calc_kurtosis {QCGWAS}

Skewness and Kurtosis

Description

Functions for calculating skewness and kurtosis

Usage

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.)

See Also

For plotting skewness and kurtosis: plot_skewness.

Examples

  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)