nsamp {probs} | R Documentation |
Number of Samples from an Urn
Description
Calculates the number of samples from an urn under different sampling scenarios.
Usage
nsamp(n, k, replace = FALSE, ordered = FALSE)
Arguments
n |
an integer or integer vector. |
k |
an integer or integer vector. |
replace |
logical indicating whether sampling should be done with replacement. |
ordered |
logical indicating whether order among samples is important. |
Details
The nsamp()
function will calculate the number of samples from an urn under assorted assumptions on the sampling procedure. The arguments are: n
, the number of (distinguishable) objects in the urn, k
, the sample size, and replace
, ordered
as documented in urnsamples
.
nsamp()
is vectorized, so that entering vectors instead of numbers for n
, k
, replace
, and ordered
results in a vector of corresponding answers.
The formulas used in the four possible combinations of replace
and ordered
are as follows:
When
replace = TRUE
andordered = TRUE
, the value isn^k
.When
replace = FALSE
andordered = TRUE
, the value isn!/(n-k)!
.When
replace = FALSE
andordered = FALSE
, the value isn!/[k!(n-k)!]
.When
replace = TRUE
andordered = FALSE
, the value is(n-1+k)!/[(n-1)!k!]
.
Value
A number.
Author(s)
G. Jay Kerns gkerns@ysu.edu.
See Also
Examples
nsamp(n = 3, k = 2, replace = TRUE, ordered = TRUE)
nsamp(n = 3, k = 2, replace = TRUE, ordered = FALSE)
nsamp(n = 3, k = 2, replace = FALSE, ordered = FALSE)
nsamp(n = 3, k = 2, replace = FALSE, ordered = TRUE)