def calculate_cold_start_speeds_delta(cold_start_speed_model, on_engine,
    engine_coolant_temperatures, engine_speeds_out_hot, idle_engine_speed):
    """
    Calculates the engine speed delta and phases due to the cold start [RPM, -].

    :param cold_start_speed_model:
        Cold start speed model.
    :type cold_start_speed_model: ColdStartModel

    :param on_engine:
        If the engine is on [-].
    :type on_engine: numpy.array

    :param engine_coolant_temperatures:
        Engine coolant temperature vector [°C].
    :type engine_coolant_temperatures: numpy.array

    :param engine_speeds_out_hot:
        Engine speed at hot condition [RPM].
    :type engine_speeds_out_hot: numpy.array

    :param idle_engine_speed:
        Engine speed idle median and std [RPM].
    :type idle_engine_speed: (float, float)

    :return:
        Engine speed delta due to the cold start and its phases [RPM, -].
    :rtype: numpy.array, numpy.array
    """
    delta = cold_start_speed_model(idle_engine_speed, on_engine,
        engine_coolant_temperatures, engine_speeds_out_hot)
    return delta
