Calculate by how many standard deviations y_new exceeds upper control limit (UCL)

Source: R/ucls.R

Calculates factor f, with observed y_new exceeding UCL by f * sd(y_new). Returns negative value if observed y_new is lower than ucl. Returns Inf if theta_hat is 0.

factor_exceeding(theta_hat, n_new, y_new, ucl)

Arguments

theta_hat

Estimate (unless known) of rate parameter theta

n_new

New value for exposure (reference counts), must at least be 1

y_new

New count values of interest

ucl

Upper control limit (UCL), must be greater than 0

Value

Factor f, with observed y_new exceeding UCL by f * sd(y_new)

Details

Assuming a Poisson distribution with lambda_hat = theta_hat * n_new, the estimated standard deviation of y_new is sqrt(lambda_hat).