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")