Functions and CALL Routines 
Returns the deviance based on a probability distribution.
DEVIANCE(distribution, variable,
shapeparameters<,>)


distribution

is a character constant, variable, or expression
that identifies the distribution. Valid distributions are listed in the following
table:
Distribution 
Argument 
Bernoulli 
'BERNOULLI'  'BERN' 
Binomial 
'BINOMIAL'  'BINO' 
Gamma 
'GAMMA' 
Inverse Gauss (Wald) 
'IGAUSS'  'WALD' 
Normal 
'NORMAL'  'GAUSSIAN' 
Poisson 
'POISSON'  'POIS' 

variable

is a numeric constant, variable, or expression.

shapeparameter

are one or more distributionspecific numeric
parameters that characterize the shape of the distribution.


is an optional numeric small value used
for all of the distributions, except for the normal distribution.
DEVIANCE('BERNOULLI', variable, p<,
>)

where

variable

is a binary numeric random variable that
has the value of 1 for success and 0 for failure.

p

is a numeric probability of success with p
1.


is an optional positive numeric value that
is used to bound p. Any value of p in the interval
0 p is replaced by . Any value of p in the interval 1  p 1 is replaced
by 1  .
The DEVIANCE function returns the deviance from a Bernoulli
distribution with a probability of success p, where success is
defined as a random variable value of 1. The equation follows:
DEVIANCE('BINO', variable, , n<, >)

where

variable

is a numeric random variable that contains
the number of successes.
Range: 
0 variable 1 


is a numeric mean parameter.

n

is an integer number of Bernoulli trials
parameter
Range: 
n 0 


is an optional positive numeric value that
is used to bound . Any value of in the
interval 0 n is replaced by n. Any value of in the interval n(1  )
n is replaced by n(1  ).
The DEVIANCE function returns the
deviance from a binomial
distribution, with a probability of success p, and a number of
independent Bernoulli trials n. The following equation describes
the DEVIANCE function for the Binomial distribution, where x
is the random variable.
DEVIANCE('GAMMA', variable, <,
>)

where

variable

is a numeric random variable.
Range: 
variable



is a numeric mean parameter.


is an optional positive numeric value that
is used to bound variable and . Any value of variable in the interval 0 variable is replaced by
. Any value of
in the interval 0 is replaced
by .
The DEVIANCE function returns the deviance from a gamma
distribution with a mean parameter . The following equation
describes the DEVIANCE function for the gamma distribution, where x is the random variable:
DEVIANCE('IGAUSS'  'WALD', variable, <,
>)

where

variable

is a numeric random variable.
Range: 
variable



is a numeric mean parameter.


is an optional positive numeric value that
is used to bound variable and . Any value of variable in the interval 0 variable is replaced by
. Any value of
in the interval 0 is replaced
by .
The DEVIANCE function returns the deviance from an inverse
Gaussian distribution with a mean parameter . The following
equation describes the DEVIANCE function for the inverse Gaussian distribution,
where x is the random variable:
DEVIANCE('NORMAL'  'GAUSSIAN', variable,
)

where

variable

is a numeric random variable.


is a numeric mean parameter.
The DEVIANCE function returns the deviance from a normal
distribution with a mean parameter . The following equation
describes the DEVIANCE function for the normal distribution, where x is the random variable:
DEVIANCE('POISSON', variable, <,
>)

where

variable

is a numeric random variable.
Range: 
variable
0 


is a numeric mean parameter.


is an optional positive numeric value that
is used to bound . Any value of in the
interval 0 is replaced by .
The DEVIANCE function returns the
deviance from a Poisson
distribution with a mean parameter . The following equation
describes the DEVIANCE function for the Poisson distribution, where x is the random variable:
Copyright © 2011 by SAS Institute Inc., Cary, NC, USA. All rights reserved.