The Crab pulsar produces extremely intense, short-duration radio bursts known as giant pulses (GPs). We introduce a cumulative-energy diagnostic to quantify the apparent spectral extent of individual Crab giant pulses across the ultra-wideband low-frequency (UWL) receiver band, aiming to build a reproducible method for describing the frequency-domain concentration of emission and to characterize the observed spectral diversity of Crab GPs. Using UWL receiver on the Murriyang (Parkes) radio telescope, we present a systematic study of GPs from the Crab pulsar (PSR J0534+2200). We introduce an empirical classification scheme based on the cumulative distribution function of the pulse energy as a function of observing frequency. We use this diagnostic to separate events with apparent spectral concentration from events with broader spectral coverage. Under this empirical classification scheme, most detected events show apparent spectral concentration within a limited frequency range. Events classified as apparently spectrally concentrated contain most of their measured relative energy within limited frequency ranges, whereas broadband events show more extended spectral coverage. We emphasize that this classification describes the observed spectral extent and should not by itself be interpreted as proof of intrinsically narrow-band emission. Spectral fitting shows that most apparently spectrally concentrated (ASC) GPs have negative spectral indices, while a few events exhibit positive slopes, indicating substantial spectral diversity within the sample. The 3$\sigma$ widths of ASC main pulse GPs appear to cluster around two characteristic ranges, although this feature should be interpreted with caution given the finite time resolution of the data. The energy distribution of ASC main pulse GPs is broadly consistent with a log-normal functional form at low-to-intermediate energies and resembles a power-law-like tail at the high-energy end. The waiting-time distribution can be described by a Weibull function, while a sliding-window comparison with Monte Carlo realizations of a Poisson distribution shows no statistically significant deviation from temporal independence over the present 18.9-min observing span. The CDF-based classification method developed here is transferable to other wideband receiver data, provided that careful consideration is given to the instrumental bandpass, frequency-dependent sensitivity, RFI masking, and signal-to-noise thresholds. These results provide observational constraints on the phenomenology of Crab GPs and may be useful for future studies of pulsar coherent emission and related radio transients.

We present a systematic study of giant pulses (GPs) from the Crab pulsar (PSR J0534+2200) using ultra-wideband observations with the Parkes radio telescope. We introduce an empirical classification scheme based on the cumulative distribution function (CDF) of pulse energy in frequency, separating the detected events into narrow-band and broadband GPs, with the former dominating the present sample. The narrow-band events concentrate most of their energy within limited frequency ranges, whereas broadband events show more extended spectral coverage. Spectral fitting shows that most narrow-band GPs have negative spectral indices, while a few events exhibit positive slopes, indicating substantial spectral diversity within the sample. The 3σ widths of narrow-band main pulse GPs appear to cluster around two characteristic ranges, although this feature should be interpreted with caution given the time resolution of the data. The energy distribution of narrow-band main pulse GPs is broadly consistent with a log-normal form at low-to-intermediate energies and a power-law-like tail at the high-energy end. The waiting-time distribution can be described by a Weibull function, while a sliding-window comparison with Monte Carlo Poisson realizations shows no statistically significant deviation from temporal independence over the present 18.9-minute observing span. These results provide observational constraints on the phenomenology of Crab giant pulses and may be useful for future studies of pulsar coherent emission and related radio transients.