Estimate Quantiles of an Exponential Distribution

Description

Estimate quantiles of an exponential distribution.

Usage

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  eqexp(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 an exponential distribution (e.g., eexp). 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 rate parameter. Currently the only possible value is "mle/mme" (maximum likelihood/method of moments; the default). See the DETAILS section of the help file for eexp 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 eqexp returns estimated quantiles as well as the estimate of the rate parameter.

Quantiles are estimated by 1) estimating the rate parameter by calling eexp, and then 2) calling the function qexp and using the estimated value for rate.

Value

If x is a numeric vector, eqexp 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, eqexp 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 exponential distribution is a special case of the gamma distribution, and takes on positive real values. A major use of the exponential distribution is in life testing where it is used to model the lifetime of a product, part, person, etc.

The exponential distribution is the only continuous distribution with a “lack of memory” property. That is, if the lifetime of a part follows the exponential distribution, then the distribution of the time until failure is the same as the distribution of the time until failure given that the part has survived to time t.

The exponential distribution is related to the double exponential (also called Laplace) distribution, and to the extreme value 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. (1994). Continuous Univariate Distributions, Volume 1. Second Edition. John Wiley and Sons, New York.

See Also

eexp, Exponential, estimate.object.

Examples

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  # Generate 20 observations from an exponential distribution with parameter 
  # rate=2, then estimate the parameter and estimate the 90th percentile. 
  # (Note: the call to set.seed simply allows you to reproduce this example.)

  set.seed(250) 
  dat <- rexp(20, rate = 2) 
  eqexp(dat, p = 0.9) 

  #Results of Distribution Parameter Estimation
  #--------------------------------------------
  #
  #Assumed Distribution:            Exponential
  #
  #Estimated Parameter(s):          rate = 2.260587
  #
  #Estimation Method:               mle/mme
  #
  #Estimated Quantile(s):           90'th %ile = 1.018578
  #
  #Quantile Estimation Method:      Quantile(s) Based on
  #                                 mle/mme Estimators
  #
  #Data:                            dat
  #
  #Sample Size:                     20
  #

  #----------

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

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