# dLiland: The distribution of distances between discrete events in... In fixedTimeEvents: The Distribution of Distances Between Discrete Events in Fixed Time

## Description

Density, distribution function, quantile function and random generation for the Liland distribution with `R` trials and `r` successes.

## Usage

 ```1 2 3 4``` ```dLiland(x, R, r, warn = FALSE) pLiland(q, R, r, lower.tail = TRUE, warn = FALSE) qLiland(p, R, r) rLiland(n, R, r) ```

## Arguments

 `x, q` vector of quantiles. `p` vector of probabilities. `n` number of observations. `R` number of trials. `r` number of successes. `warn` logical indicating if a warning should be issued if approximation is used. `lower.tail` logical indicating if the lower tail of the distribution should be summed.

## Details

The Liland distribution has probability mass

f(X=x;R,r) = binomial(R-x|r-1)/binomial(R|r)

where x is the distance between consecutive successes, R is the number of trials and r is the number of successes.

## Value

`dLiland` gives the probability mass, `pLiland` gives the distribution function, `qLiland` gives the quantile function, and `rLiland` generates random Liland values.

## Author(s)

Kristian Hovde Liland

## References

Liland, KH & Snipen, L, FixedTimeEvents: An R package for the distribution of distances between discrete events in fixed time, SoftwareX 5 (2016).

`Liland`, `Liland.test`, `simLiland`
 ``` 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17``` ```dLiland(19, R = 1949, r = 162) pLiland(19, R = 1949, r = 162) qLiland(0.5, R = 1949, r = 162) plot( pLiland(1:100, R = 1949, r = 162) ) ## QQ-plot of Liland distribution and random Liland values R <- 2000 r <- 120 n <- 1000 samp <- rLiland(n,R,r) theo <- qLiland(ppoints(n),R,r) qqplot(theo,samp, xlab='F(x;2000,120)', ylab='Sample (1000)', axes=FALSE) axis(1,at=c(0,40,80,120)) axis(2,at=c(0,40,80,120)) box() qqline(samp, distribution = function(p)qLiland(p,R=2000,r=120), col='gray',lty=2) ```