# calc_kurtosis: Skewness and Kurtosis In QCGWAS: Quality Control of Genome Wide Association Study results

## Description

Functions for calculating skewness and kurtosis

## Usage

 ```1 2 3 4 5 6``` ```calc_kurtosis(input, FRQ_val = NULL, HWE_val = NULL, cal_val = NULL, imp_val = NULL, ...) calc_skewness(input, FRQ_val = NULL, HWE_val = NULL, cal_val = NULL, imp_val = NULL, ...) ```

## Arguments

 `input` either a vector of effect sizes or a data frame using the standard column names. `FRQ_val, HWE_val, cal_val, imp_val, ...` arguments passed to `HQ_filter`.

## Details

Kurtosis is a measure of how well a distribution matches a Gaussian distribution. A Gaussian distribution has a kurtosis of `0`. Negative kurtosis indicates a flatter distribution curve, while positive kurtosis indicates a sharper, thinner curve.

Skewness is a measure of distribution asymmetry. A symmetrical distribution has skewness `0`. A positive skewness indicates a long tail towards higher values, while a negative skewness indicates a long tail towards lower values.

Kurtosis is calculated as:

`sum( (ES - mean(ES))^4) / ((length(ES)-1) * sd(ES)^4 )`

Skewness is calculated as:

`sum( (ES - mean(ES))^3) / ((length(ES)-1) * sd(ES)^3 )`

## Value

Respectively the kurtosis and skewness of the input effect-size distribution.

## Note

Both functions accept vectors as `input`. If `input` is a data frame, the column names must match the standard names used by `QC_GWAS` (`"EFFECT"` for effect sizes, `"EFF_ALL_FREQ"` for allele frequency, etc.)

For plotting skewness and kurtosis: `plot_skewness`.
 ```1 2 3 4 5 6 7 8``` ``` data("gwa_sample") calc_kurtosis(gwa_sample\$EFFECT) calc_kurtosis(gwa_sample) calc_kurtosis(gwa_sample\$EFF_ALL_FREQ) calc_kurtosis(gwa_sample, FRQ_val = 0.05, cal_val = 0.95, filter_NA = FALSE) ```