spcal.poisson

Poission limits of criticality and detection.

Formulas used here are taken from the MARLAP manual.

The limit of crticality should be used for all particle detection descisions, not the limit of detection. For an explaination of why, see the manual linked above.

spcal.poisson.currie(ub: float | ndarray, alpha: float = 0.05, beta: float = 0.05, eta: float = 1.0, epsilon: float = 0.0) → tuple[float | ndarray, float | ndarray]

Calculates Sc and Sd for mean background ‘ub’.

For low backgrounds (ub < 10), ‘epsilon’ of 0.5 is recommended [1].

Parameters:

  • nb – mean of background

  • alpha – false positive rate

  • beta – false negative rate

  • eta – (r+1)/r, where r is number of background replicates

  • epsilon – correction term for low backgrounds

Returns:

Sc, net critical value Sd, minimum detection net value

References

spcal.poisson.formula_a(Nb: float | ndarray, alpha: float = 0.05, beta: float = 0.05, t_sample: float = 1.0, t_blank: float = 1.0) → tuple[float | ndarray, float | ndarray]

Calculates Sc and Sd for net background ‘Nb’.

Uses the equations from the MARLAP manual, 20.48, 20.73 [2]. Reccomended for mean backgrounds > 100. Sc equivilent to currie(ub=Nb) if t_sample = t_blank.

Parameters:

  • nb – mean of background

  • alpha – false positive rate

  • beta – false negative rate

Returns:

Sc, net critical value Sd, minimum detection net value

References

spcal.poisson.formula_c(Nb: float | ndarray, alpha: float = 0.05, beta: float = 0.05, t_sample: float = 1.0, t_blank: float = 1.0) → tuple[float | ndarray, float | ndarray]

Calculates Sc and Sd for net background ‘Nb’.

Uses the equations from the MARLAP manual, 20.52, 20.73 [3]. Reccomended for low mean backgrounds. Sc equivilent to ‘decision threshold’ of ISO 11929-1.

Parameters:

  • nb – mean of background

  • alpha – false positive rate

  • beta – false negative rate

Returns:

Sc, net critical value Sd, minimum detection net value

References

spcal.poisson.stapleton_approximation(Nb: float | ndarray, alpha: float = 0.05, beta: float = 0.05, t_sample: float = 1.0, t_blank: float = 1.0) → tuple[float | ndarray, float | ndarray]

Calculates Sc and Sd for net background ‘Nb’.

Uses the equations from the MARLAP manual, 20.54, 20.74 [4]. Reccomended for low mean backgrounds.

Parameters:

  • nb – mean of background

  • alpha – false positive rate

  • beta – false negative rate

Returns:

Sc, net critical value Sd, minimum detection net value

References