Estimate Quantiles of a Geometric Distribution
Estimate quantiles of a geometric distribution.
eqgeom(x, p = 0.5, method = "mle/mme", digits = 0)
x |
a numeric vector of observations, or an object resulting from a call to an
estimating function that assumes a geometric distribution
(e.g., |
p |
numeric vector of probabilities for which quantiles will be estimated.
All values of |
method |
character string specifying the method to use to estimate the probability parameter.
Possible values are |
digits |
an integer indicating the number of decimal places to round to when printing out
the value of |
The function eqgeom returns estimated quantiles as well as
the estimate of the rate parameter.
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.
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.
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 A. Kemp. (1992). Univariate Discrete Distributions. Second Edition. John Wiley and Sons, New York, Chapter 5.
# 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 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 #---------- # Clean up #--------- rm(dat)
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