vector_cum_power_law

zdm.energetics.vector_cum_power_law(Eth, *params)[source]

Cumulative power-law luminosity function.

Computes the fraction of bursts with energy above threshold Eth for a power-law distribution dN/dE ~ E^gamma between Emin and Emax.

Parameters:

  • Eth (ndarray) – Energy threshold values in erg.

  • *params (tuple) – (Emin, Emax, gamma) - minimum energy, maximum energy, power-law index. Gamma is typically negative (e.g., -1.5).

Returns:

Fraction of bursts with E > Eth. Returns 1 for Eth < Emin, 0 for Eth > Emax.

Return type:

ndarray