Estimate Quantiles of a Weibull Distribution
Estimate quantiles of a Weibull distribution.
eqweibull(x, p = 0.5, method = "mle", digits = 0)
x |
a numeric vector of observations, or an object resulting from a call to an
estimating function that assumes a Weibull distribution
(e.g., |
p |
numeric vector of probabilities for which quantiles will be estimated.
All values of |
method |
character string specifying the method of estimating the distribution parameters.
Possible values are
|
digits |
an integer indicating the number of decimal places to round to when printing out
the value of |
The function eqweibull returns estimated quantiles as well as
estimates of the shape and scale parameters.
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.
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=β is equivalent to an exponential random variable with
parameter rate=1/β.
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=α and scale=β, then
Y = -log(X) \;\;\;\; (10)
is a random variable from an extreme value distribution with parameters
location=-log(β) and scale=1/α.
Steven P. Millard (EnvStats@ProbStatInfo.com)
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.
# 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)
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