ds.kurtosis.RdThis function calculates the kurtosis of a numeric variable.
ds.kurtosis(x = NULL, method = 1, type = "both", datasources = NULL)a string character, the name of a numeric variable.
an integer between 1 and 3 selecting one of the algorithms for computing kurtosis detailed below. The default value is set to 1.
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'.
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.
a matrix showing the kurtosis of the input numeric variable, the number of valid observations and the validity message.
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.