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The MCMC Procedure |
Standard Distributions |
Table 52.3 through Table 52.30 show all densities that PROC MCMC recognizes. These densities can be used in the MODEL, PRIOR, and HYPERPRIOR statements. See the section Using Density Functions in the Programming Statements for information about how to use distributions in the programming statements. To specify an arbitrary distribution, you can use the functions GENERAL and DGENERAL. See the section Specifying a New Distribution for more details. See the section Truncation and Censoring for tips on how to work with truncated distributions and censoring data.
PROC specification |
beta( |
density |
|
parameter restriction |
|
range |
|
mean |
|
variance |
|
mode |
|
random number |
if |
PROC specification |
binary( |
density |
|
parameter restriction |
|
range |
|
mean |
round |
variance |
|
mode |
|
random number |
generate |
PROC specification |
binomial( |
density |
|
parameter restriction |
|
range |
|
mean |
|
variance |
|
mode |
|
PROC specification |
cauchy( |
density |
|
parameter restriction |
|
range |
|
mean |
does not exist |
variance |
does not exist |
mode |
|
random number |
generate |
PROC specification |
chisq( |
density |
|
parameter restriction |
|
range |
|
mean |
|
variance |
|
mode |
|
random number |
|
PROC specification |
expchisq( |
density |
|
parameter restriction |
|
range |
|
mode |
|
random number |
generate |
relationship to the |
|
PROC specification |
expexpon(scale = |
expexpon(iscale = |
density |
|
|
parameter restriction |
|
|
range |
|
same |
mode |
|
|
random number |
generate |
|
relationship to the Expon distribution |
|
PROC specification |
expgamma( |
expgamma( |
density |
|
|
parameter restriction |
|
|
range |
|
same |
mode |
|
|
random number |
generate |
|
relationship to the |
|
PROC specification |
expichisq( |
density |
|
parameter restriction |
|
range |
|
mode |
|
random number |
generate |
relationship to the |
|
PROC specification |
expigamma( |
expigamma( |
density |
|
|
parameter restriction |
|
|
range |
|
same |
mode |
|
|
random number |
generate |
|
relationship to the |
|
PROC specification |
expsichisq( |
density |
|
parameter restriction |
|
range |
|
mode |
|
random number |
generate |
relationship to the |
|
PROC specification |
expon(scale = |
expon(iscale = |
density |
|
|
parameter restriction |
|
|
range |
|
same |
mean |
|
|
variance |
|
|
mode |
|
|
random number |
the exponential distribution is a special case of the gamma distribution: |
PROC specification |
gamma( |
gamma( |
density |
|
|
parameter restriction |
|
|
range |
|
same |
mean |
|
|
variance |
|
|
mode |
|
|
random number |
see (McGrath and Irving; 1973) |
PROC specification |
geo( |
density 1 |
|
parameter restriction |
|
range |
|
mean |
round( |
variance |
|
mode |
|
random number |
based on samples obtained from a Bernoulli distribution with probability |
PROC specification |
ichisq( |
density |
|
parameter restriction |
|
range |
|
mean |
|
variance |
|
mode |
|
random number |
inverse |
PROC specification |
igamma( |
igamma( |
density |
|
|
parameter restriction |
|
|
range |
|
same |
mean |
|
|
variance |
|
|
mode |
|
|
random number |
generate |
|
relationship to the gamma distribution |
|
PROC specification |
laplace( |
laplace( |
density |
|
|
parameter restriction |
|
|
range |
|
same |
mean |
|
|
variance |
|
|
mode |
|
|
random number |
inverse CDF. |
PROC specification |
logistic( |
density |
|
parameter restriction |
|
range |
|
mean |
|
variance |
|
mode |
|
random number |
inverse CDF method with |
PROC specification |
lognormal( |
lognormal( |
lognormal( |
density |
|
|
|
parameter restriction |
|
|
|
range |
|
same |
same |
mean |
|
|
|
variance |
|
|
|
mode |
|
|
|
random number |
generate |
PROC specification |
negbin( |
density |
|
parameter restriction |
|
range |
|
mean |
round |
variance |
|
mode |
|
random number |
generate |
PROC specification |
normal( |
normal( |
normal( |
density |
|
|
|
parameter restriction |
|
|
|
range |
|
same |
same |
mean |
|
same |
same |
variance |
|
|
|
mode |
|
same |
same |
PROC specification |
pareto( |
density |
|
parameter restriction |
|
range |
|
mean |
|
variance |
|
mode |
|
random number |
inverse CDF method with |
useful transformation |
|
PROC specification |
poisson( |
density |
|
parameter restriction |
|
range |
|
mean |
|
variance |
|
mode |
round |
PROC specification |
sichisq( |
density |
|
parameter restriction |
|
range |
|
mean |
|
variance |
|
mode |
|
random number |
scaled inverse |
PROC specification |
t( |
t( |
t( |
density |
|
|
|
parm restriction |
|
|
|
range |
|
same |
same |
mean |
|
same |
same |
variance |
|
|
|
mode |
|
same |
same |
random number |
|
PROC specification |
uniform( |
density |
|
parameter restriction |
none |
range |
|
mean |
|
variance |
|
mode |
does not exist |
random number |
Mersenne Twister (Matsumoto and Kurita; 1992, 1994; Matsumoto and Nishimura; 1998) |
PROC specification |
wald( |
density |
|
parameter restriction |
|
range |
|
mean |
|
variance |
|
mode |
|
random number |
generate |
PROC specification |
weibull( |
density |
|
parameter restriction |
|
range |
|
mean |
|
variance |
|
mode |
|
random number |
inverse CDF method with |
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