| poistol.int {tolerance} | R Documentation |
Provides 1-sided or 2-sided tolerance intervals for Poisson random variables. From a statistical quality control perspective, these limits bound the number of occurrences (which follow a Poisson distribution) in a specified future time period.
poistol.int(x, n, m, alpha = 0.05, P = 0.99, side = 1,
method = c("TAB", "LS"))
x |
The number of occurrences of the event in time period n. |
n |
The time period of the original measurements. |
m |
The specified future length of time. |
alpha |
The level chosen such that 1-alpha is the confidence level. |
P |
The proportion of occurrences in future time lengths of size m
to be covered by this tolerance interval. |
side |
Whether a 1-sided or 2-sided tolerance interval is required (determined by side = 1 or side = 2,
respectively). |
method |
The method for calculating the lower and upper confidence bounds, which are used in the calculation
of the tolerance bounds. The default method is "TAB", which is the tabular method and is usually preferred for a smaller
number of occurrences. "LS" gives the large-sample method, which is usually preferred when the number of occurrences is
x>20. |
poistol.int returns a data frame with items:
alpha |
The specified significance level. |
P |
The proportion of occurrences in future time periods of length m. |
lambda.hat |
The mean occurrence rate per unit time, calculated by x/n. |
1-sided.lower |
The 1-sided lower tolerance bound. This is given only if side = 1. |
1-sided.upper |
The 1-sided upper tolerance bound. This is given only if side = 1. |
2-sided.lower |
The 2-sided lower tolerance bound. This is given only if side = 2. |
2-sided.upper |
The 2-sided upper tolerance bound. This is given only if side = 2. |
Hahn, G. J. and Chandra, R. (1981), Tolerance Intervals for Poisson and Binomial Variables, Journal of Quality Technology, 13, 100–110.
## 95%/90% 1-sided Poisson tolerance limits for future
## occurrences in a period of length of 3. Both methods
## are presented for comparison.
poistol.int(x = 45, n = 9, m = 3, alpha = 0.05, P = 0.90,
side = 1, method = "TAB")
poistol.int(x = 45, n = 9, m = 3, alpha = 0.05, P = 0.90,
side = 1, method = "LS")