transformMoment: Transform raw moments into central moments and vice versa

In CharlotteJana/momcalc: Symbolic Moment Calculation

Description

Let X be a random variable and Y the corresponding centered variable, i.e. Y = X - μ. Let p be the order of the desired moment.

If type = 'raw', this function returns

E(X^p) = ∑ choose(p,k)*μ^(p-k)*E(Y^k),

where the sum is taken over any row k in expand.grid(lapply(1:n, function(i) 0:p[i])).

The values of E(Y^k) are replaced by

• centralMoment[[i]], if k = centralMomentOrders[i, ]

• transformMoment(type = 'central', ...), if k is a row in rawMomentOrders

• symbolicMoments(closure, k), if k is neither a row in centralMomentOrders nor in rawMomentOrders

If type = 'central', this function returns

E(Y^p) = ∑ (-1)^(p-k)*choose(p,k)*μ^(p-k)*E(X^k),

where the sum is taken over any row k in expand.grid(lapply(1:n, function(i) 0:p[i])).

The values of E(X^k) are replaced by

• rawMoment[[i]], if k = rawMomentOrders[i, ]

• transformMoment(type = 'raw', ...), if k is not a row in rawMomentOrders

Usage

transformMoment(order, type, momentList, closure = "zero",
  simplify = TRUE)

Arguments

order	numeric vector giving the order of the desired moment.
type	string, either 'central' or 'raw'.
momentList	object of class momentList.
closure	string giving the closure method to use if a central moment is unknown. Possible values are the same as for argument distribution of symbolicMoments.
simplify	bool indiciating if the resulting expressions should be simplified. Function Simplify from package Deriv is used for simplification.

Value

This function returns an object of class 'momentList'.

CharlotteJana/momcalc documentation built on Oct. 17, 2019, 7:21 a.m.