eqweibull {EnvStats} R Documentation

## Estimate Quantiles of a Weibull Distribution

### Description

Estimate quantiles of a Weibull distribution.

### Usage

  eqweibull(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 Weibull distribution (e.g., eweibull). 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. Possible values are "mle" (maximum likelihood; the default), "mme" (methods of moments), and "mmue" (method of moments based on the unbiased estimator of variance). See the DETAILS section of the help file for eweibull 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 eqweibull returns estimated quantiles as well as estimates of the shape and scale parameters.

Quantiles are estimated by 1) estimating the shape and scale parameters by calling eweibull, and then 2) calling the function qweibull and using the estimated values for shape and scale.

### Value

If x is a numeric vector, eqweibull 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, eqweibull 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 Weibull distribution is named after the Swedish physicist Waloddi Weibull, who used this distribution to model breaking strengths of materials. The Weibull distribution has been extensively applied in the fields of reliability and quality control.

The exponential distribution is a special case of the Weibull distribution: a Weibull random variable with parameters shape=1 and scale=\beta is equivalent to an exponential random variable with parameter rate=1/\beta.

The Weibull distribution is related to the Type I extreme value (Gumbel) distribution as follows: if X is a random variable from a Weibull distribution with parameters shape=\alpha and scale=\beta, then

Y = -log(X) \;\;\;\; (10)

is a random variable from an extreme value distribution with parameters location=-log(\beta) and scale=1/\alpha.

### 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.

eweibull, Weibull, Exponential, EVD, estimate.object.

### Examples

  # Generate 20 observations from a Weibull distribution with parameters
# shape=2 and scale=3, 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 <- rweibull(20, shape = 2, scale = 3)
eqweibull(dat, p = 0.9)

#Results of Distribution Parameter Estimation
#--------------------------------------------
#
#Assumed Distribution:            Weibull
#
#Estimated Parameter(s):          shape = 2.673098
#                                 scale = 3.047762
#
#Estimation Method:               mle
#
#Estimated Quantile(s):           90'th %ile = 4.163755
#
#Quantile Estimation Method:      Quantile(s) Based on
#                                 mle Estimators
#
#Data:                            dat
#
#Sample Size:                     20

#----------

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


[Package EnvStats version 2.8.1 Index]