Description Usage Arguments Details Author(s) References
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’.
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)
|
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 |
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.
Chel Hee Lee chl948@mail.usask.ca
Lee, C.H. (2014) Imprecise Prior for Imprecise Inference on Poisson Sampling Models, PhD Thesis, University of Saskatchewan
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