eqgeom {EnvStats} | R Documentation |

## Estimate Quantiles of a Geometric Distribution

### Description

Estimate quantiles of a geometric distribution.

### Usage

```
eqgeom(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 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 |

### Details

The function `eqgeom`

returns estimated quantiles as well as
the estimate of the rate parameter.

Quantiles are estimated by 1) estimating the probability parameter by
calling `egeom`

, and then 2) calling the function
`qgeom`

and using the estimated value for
the probability parameter.

### Value

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`

.

### Note

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.

### 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 A. Kemp. (1992).
*Univariate Discrete Distributions*. Second Edition. John Wiley and Sons,
New York, Chapter 5.

### See Also

`egeom`

, Geometric, `enbinom`

,
NegBinomial, `estimate.object`

.

### Examples

```
# 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)
```

*EnvStats*version 2.8.1 Index]