. This argument is used only when method="lse"

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.

Value

• If x is a numeric vector, eqpareto 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, eqpareto 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.

Details

The function eqpareto 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 epareto, and then 2) calling the function qpareto and using the estimated values for location and scale.

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. (1994). Continuous Univariate Distributions, Volume 1. Second Edition. John Wiley and Sons, New York.

See Also

epareto, Pareto, estimate.object.

Examples

# Generate 30 observations from a Pareto distribution with 
  # parameters location=1 and shape=1 then estimate the parameters 
  # and the 90'th percentile.
  # (Note: the call to set.seed simply allows you to reproduce this example.)

  set.seed(250) 
  dat <- rpareto(30, location = 1, shape = 1) 
  eqpareto(dat, p = 0.9) 

  #Results of Distribution Parameter Estimation
  #--------------------------------------------
  #
  #Assumed Distribution:            Pareto
  #
  #Estimated Parameter(s):          location = 1.009046
  #                                 shape    = 1.079850
  #
  #Estimation Method:               mle
  #
  #Estimated Quantile(s):           90'th %ile = 8.510708
  #
  #Quantile Estimation Method:      Quantile(s) Based on
  #                                 mle Estimators
  #
  #Data:                            dat
  #
  #Sample Size:                     30

  #----------

  # Clean up
  #---------
  rm(dat)