# descdist: Description of an empirical distribution for non-censored... In fitdistrplus: Help to Fit of a Parametric Distribution to Non-Censored or Censored Data

## Description

Computes descriptive parameters of an empirical distribution for non-censored data and provides a skewness-kurtosis plot.

## Usage

 ```1 2 3 4 5``` ```descdist(data, discrete = FALSE, boot = NULL, method = "unbiased", graph = TRUE, obs.col = "darkblue", obs.pch = 16, boot.col = "orange") ## S3 method for class 'descdist' print(x, ...) ```

## Arguments

 `data` A numeric vector. `discrete` If `TRUE`, the distribution is considered as discrete. `boot` If not `NULL`, `boot` values of skewness and kurtosis are plotted from bootstrap samples of `data`. `boot` must be fixed in this case to an integer above 10. `method` "unbiased" for unbiased estimated values of statistics or "sample" for sample values. `graph` If `FALSE`, the skewness-kurtosis graph is not plotted. `obs.col` Color used for the observed point on the skewness-kurtosis graph. `obs.pch` plotting character used for the observed point on the skewness-kurtosis graph. `boot.col` Color used for bootstrap sample of points on the skewness-kurtosis graph. `x` An object of class `"descdist"`. `...` Further arguments to be passed to generic functions

## Details

Minimum, maximum, median, mean, sample sd, and sample (if `method=="sample"`) or by default unbiased estimations of skewness and Pearsons's kurtosis values are printed (Sokal and Rohlf, 1995). A skewness-kurtosis plot such as the one proposed by Cullen and Frey (1999) is given for the empirical distribution. On this plot, values for common distributions are also displayed as a tools to help the choice of distributions to fit to data. For some distributions (normal, uniform, logistic, exponential for example), there is only one possible value for the skewness and the kurtosis (for a normal distribution for example, skewness = 0 and kurtosis = 3), and the distribution is thus represented by a point on the plot. For other distributions, areas of possible values are represented, consisting in lines (gamma and lognormal distributions for example), or larger areas (beta distribution for example). The Weibull distribution is not represented on the graph but it is indicated on the legend that shapes close to lognormal and gamma distributions may be obtained with this distribution.

In order to take into account the uncertainty of the estimated values of kurtosis and skewness from data, the data set may be bootstraped by fixing the argument `boot` to an integer above 10. `boot` values of skewness and kurtosis corresponding to the `boot` bootstrap samples are then computed and reported in blue color on the skewness-kurtosis plot.

If `discrete` is `TRUE`, the represented distributions are the Poisson, negative binomial distributions, and the normal distribution to which previous discrete distributions may converge. If `discrete` is `FALSE`, these are uniform, normal, logistic, lognormal, beta and gamma distributions.

## Value

`descdist` returns a list with 7 components,

 ` min ` the minimum value ` max ` the maximum value ` median ` the median value ` mean ` the mean value ` sd ` the standard deviation sample or estimated value ` skewness ` the skewness sample or estimated value ` kurtosis ` the kurtosis sample or estimated value `method` the method specified in input ("unbiased" for unbiased estimated values of statistics or "sample" for sample values.

## Author(s)

Marie-Laure Delignette-Muller and Christophe Dutang.

## References

Cullen AC and Frey HC (1999), Probabilistic techniques in exposure assessment. Plenum Press, USA, pp. 81-159.

Evans M, Hastings N and Peacock B (2000), Statistical distributions. John Wiley and Sons Inc.

Sokal RR and Rohlf FJ (1995), Biometry. W.H. Freeman and Company, USA, pp. 111-115.

Delignette-Muller ML and Dutang C (2015), fitdistrplus: An R Package for Fitting Distributions. Journal of Statistical Software, 64(4), 1-34.

## See Also

`plotdist`

## 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``` ```# (1) Description of a sample from a normal distribution # with and without uncertainty on skewness and kurtosis estimated by bootstrap # set.seed(1234) x1 <- rnorm(100) descdist(x1) descdist(x1,boot=500) # (2) Description of a sample from a beta distribution # with uncertainty on skewness and kurtosis estimated by bootstrap # with changing of default colors and plotting character for observed point # descdist(rbeta(100,shape1=0.05,shape2=1),boot=500, obs.col="blue", obs.pch = 15, boot.col="yellow") # (3) Description of a sample from a gamma distribution # with uncertainty on skewness and kurtosis estimated by bootstrap # without plotting # descdist(rgamma(100,shape=2,rate=1),boot=500,graph=FALSE) # (3) Description of a sample from a Poisson distribution # with uncertainty on skewness and kurtosis estimated by bootstrap # descdist(rpois(100,lambda=2),discrete=TRUE,boot=500) # (4) Description of serving size data # with uncertainty on skewness and kurtosis estimated by bootstrap # data(groundbeef) serving <- groundbeef\$serving descdist(serving, boot=500) ```

### Example output

```Loading required package: MASS
Loading required package: survival
summary statistics
------
min:  -2.345698   max:  2.548991
median:  -0.384628
mean:  -0.1567617
estimated sd:  1.004405
estimated skewness:  0.6052442
estimated kurtosis:  3.102441
summary statistics
------
min:  -2.345698   max:  2.548991
median:  -0.384628
mean:  -0.1567617
estimated sd:  1.004405
estimated skewness:  0.6052442
estimated kurtosis:  3.102441
summary statistics
------
min:  1.205022e-50   max:  0.7978486
median:  6.951827e-07
mean:  0.04291667
estimated sd:  0.1283757
estimated skewness:  3.823696
estimated kurtosis:  18.84779
summary statistics
------
min:  0.04021483   max:  5.748009
median:  1.657709
mean:  1.87063
estimated sd:  1.247628
estimated skewness:  1.112768
estimated kurtosis:  4.305996
summary statistics
------
min:  0   max:  7
median:  2
mean:  2.08
estimated sd:  1.461147
estimated skewness:  0.631824
estimated kurtosis:  3.435681
summary statistics
------
min:  10   max:  200
median:  79
mean:  73.64567
estimated sd:  35.88487
estimated skewness:  0.7352745
estimated kurtosis:  3.551384
```

fitdistrplus documentation built on May 2, 2019, 7:24 a.m.