ds.kurtosis: Calculates the kurtosis of a numeric variable
In datashield/dsBaseClient: DataSHIELD Client Functions

ds.kurtosis

R Documentation

Calculates the kurtosis of a numeric variable

Description

This function calculates the kurtosis of a numeric variable.

Usage

ds.kurtosis(x = NULL, method = 1, type = "both", datasources = NULL)

Arguments

`x`	a string character, the name of a numeric variable.
`method`	an integer between 1 and 3 selecting one of the algorithms for computing kurtosis detailed below. The default value is set to 1.
`type`	a character which represents the type of analysis to carry out. If `type` is set to 'combine', 'combined', 'combines' or 'c', the global kurtosis is returned if `type` is set to 'split', 'splits' or 's', the kurtosis is returned separately for each study. if `type` is set to 'both' or 'b', both sets of outputs are produced. The default value is set to 'both'.
`datasources`	a list of `DSConnection-class` objects obtained after login. If the `datasources` argument is not specified the default set of connections will be used: see `datashield.connections_default`.

Details

The function calculates the kurtosis of an input variable x with three different methods. The method is specified by the argument method. If x contains any missings, the function removes those before the calculation of the kurtosis. If method is set to 1 the following formula is used kurtosis= \frac{\sum_{i=1}^{N} (x_i - \bar(x))^4 /N}{(\sum_{i=1}^{N} ((x_i - \bar(x))^2) /N)^(2) } - 3, where \bar{x} is the mean of x and N is the number of observations. If method is set to 2 the following formula is used kurtosis= ((N+1)*(\frac{\sum_{i=1}^{N} (x_i - \bar(x))^4 /N}{(\sum_{i=1}^{N} ((x_i - \bar(x))^2) /N)^(2) } - 3) + 6)*((N-1)/((N-2)*(N-3))). If method is set to 3 the following formula is used kurtosis= (\frac{\sum_{i=1}^{N} (x_i - \bar(x))^4 /N}{(\sum_{i=1}^{N} ((x_i - \bar(x))^2) /N)^(2) })*(1-1/N)^2 - 3. This function is similar to the function kurtosis in R package e1071.