Generation of a seasonal trend — seasonal

This function generates a time trend for given time points in the trial according to a periodic function.

Usage

seasonal_trend(j, lambda, n_wave, n_total, trend_mean, trend_var)

Arguments

j: Time points for which the trend should be generated.
lambda: Strength of time trend.
n_wave: How many cycles (waves) should the time trend have (\(\psi\)).
n_total: Total sample size in the trial.
trend_mean: Integer. In case of random time trends, the strength of the time trend will be generated from N(trend_mean, trend_var).
trend_var: Integer. In case of random time trends, the strength of the time trend will be generated from N(trend_mean, trend_var).

Value

Time trend for time points j.

Details

The time trend is generated according to the function \(f(j) = \lambda \cdot \mathrm{sin} \big( \psi \cdot 2\pi \cdot \frac{j-1}{N-1} \big)\), where \(N\) is the total sample size (parameter n_total) and the parameter \(\psi\) corresponds to the input parameter n_wave.

Author

Marta Bofill Roig, Pavla Krotka