cpm: Conjugate Prior Measure

Description Usage Arguments Details Author(s) References

View source: R/imPoisC.R

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.