summary.fptl  R Documentation 
summary.fptl
summary method for class “fptl”.
is.summary.fptl
tests if its argument is an object of class “summary.fptl”.
print.summary.fptl
shows an object of class “summary.fptl”.
## S3 method for class 'fptl'
summary(object, zeroSlope = 0.01, p0.tol = 8, k = 3, ...)
is.summary.fptl(obj)
## S3 method for class 'summary.fptl'
print(x, ...)
object 
an object of class ‘fptl’, a result of a call to 
obj 
an R object to be tested. 
x 
an object of class ‘summary.fptl’, a result of a call to 
zeroSlope 
maximum slope required to consider that a growing function is constant. 
p0.tol 
controls where the FirstPassageTime Location function begins to increase significantly. 
k 
controls whether the FirstPassageTime Location function decreases very slowly. 
... 
other arguments passed to functions. 
The summary.fptl
function extracts the information contained in object
about the
location of the variation range of a conditioned firstpassagetime (f.p.t.) variable.
It makes an internal call to growth.intervals
function in order to determine the time instants
t_i, \ i=1, \ldots, m
, from which the FirstPassageTime Location (FPTL)
function starts growing, and its local maximums t_{max,i}
. For this, zeroSlope
argument
is considered.
If there is no growth subinterval, the execution of the function summary.fptl
is stopped and an error is reported.
Otherwise, for each of the subintervals I_{i} = [t_{i},t_{i+1}]
the function determines:
The first time instant t_i^* \in [t_i, t_{max,i}]
at which the function is bigger than
or equal to
p_i^* = p_i + 10^{p0.tol}(p_{max,i}  p_i) \ ,
where p_i = FPTL(t_i)
and p_{max,i} = FPTL(t_{max,i}) \ .
10^{p0.tol}
is the ratio of the global increase of the function in the growth subinterval [t_i, t_{max,i}]
that
should be reached to consider that it begins to increase significantly.
The first time instant t_{max,i}^{} \in [t_i, t_{max,i}]
at which the FPTL function is
bigger than or equal to
p_{max,i}^{} = p_{max,i} \big( 1  0.05(p_{max,i}  p_i) \big) \ .
The last time instant t_{max,i}^{+} \in \big[ t_{max,i}, \thinspace T_i \big]
at which the FPTL function is bigger
than or equal to
p_{max,i}^{+} = max \left\{ 1  (1  p_{max,i}^2)^{(1+q)/2}, FPTL(T_i) \right\},
where
T_i = min \big\{ t_{max,i} + k \thinspace (t_{max,i}t_i^*)(1  p_{max,i}),
\thinspace t_{i+1} \big\}
and
q = \displaystyle{\frac{p_{max,i}  p_i}{p_{max,i}}} \ .
print.summary.fptl
displays an object of class “summary.fptl” for immediate understanding of the information it contains.
The summary.fptl
function computes and returns an object of class “summary.fptl” and length 1.
An object of class “summary.fptl” is a list of length 1 for a conditioned f.p.t problem, or of the same length as the number of
values selected from the nondegenerate initial distribution for an unconditioned f.p.t problem.
Each component of the list is again a named list with two components:
instants 
a matrix whose columns correspond to 
FPTLValues 
the matrix of values of the FPTL function on 
It also includes four additional attributes:
Call  a list of the unevaluated calls to the summary.fptl function, substituting each name 
in these calls by its value when the latter has length 1.  
FPTLCall  a list of the unevaluated calls to the FPTL function that resulted in the objects 
used as object argument in Call . 

dp  the common object used as dp argument in the unevaluated calls to the FPTL 
function in FPTLCall . 

vars  NULL or a list containing the common values of names in FPTLCall for those names 
with values of length greater than 1.  
For an unconditioned f.p.t problem, the object includes the additional attribute id
specifying the nondegenerate initial distribution.
The attribute “summary.fptl
” of the value (of class “fpt.density”) of the Approx.fpt.density
function is
an object of class summary.fptl
of length 1 for a conditioned problem, and of length greather than 1 for an unconditioned problem.
It is created from one or successive internal calls to the summary.fptl
function.
is.summary.fptl
returns TRUE
or FALSE
depending on whether its argument is an object of class
“summary.fptl” or not.
Patricia RománRomán, Juan J. SerranoPérez and Francisco TorresRuiz.
Román, P., Serrano, J. J., Torres, F. (2008) Firstpassagetime location function: Application to determine firstpassagetime densities in diffusion processes. Comput. Stat. Data Anal., 52, 4132–4146.
P. RománRomán, J.J. SerranoPérez, F. TorresRuiz. (2012) An R package for an efficient approximation of firstpassagetime densities for diffusion processes based on the FPTL function. Applied Mathematics and Computation, 218, 8408–8428.
P. RománRomán, J.J. SerranoPérez, F. TorresRuiz. (2014) More general problems on firstpassage times for diffusion processes: A new version of the fptdApprox R package. Applied Mathematics and Computation, 244, 432–446.
Approx.cfpt.density
to approximate densities of f.p.t. variables conditioned to a fixed initial value
from objects of class “summary.fptl” and create objects of class “fpt.density”.
Approx.fpt.density
to approximate densities of conditioned or unconditioned f.p.t. variables and create objects of
class “fpt.density” from objects of class “dp”.
FPTL
to evaluate the FPTL function and create objects of class “fptl”.
report.summary.fptl
to generate a report.
growth.intervals
to study the growth of the vector of values resulting from the evaluation of a function.
## Continuing the FPTL(.) example:
## Summarizing an object of class fptl
yy < summary(y)
yy
print(yy, digits=10)
yy1 < summary(y, zeroSlope = 0.001)
yy1
yy2 < summary(y, zeroSlope = 0.001, p0.tol = 10)
yy2
zz < summary(z)
zz
## Testing summary.fptl objects
is.summary.fptl(yy)
is.summary.fptl(zz)
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