Standard Distributions |
The section Univariate Distributions (Table 54.7 through Table 54.34) lists all univariate distributions that PROC MCMC recognizes. The section Multivariate Distributions (Table 54.35 through Table 54.38) lists all multivariate distributions that PROC MCMC recognizes. With the exception of the multinomial distribution, all these distributions can be used in the MODEL, PRIOR, and HYPERPRIOR statements. The multinomial distribution is supported only in the MODEL statement. The RANDOM statement supports a limited number of distributions; see Table 54.4 for the complete list.
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 GENERAL and DGENERAL functions. See the section Specifying a New Distribution for more details. See the section Truncation and Censoring for tips about how to work with truncated distributions and censoring data.
PROC specification |
beta( |
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If |
PROC specification |
binary( |
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round |
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Random number |
Generate |
PROC specification |
binomial( |
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PROC specification |
cauchy( |
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Does not exist. |
Variance |
Does not exist. |
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Generate |
PROC specification |
chisq( |
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PROC specification |
expchisq( |
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Generate |
Relationship to the |
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PROC specification |
expexpon(scale = |
expexpon(iscale = |
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Relationship to the exponential distribution |
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PROC specification |
expgamma( |
expgamma( |
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PROC specification |
expichisq( |
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PROC specification |
expigamma( |
expigamma( |
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PROC specification |
expsichisq( |
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Relationship to the |
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PROC specification |
expon(scale = |
expon(iscale = |
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The exponential distribution is a special case of the gamma distribution: |
PROC specification |
gamma( |
gamma( |
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See (McGrath and Irving; 1973). |
PROC specification |
geo( |
Density 1 |
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round( |
Variance |
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Random number |
Based on samples obtained from a Bernoulli distribution with probability |
PROC specification |
ichisq( |
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Random number |
Inverse |
PROC specification |
igamma( |
igamma( |
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Relationship to the gamma distribution |
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PROC specification |
laplace( |
laplace( |
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Inverse CDF. |
PROC specification |
logistic( |
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Inverse CDF method with |
PROC specification |
lognormal( |
lognormal( |
lognormal( |
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Same |
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Generate |
PROC specification |
negbin( |
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round |
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Random number |
Generate |
PROC specification |
normal( |
normal( |
normal( |
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Same |
Same |
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Same |
Same |
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Same |
Same |
PROC specification |
pareto( |
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Inverse CDF method with |
Useful transformation |
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PROC specification |
poisson( |
Density |
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Parameter restriction |
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round |
PROC specification |
sichisq( |
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Random number |
Scaled inverse |
PROC specification |
t( |
t( |
t( |
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Parm restriction |
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Same |
Same |
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Same |
Same |
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Same |
Same |
Random number |
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PROC specification |
uniform( |
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Parameter restriction |
none |
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Does not exist |
Random number |
Mersenne Twister (Matsumoto and Kurita; 1992, 1994; Matsumoto and Nishimura; 1998) |
PROC specification |
wald( |
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Generate |
PROC specification |
weibull( |
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Inverse CDF method with |
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PROC specification |
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Density |
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PROC specification |
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Density |
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PROC specification |
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Density |
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Parameter restriction |
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