Estimate Quantiles of a Uniform Distribution
Estimate quantiles of a uniform distribution.
equnif(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 uniform 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.
The possible values are
|
digits |
an integer indicating the number of decimal places to round to when printing out
the value of |
The function equnif returns estimated quantiles as well as
estimates of the location and scale parameters.
If x is a numeric vector, equnif 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, equnif
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 uniform distribution (also called the rectangular
distribution) with parameters min and max takes on values on the
real line between min and max with equal probability. It has been
used to represent the distribution of round-off errors in tabulated values. Another
important application is that the distribution of the cumulative distribution
function (cdf) of any kind of continuous random variable follows a uniform
distribution with parameters min=0 and max=1.
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. (1995). Continuous Univariate Distributions, Volume 2. Second Edition. John Wiley and Sons, New York.
# Generate 20 observations from a uniform distribution with parameters # min=-2 and max=3, then estimate the parameters via maximum likelihood # and estimate the 90th percentile. # (Note: the call to set.seed simply allows you to reproduce this example.) set.seed(250) dat <- runif(20, min = -2, max = 3) equnif(dat, p = 0.9) #Results of Distribution Parameter Estimation #-------------------------------------------- # #Assumed Distribution: Uniform # #Estimated Parameter(s): min = -1.574529 # max = 2.837006 # #Estimation Method: mle # #Estimated Quantile(s): 90'th %ile = 2.395852 # #Quantile Estimation Method: Quantile(s) Based on # mle Estimators # #Data: dat # #Sample Size: 20 #---------- # Clean up rm(dat)
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