ds.kurtosis {dsBaseClient} 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{∑_{i=1}^{N} (x_i - \bar(x))^4 /N}{(∑_{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{∑_{i=1}^{N} (x_i - \bar(x))^4 /N}{(∑_{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{∑_{i=1}^{N} (x_i - \bar(x))^4 /N}{(∑_{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.

### Value

a matrix showing the kurtosis of the input numeric variable, the number of valid observations and the validity message.

### Author(s)

Demetris Avraam, for DataSHIELD Development Team

[Package dsBaseClient version 6.1.1 ]