Density, distribution function, quantile function and
random generation for the BISA distribution with location
loc and scale scale.
qbisa(p, shape, scale = 1)pbisa(q, shape, scale = 1)
dbisa(x, shape, scale = 1)
rbisa(n, shape, scale = 1)
Vector of probabilities
Shape parameter
Scale parameter
Vector of quantiles
Vector of quantiles
Number of observations
dbisa gives the density,
pbisa gives the distribution function,
qbisa gives the quantile function, and
rbisa generates random observations.
The length of the result is determined by n
for rbisa, and is the maximum of the lengths
of the numerical arguments for the other functions.
The numerical arguments other than n are
recycled to the length of the result.
If shape is not specified, a default
value of 1 is used.
The Birmbaum-Saunders distribution with shape \(\beta\) and scale \(\theta\) has density
$$f(x;\theta,\beta) = \frac{\sqrt{\frac{x}{\theta}}+\sqrt{\frac{\theta}{x}}}{2\beta x}\phi_{_{NOR}(z)},\quad x \ge 0 $$
where \(\phi_{_{NOR}}(z)\) is the density of the standard normal distribution and
$$z = \frac{1}{\beta}\left(\sqrt{\frac{x}{\theta}}-\sqrt{\frac{\theta}{x} } \right)$$.