smail

skypy.galaxies.redshift.smail(z_median, alpha, beta, size=None)

Redshifts following the Smail et al. (1994) model.

The redshift follows the Smail et al. [1] redshift distribution.

Parameters

z_medianfloat or array_like of floats

Median redshift of the distribution, must be positive.

alphafloat or array_like of floats

Power law exponent (z/z0)^alpha, must be positive.

betafloat or array_like of floats

Log-power law exponent exp[-(z/z0)^beta], must be positive.

sizeNone or int or tuple

Size of the output. If None, the size is inferred from the arguments. Default is None.

Notes

The probability distribution function \(p(z)\) for redshift \(z\) is given by Amara & Refregier [2] as

\[p(z) \sim \left(\frac{z}{z_0}\right)^\alpha \exp\left[-\left(\frac{z}{z_0}\right)^\beta\right] \;.\]

This is the generalised gamma distribution.

References

1

Smail I., Ellis R. S., Fitchett M. J., 1994, MNRAS, 270, 245

2

Amara A., Refregier A., 2007, MNRAS, 381, 1018