apply_dpqr | R Documentation |

`distributions3`

objectsVarious utility functions to implement methods for distributions with a
unified workflow, in particular to facilitate working with vectorized
`distributions3`

objects.
These are particularly useful in the computation of densities, probabilities, quantiles,
and random samples when classical d/p/q/r functions are readily available for
the distribution of interest.

```
apply_dpqr(d, FUN, at, elementwise = NULL, drop = TRUE, type = NULL, ...)
make_support(min, max, d, drop = TRUE)
make_positive_integer(n)
```

`d` |
A |

`FUN` |
Function to be computed. Function should be of type |

`at` |
Specification of values at which |

`elementwise` |
logical. Should each element of |

`drop` |
logical. Should the result be simplified to a vector if possible (by
dropping the dimension attribute)? If |

`type` |
Character string used for naming, typically one of |

`...` |
Arguments to be passed to |

`min` , `max` |
Numeric vectors. Minima and maxima of the supports of a |

`n` |
numeric. Number of observations for computing random draws. If |

```
## Implementing a new distribution based on the provided utility functions
## Illustration: Gaussian distribution
## Note: Gaussian() is really just a copy of Normal() with a different class/distribution name
## Generator function for the distribution object.
Gaussian <- function(mu = 0, sigma = 1) {
stopifnot(
"parameter lengths do not match (only scalars are allowed to be recycled)" =
length(mu) == length(sigma) | length(mu) == 1 | length(sigma) == 1
)
d <- data.frame(mu = mu, sigma = sigma)
class(d) <- c("Gaussian", "distribution")
d
}
## Set up a vector Y containing four Gaussian distributions:
Y <- Gaussian(mu = 1:4, sigma = c(1, 1, 2, 2))
Y
## Extract the underlying parameters:
as.matrix(Y)
## Extractor functions for moments of the distribution include
## mean(), variance(), skewness(), kurtosis().
## These can be typically be defined as functions of the list of parameters.
mean.Gaussian <- function(x, ...) {
rlang::check_dots_used()
setNames(x$mu, names(x))
}
## Analogously for other moments, see distributions3:::variance.Normal etc.
mean(Y)
## The support() method should return a matrix of "min" and "max" for the
## distribution. The make_support() function helps to set the right names and
## dimension.
support.Gaussian <- function(d, drop = TRUE, ...) {
min <- rep(-Inf, length(d))
max <- rep(Inf, length(d))
make_support(min, max, d, drop = drop)
}
support(Y)
## Evaluating certain functions associated with the distribution, e.g.,
## pdf(), log_pdf(), cdf() quantile(), random(), etc. The apply_dpqr()
## function helps to call the typical d/p/q/r functions (like dnorm,
## pnorm, etc.) and set suitable names and dimension.
pdf.Gaussian <- function(d, x, elementwise = NULL, drop = TRUE, ...) {
FUN <- function(at, d) dnorm(x = at, mean = d$mu, sd = d$sigma, ...)
apply_dpqr(d = d, FUN = FUN, at = x, type = "density", elementwise = elementwise, drop = drop)
}
## Evaluate all densities at the same argument (returns vector):
pdf(Y, 0)
## Evaluate all densities at several arguments (returns matrix):
pdf(Y, c(0, 5))
## Evaluate each density at a different argument (returns vector):
pdf(Y, 4:1)
## Force evaluation of each density at a different argument (returns vector)
## or at all arguments (returns matrix):
pdf(Y, 4:1, elementwise = TRUE)
pdf(Y, 4:1, elementwise = FALSE)
## Drawing random() samples also uses apply_dpqr() with the argument
## n assured to be a positive integer.
random.Gaussian <- function(x, n = 1L, drop = TRUE, ...) {
n <- make_positive_integer(n)
if (n == 0L) {
return(numeric(0L))
}
FUN <- function(at, d) rnorm(n = at, mean = d$mu, sd = d$sigma)
apply_dpqr(d = x, FUN = FUN, at = n, type = "random", drop = drop)
}
## One random sample for each distribution (returns vector):
random(Y, 1)
## Several random samples for each distribution (returns matrix):
random(Y, 3)
## For further analogous methods see the "Normal" distribution provided
## in distributions3.
methods(class = "Normal")
```

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