univariate: Functions to compute statistics on univariate distributions In descstat: Tools for Descriptive Statistics

Description

descstat provide functions to compute statistics on an univariate distribution. This includes central tendency, dispersion, shape and concentration.

Usage

 ``` 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 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95``` ```variance(x, ...) gmean(x, r = 1, ...) gini(x, ...) stdev(x, ...) madev(x, ...) modval(x, ...) medial(x, ...) kurtosis(x, ...) skewness(x, ...) ## Default S3 method: variance(x, w = NULL, ...) ## Default S3 method: gmean(x, r = 1, ...) ## Default S3 method: stdev(x, w = NULL, ...) ## Default S3 method: madev(x, w = NULL, center = c("median", "mean"), ...) ## Default S3 method: skewness(x, ...) ## Default S3 method: kurtosis(x, ...) ## S3 method for class 'freq_table' mean(x, ...) ## S3 method for class 'freq_table' gmean(x, r = 1, ...) ## S3 method for class 'freq_table' variance(x, ...) ## S3 method for class 'freq_table' stdev(x, ...) ## S3 method for class 'freq_table' skewness(x, ...) ## S3 method for class 'freq_table' kurtosis(x, ...) ## S3 method for class 'freq_table' madev(x, center = c("median", "mean"), ...) ## S3 method for class 'freq_table' modval(x, ...) ## S3 method for class 'freq_table' quantile(x, y = c("value", "mass"), probs = c(0.25, 0.5, 0.75), ...) ## S3 method for class 'freq_table' median(x, ..., y = c("value", "mass")) ## S3 method for class 'freq_table' medial(x, ...) ## S3 method for class 'freq_table' gini(x, ...) ## S3 method for class 'cont_table' modval(x, ...) ## S3 method for class 'cont_table' gini(x, ...) ## S3 method for class 'cont_table' skewness(x, ...) ## S3 method for class 'cont_table' kurtosis(x, ...) ## S3 method for class 'cont_table' madev(x, center = c("median", "mean"), ...) ## S3 method for class 'cont_table' mean(x, ...) ## S3 method for class 'cont_table' variance(x, ...) ## S3 method for class 'cont_table' stdev(x, ...) ```

Arguments

 `x` a series or a `freq_table` or a `cont_table` object, `...` further arguments, `r` the order of the mean for the `gmean` function, `w` a vector of weights, `center` the center value used to compute the mean absolute deviations, one of `"median"` or `"mean"`, `y` for the quantile method, one of `"value"` or `"mass"`, `probs` the probabilities for which the quantiles have to be computed.

Details

The following functions are provided:

• central tendency: `mean`, `median`, `medial`, `modval` (for the mode),

• dispersion: `variance`, `stdev`, `maddev` (for mean absolute deviation) and quantile,

• shape: `skewness` and `kurtosis`,

• concentration: `gini`.

When a generic function exists in base R (or in the `stats` package), methods are provided for `freq_table` or `cont_table`, this is a case for `mean`, `median` and `quantile`. When a function exists, but is not generic, we provide a generic and relevant methods using different names (`stdev`, `variance` and `madev` instead respectively of `sd`, `var` and `mad`). Finally some function don't exist in base R and recommended packages, we therefore provide a `modval` function to compute the mode, `gini` for the Gini concentration index, `skewness` and `kurtosis` for Fisher's shape statistics and `gmean` for generalized means (which include the geometric, the quadratic and the harmonic means).

`madev` has a center argument which indicates whether the deviations should be computed respective to the mean or to the median.

`gmean` has a `r` argument: values of -1, 0, 1 and 2 lead respectively to the harmonic, geometric, arithmetic and quadratic means.

Value

a numeric or a tibble.

Yves Croissant

Examples

 ``` 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16``` ```library("dplyr") z <- wages %>% freq_table(wage) z %>% median # the medial is the 0.5 quantile of the mass of the distribution z %>% medial # the modval function returns the mode, it is a one line tibble z %>% modval z %>% quantile(probs = c(0.25, 0.5, 0.75)) # quantiles can compute for the frequency (the default) or the mass # of the series z %>% quantile(y = "mass", probs = c(0.25, 0.5, 0.75)) # univariate statistics can be computed on the joint, marginal or # conditional distributions for cont_table objects wages %>% cont_table(wage, size) %>% joint wages %>% cont_table(wage, size) %>% marginal(size) %>% mean wages %>% cont_table(wage, size) %>% conditional(size) %>% mean ```

descstat documentation built on Feb. 17, 2021, 5:07 p.m.