Evaluates the binomial cumulative probability distribution
function.
Namespace: Imsl.StatAssembly: ImslCS (in ImslCS.dll) Version: 6.5.2.0
Syntax public static double Binomial(
int k,
int n,
double pin
)
Public Shared Function Binomial (
k As Integer,
n As Integer,
pin As Double
) As Double
public:
static double Binomial(
int k,
int n,
double pin
)
static member Binomial :
k : int *
n : int *
pin : float -> float
Parameters
- k
- Type: SystemInt32
The int argument for which the binomial distribution
function is to be evaluated.
- n
- Type: SystemInt32
The int number of Bernoulli trials.
- pin
- Type: SystemDouble
A double scalar value representing the probability of
success on each independent trial.
Return Value
Type:
Double
A
double scalar value representing the probability that a
binomial random variable takes a value less than or equal to
k. This value is the probability that
k or fewer successes occur in
n independent Bernoulli trials, each of which
has a
pin probability of success.
Remarks Method Cdf.Binomial evaluates the distribution function of
a binomial random variable with parameters n and
p with p=pin. It does this by
summing probabilities of the random variable taking on the specific
values in its range. These probabilities are computed by the
recursive relationship
To avoid the possibility of underflow, the probabilities are
computed forward from 0, if k is not greater
than n times p, and are computed backward
from n, otherwise. The smallest positive machine
number, , is used as the starting
value for summing the probabilities, which are rescaled by
if forward computation is
performed and by if backward
computation is done. For the special case of p = 0,
Cdf.Binomial is set to 1; and for the case p = 1,
Cdf.Binomial is set to 1 if k = n and to 0 otherwise.
See Also