Probability Mass Functions

In developing Tweedie functions for queuing models (see ramp.falciparum), we use zero truncated functions to model the multiplicity of exposure (MoE).

library(ramp.func)

Zero Truncated Poisson

x <- 1:20
dx <- dPOIStrunc(1:20, 1)
sum(dx)

## [1] 1

sum(x*dx)

## [1] 1.581977

F_moe <- make_POIStrunc(1)
plot(F_moe(1:20), type = "h", lwd=2, 
     ylim = c(0, F_moe(1)), xlab = "x", 
     ylab = expression(F[MoE]))

Zero Truncated Negative Binomial

x <- 1:40
dx <- dNBtrunc(x, 1, .5)
sum(dx)

## [1] 1

sum(x*dx)

## [1] 2.366024

F_moe <- make_NBtrunc(1, .5)
plot(F_moe(1:20), type = "h", lwd=2, 
     ylim = c(0, F_moe(1)), xlab = "x", 
     ylab = expression(F[MoE]))