descdist: Description of an empirical distribution for non-censored...

Description Usage Arguments Details Value Author(s) References See Also Examples

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.