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

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 [e-mail]

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.