getDistribution: Returns a 2-point support feasible distribution function for...

In cmottet/RobustTail: RobustTail

Description

Returns a 2-point support feasible distribution function for program (5), i.e. a distribution function with two point masses (p1,p2) and supports (x1,x2) satisfying the three equations p1 + p2 = 1, p1x1 + p2x2 = mu, and m1x1^2 + p2x2^2 = sigma.

Usage

getDistribution(mu, sigma, x1 = NULL)

Arguments

mu	First moment of the distribution function
sigma	Second moment of the distribution function
x1	A real number between 0 and mu. Default value is NULL, in which case, x1 is drawn from a uniform distribution over [0,mu]

Value

a list composed of

p	a vector containing the point masses
x	a vector containing the point support

Examples

###
### Feasible system
###
mu <- 1 ; sigma <- 2
P <- getDistribution(mu,sigma, x1 = mu/2)
P

# Check that the 3 equality constraints are satisfied
data.frame(moments = with(P,c(sum(p), sum(p*x), sum(p*x^2))), truth = c(1, mu,sigma))

###
### Unfeasible system
###
 mu <- 2 ; sigma <- 2
getDistribution(mu,sigma)

###
### Unique solution
###
mu <- 1 ; sigma <- 1
getDistribution(mu,sigma)

cmottet/RobustTail documentation built on May 13, 2019, 8:44 p.m.