Estimate Quantiles of a Geometric Distribution

Estimate quantiles of a geometric distribution.

eqgeom(x, p = 0.5, method = "mle/mme", digits = 0)

Arguments

x: a numeric vector of observations, or an object resulting from a call to an estimating function that assumes a geometric distribution (e.g., egeom). 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 probability parameter. Possible values are "mle/mme" (maximum likelihood and method of moments; the default) and "mvue" (minimum variance unbiased). You cannot use method="mvue" if length(x)=1. See the DETAILS section of the help file for egeom 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 eqgeom returns estimated quantiles as well as the estimate of the rate parameter.

Quantiles are estimated by 1) estimating the probability parameter by calling egeom, and then 2) calling the function qgeom and using the estimated value for the probability parameter.

Value

If x is a numeric vector, eqgeom 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, eqgeom 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.

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 A. Kemp. (1992). Univariate Discrete Distributions. Second Edition. John Wiley and Sons, New York, Chapter 5.

Author

Steven P. Millard (EnvStats@ProbStatInfo.com)

Note

The geometric distribution with parameter prob=\(p\) is a special case of the negative binomial distribution with parameters size=1 and prob=p.

The negative binomial distribution has its roots in a gambling game where participants would bet on the number of tosses of a coin necessary to achieve a fixed number of heads. The negative binomial distribution has been applied in a wide variety of fields, including accident statistics, birth-and-death processes, and modeling spatial distributions of biological organisms.

Examples

  # Generate an observation from a geometric distribution with parameter 
  # prob=0.2, then estimate the parameter prob and the 90'th percentile. 
  # (Note: the call to set.seed simply allows you to reproduce this example.)

  set.seed(250) 
  dat <- rgeom(1, prob = 0.2) 
  dat 
#> [1] 4
  #[1] 4 

  eqgeom(dat, p = 0.9)
#> 
#> Results of Distribution Parameter Estimation
#> --------------------------------------------
#> 
#> Assumed Distribution:            Geometric
#> 
#> Estimated Parameter(s):          prob = 0.2
#> 
#> Estimation Method:               mle/mme
#> 
#> Estimated Quantile(s):           90'th %ile = 10
#> 
#> Quantile Estimation Method:      Quantile(s) Based on
#>                                  mle/mme Estimators
#> 
#> Data:                            dat
#> 
#> Sample Size:                     1
#> 

  #Results of Distribution Parameter Estimation
  #--------------------------------------------
  #
  #Assumed Distribution:            Geometric
  #
  #Estimated Parameter(s):          prob = 0.2
  #
  #Estimation Method:               mle/mme
  #
  #Estimated Quantile(s):           90'th %ile = 10
  #
  #Quantile Estimation Method:      Quantile(s) Based on
  #                                 mle/mme Estimators
  #
  #Data:                            dat
  #
  #Sample Size:                     1

  #----------

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