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Table A.1.
The long form and meaning of the parameters and abbreviations used in this work.
| Name | Meaning |
|---|---|
| Parameters | |
| A2 | Statistic of Anderson-Darling test (Eq. 11) |
| α | Parameter defined by α ≡ −3/(2B) (Eq. 2) |
| B | Power-law index that modifies the uniform sampling U(0, 1) in number density model (Eq. 1) |
| β | Telescope sensitivity degradation factor (Eq. 10) |
| D(z) | Proper distance (Eq. 9) |
| dL(z) | Luminosity distance (Eq. 9) |
| DMhost | DM contributed by the host galaxy (Eq. 6) |
| DMhost, mean, DMhost, std | mean and standard deviation of host galaxy DM in the log-normal distribution model |
| DMMW | DM contributed by the Milky Way (Eq. 6) |
| DMIGM | DM contributed by the intergalactic medium (Eq. 6) |
| DMIGM, slope | Slope of intergalactic medium DM in Macquart relation |
| DMsrc | DM contributed by the circumburst environment |
| DMtotal | Total DM (Eq. 6) |
| fb | Beaming fraction (Sect. 5.2) |
| fd | Delayed formation fraction (Sect. 5.3) |
| G | Telescope gain (Eq. 10) |
| γ | Spectral index (Sect. 2.2.3) |
| I | Beam intensity (Eq. 10) |
| li | Luminosity index in the power-law distribution model (Sect. 2.2.4) |
| Lmin, Lmax | Minimum and maximum luminosity in the power-law distribution model (Sect. 2.2.4) |
| Lbol | Bolometric luminosity (Sect. 2.2.4) |
| lnL | Log likelihood function (Eq. 11) |
| ν1, ν2 | Minimum and maximum observing frequency of a telescope (Eq. 8) |
| νlow, νhigh | Minimum and maximum frequency range that are used to calculate  (Eq. 8) |
| pK − S | p-value of Kolmogorov-Smirnov test |
| ρ | Local volumetric rate of FRBs (Sect. 5.2) |
 |
Peak flux density (Eq. 8) |
| τd | Formation delay (Sect. 5.3) |
| tDM | Intrachannel dispersion smearing time (Eq. 5) |
| tscat | Scattering time (Eq. 5) |
| tsamp | Sampling time (Eq. 5) |
| Tsys | System temperature (Eq. 10) |
| Vco, FRB | Comoving volume confined by the redshift of an FRB (Eq. 1) |
| Vco, max | Maximum comoving volume corresponding to a given maximum redshift (Eq. 1) |
| wint | Intrinsic pulse width (Eq. 3) |
| wint, mean, wint, std | mean and standard deviation of intrinsic pulse width in the log-normal distribution model (Sect. 2.2.5) |
| warr | Pulse width arriving at Earth (Eq. 4) |
| weff | Effective pulse width (Eq. 5) |
| Acronyms | |
| BIC | Bayesian information criterion |
| CDF | Cumulative distribution function |
| DTD | Delay time distribution |
| GoF | Goodness-of-fit |
| IGM | intergalactic medium |
| ISM | Interstellar medium |
| MC | Monte Carlo |
| MCMC | Markov chain Monte Carlo |
| MLE | Maximum likelihood estimation |
| Probability density function | |
| RFI | Radio frequency interference |
| SEFD | System equivalent flux density |
| SFR | Star formation rate |
| S/N | Signal-to-noise ratio |
| TNS | Transient Name Server |
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