new_qfrm {qfratio}

Construct qfrm object

Description

These are internal “constructor” functions used to make qfrm and qfpm objects, which are used as a return value from the qfrm, qfmrm, and qfpm functions.

Usage

new_qfrm(
  statistic,
  error_bound = NULL,
  terms = statistic,
  seq_error = NULL,
  exact = FALSE,
  twosided = FALSE,
  alphaout = FALSE,
  singular_arg = FALSE,
  diminished = FALSE,
  ...,
  class = character()
)

new_qfpm(statistic, exact = TRUE, ..., class = character())

Arguments

statistic

Terminal value (partial sum) for the moment. When missing, obtained as sum(terms).

error_bound

Terminal error bound. When missing, obtained as seq_error[length(seq_error)].

terms

Terms in series expression for the moment along varying polynomial degrees

seq_error

Vector of error bounds corresponding to cumsum(terms)

exact, twosided, alphaout, singular_arg

Logicals used to append attributes to the resultant error bound (see “Value”)

diminished

Logical used to append attribute to the resultant statistic and terms (see “Value”)

...

Additional arguments for accommodating subclasses

class

Character vector to (pre-)append classes to the return value

Value

new_qfrm() and new_qfpm() return a list of class qfrm and c(qfpm, qfrm), respectively. These classes are defined for the print and plot methods.

The return object is a list of 4 elements which are intended to be:

$statistic

evaluation result (sum(terms))

$terms

vector of 0th to mth order terms

$error_bound

error bound of statistic

$seq_error

vector of error bounds corresponding to partial sums (cumsum(terms))

When the result is exact, $terms can be of length 1 and equal to $statistic. This is always the case for the qfpm class.

When the relevant flags are provided in the constructor, $error_bound and $seq_error have the following attributes which control behaviors of the print and plot methods:

"exact"

indicates whether the moment is exact

"twosided"

indicates whether the error bounds are two-sided

"alphaout"

indicates whether any of the scaling factors (alphaA, alphaB, alphaD) is outside (0, 1], when error bound does not strictly hold

"singular"

indicates whether the relevant argument matrix is (numerically) singular, in which case the error bound is invalid

Similarly, when diminished = TRUE, $statistic and $terms have the attribute "diminished" being TRUE, which indicates that numerical underflow/diminishing happened during scaling (see “Scaling” in d1_i).

See Also

qfrm, qfmrm, qfpm: functions that return objects of these classes

methods.qfrm: the print and plot methods