momApp: Moment approximation for polynomial PDMPs

In CharlotteJana/pdmppoly: Moment Approximation for Polynomial PDMPs

Description

This function calculates the raw moments of a polynomial PDMP. The calculation is not based on simulated data but uses the generator of the PDMP to create a system of ordinary differential equations. The moments can be calculated from the solution of this system of ode's.

In some cases, the system of ode's is infinetly large and can therefore not be solved. A modification is necessary, meaning that all equations for moments whose order is greater than a given order will be replaced by fixed values. This process is called moment closure. There are different possibilities, which values to set. They depend on the parameter closure. The following options are implemented:

• zero: Set all values to zero.

• normal: Set values as moments of a normal distributed variable.

• lognormal: Set values as moments of a lognormal distributed variable.

• gamma: Set values as moments of a gamma distributed variable.

Parameter centralize determines, if raw or central moments should be replaced by fixed values.

Usage

momApp(obj, maxorder = 4, na.rm = TRUE, closure = c("zero", "zero",
  "normal", "lognormal", "gamma"), centralize = c(TRUE, FALSE, TRUE,
  FALSE, FALSE))

## S4 method for signature 'polyPdmpModel'
momApp(obj, maxorder = 4, na.rm = TRUE,
  closure = c("zero", "zero", "normal", "lognormal", "gamma"),
  centralize = c(TRUE, FALSE, TRUE, FALSE, FALSE))

Arguments

obj	object of class polyPdmpModel.
maxorder	integer defining the highest order of moments that are considered. Higher orders are droped and replaced by fixed values. The replacement method is specified in parameter closure.
closure	character vector. Every entry defines one possibility of moment closure, i.e. changing the system of ODEs into a closed form that is solvable. Possible values are zero, normal, lognormal or gamma.
centralize	boolean vector with the same length as closure. Entry centralize[i] defines if the replacement of moments with fixed values according to closure[i] should be performed on raw or central moments.

Value

The function returns an S3-object of class momApp. It contains 6 different elements:

• model: the polyPdmpModel obj

• out: a list. The i-th entry is the result of function ode, performed on the system of ode which was created with moment closure closure[i]. Column names are added to make the result understandable.

• moments: a data.frame with the resulting raw moments.

• maxorder: value of parameter maxorder

• closure: value of parameter closure

• centralize: value of parameter centralize

Note

This method works only for PDMPs with one discrete variable.

See Also

momApp-methods for further analysing the result.

Examples

data(genePolyBF)
a <- momApp(genePolyBF, maxorder = 4)
plot(a)
print(a)
summary(a)

CharlotteJana/pdmppoly documentation built on Sept. 4, 2019, 4:40 p.m.