# cpm: Conjugate Prior Measure In imPois: Imprecise Inference for Poisson Sampling Models

## Description

A conjugate prior measure on the canonical parameter is defined in the form of three-parameter exponenitial family of probability measure. `cpm1` computes a normalizing constant. `dcpm` and `pcpm` give density and distribution functions for the canonical variable `t`. Also see the ‘Details’.

## Usage

 ``` 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39``` ```cpm(t, xi2, xi1, xi0, log = FALSE) cpm1(t, xi2, xi1, xi0, log = FALSE) dcpm(x, pars, log.p = FALSE) pcpm(q, pars, lower.tail = TRUE, log.p = FALSE) et.pdf(y = NULL, pars) ey(y = NULL, pars) et.rt(y = NULL, pars) et.la(y = NULL, pars, const = 1000) et2.pdf(y = NULL, pars) et0.pdf(y = NULL, pars) mpm(m, xi2, xi1, xi0, log = FALSE) mpm1(m, xi2, xi1, xi0, log = FALSE) dmpm(x, pars, log.p = FALSE) em.pdf(y = NULL, pars) em.rt(y = NULL, pars) mpm.ztrunc(m, xi2, xi1, xi0, log = FALSE) mpm1.ztrunc(m, xi2, xi1, xi0, log = FALSE) dmpm.ztrunc(x, pars, log.p = FALSE) em.pdf.ztrunc(y = NULL, pars) em.rt.ztrunc(y = NULL, pars) ```

## Arguments

 `t` variable `xi2` precision `xi1` linear component `xi0` effective sample size `log` logical `x` quantile `pars` parameters of length 3 `log.p` logical; if TRUE, probabilities p are given as log(p) `q` quantiles `lower.tail` logical; if TRUE, probabilities are P[X≤ x] otherwise, P[X>x] `y` a vector of observations, by default, NULL `const` constant `m` mean parameter

## Details

A formal definition of this conjugate prior measure is given by

e^(-ξ_2θ^2 + ξ_1θ - ξ_0\exp(θ))

, where θ is a canonical variable ranged from `-Inf` to `Inf`, ξ_2 is a precision parameter, ξ_1 is a linear component, and ξ_0 is an effective sample size.

## Author(s)

Chel Hee Lee [email protected]

## References

Lee, C.H. (2014) Imprecise Prior for Imprecise Inference on Poisson Sampling Models, PhD Thesis, University of Saskatchewan

imPois documentation built on May 30, 2017, 3:32 a.m.