pb {backbone} | R Documentation |

## Poisson binomial distribution function

### Description

`pb`

computes the poisson binomial distribution function using the refined normal approximation.

### Usage

```
pb(k, p, lowertail = TRUE)
```

### Arguments

`k` |
numeric: value where the pdf should be evaluated |

`p` |
vector: vector of success probabilities |

`lowertail` |
boolean: If TRUE return both upper & lower tail probabilities, if FALSE return only upper tail probability |

### Details

The Refined Normal Approximation (RNA) offers a close approximation when `length(p)`

is
large (Hong, 2013).

### Value

vector, length 2: The first value (if lower = TRUE) is the lower tail probability, the
probability of observing `k`

or fewer successes when each trial has probability `p`

of success.
The second value is the upper tail probability, the probability of observing `k`

or more
successes when each trial has probability `p`

of success.

### References

Hong, Y. (2013). On computing the distribution function for the Poisson binomial distribution. *Computational Statistics and Data Analysis, 59*, 41-51. doi:10.1016/j.csda.2012.10.006

### Examples

```
pb(50,runif(100))
```

*backbone*version 2.1.4 Index]