# eqlogis: Estimate Quantiles of a Logistic Distribution

### Description

Estimate quantiles of a logistic distribution.

### Usage

 `1` ``` eqlogis(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 logistic distribution (e.g., `elogis`). 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 to use to estimate 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 `elogis` 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 `eqlogis` returns estimated quantiles as well as estimates of the location and scale parameters.

Quantiles are estimated by 1) estimating the location and scale parameters by calling `elogis`, and then 2) calling the function `qlogis` and using the estimated values for location and scale.

### Value

If `x` is a numeric vector, `eqlogis` 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, `eqlogis` 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 logistic distribution is defined on the real line and is unimodal and symmetric about its location parameter (the mean). It has longer tails than a normal (Gaussian) distribution. It is used to model growth curves and bioassay data.

### 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. (1995). Continuous Univariate Distributions, Volume 2. Second Edition. John Wiley and Sons, New York.

`elogis`, Logistic, `estimate.object`.

### Examples

 ``` 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32``` ``` # Generate 20 observations from a logistic distribution with # parameters location=0 and scale=1, then estimate the parameters # and estimate the 90th percentile. # (Note: the call to set.seed simply allows you to reproduce this example.) set.seed(250) dat <- rlogis(20) eqlogis(dat, p = 0.9) #Results of Distribution Parameter Estimation #-------------------------------------------- # #Assumed Distribution: Logistic # #Estimated Parameter(s): location = -0.2181845 # scale = 0.8152793 # #Estimation Method: mle # #Estimated Quantile(s): 90'th %ile = 1.573167 # #Quantile Estimation Method: Quantile(s) Based on # mle Estimators # #Data: dat # #Sample Size: 20 #---------- # Clean up rm(dat) ```

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