Optimal bin size algorithm is used. It searches for an optimal bin size between minimum bin size kmin and maximum bin size kmax with total number of meteors per bin num. If there are not enough meteors, a maximum bin size is used. For further calculations, only observing intervals with lengths smaller or equal to optimal bin are used.
Average zenithal hourly rate is calculated by the formula
$$ZHR=\frac{c+\sum_i N_i}{\sum_i \frac{T_{eff,i}}{C_i}}, i=1,2,...,k$$
where \(k\) is the number of observing periods, \(N_i\) - the raw number of meteors seen by each observer in
observing period \(i\), \(T_{eff,i}\) - the effective time or amount of time an observer actually scans the sky for meteors
during observing period \(i\), and \(C_i\) - total correction factor that accounts for all the imperfections in the observing
period \(i\) such as clouds, low radiant, low limiting magnitude.
Total correction factor is equal to
$$C_i=\frac{r^{(6.5-lmg_i)}F_i}{\sin ^{\gamma}(h_i)}$$,
where \(r\) is population index, \(lmg_i\) limiting magnitude, \(F_i\) correction factor for field-of-view obstruction,
\(h_i\) radiant elevation for each observer in observing period \(i\) and \(\gamma\) zenith exponent gamma.
In the numerator, \(c\) is included to correct for the asymmetric high and low end possibilities in
a Poisson distribution (distribution of the number of observed meteors).
Standard error of the average zenithal rate is calculated by the formula
$$\sigma=\frac{\sqrt{c+\sum_i N_i}}{\sum_i \frac{T_{eff,i}}{C_i}}, i=1,2,...,k$$.
The spatial number density of meteoroids producing meteors of magnitude at least 6.5 is (per \(10^9km^3\))
$$\rho=\frac{(10.65r-12.15)ZHR}{3600\times 178700r^{(-1.82)}V}$$,
where \(V\) is stream's geocentric velocity.
Standard error of spatial number density is approximated with
$$\sigma_{\rho}=\frac{\sigma \rho}{ZHR}$$.
Values from the data frame
radiant are used for right ascension and declination of shower radiant. If population index is not specified, it should be calculated using functions pop.index or pop.index2 and then incorporated in the calculation of ZHR (through data frame rdata).