Functions and CALL Routines 
Returns a value from a cumulative probability distribution.
CDF (distribution,quantile<,parm1, ...
,parmk>)


distribution

is a character constant, variable, or expression
that identifies the distribution. Valid distributions are as follows:
Distribution 
Argument 
Bernoulli 
BERNOULLI

Beta 
BETA

Binomial 
BINOMIAL

Cauchy 
CAUCHY

ChiSquare 
CHISQUARE

Exponential 
EXPONENTIAL

F 
F

Gamma 
GAMMA

Geometric 
GEOMETRIC

Hypergeometric 
HYPERGEOMETRIC

Laplace 
LAPLACE

Logistic 
LOGISTIC

Lognormal 
LOGNORMAL

Negative binomial 
NEGBINOMIAL

Normal 
NORMALGAUSS

Normal mixture 
NORMALMIX

Pareto 
PARETO

Poisson 
POISSON

T 
T

Uniform 
UNIFORM

Wald (inverse Gaussian) 
WALDIGAUSS

Weibull 
WEIBULL

Note: Except for T, F, and NORMALMIX,
you can minimally identify any distribution by its first four characters.

quantile

is a numeric constant, variable, or expression
that specifies the value of the random variable.

parm1, ... ,parmk

are optional constants, variables, or expressions
that specify shape, location,
or scale parameters appropriate for the specific
distribution.
See: 
Details for complete information about these
parameters 
The CDF function computes the left cumulative
distribution function from various continuous and discrete probability distributions.
Note: The
QUANTILE function returns the quantile from a
distribution that you specify. The QUANTILE function is the inverse of the
CDF function. For more information, see QUANTILE Function
.
where

x

is a numeric random variable.

p

is a numeric probability of success.
Range: 
0 p
1 
The CDF function for the Bernoulli distribution returns
the probability that an observation from a Bernoulli distribution, with probability
of success equal to p, is less than or equal to x.
The equation follows:
Note: There are no location or scale parameters for this distribution.
where

x

is a numeric random variable.

a

is a numeric shape parameter.

b

is a numeric shape parameter.

l

is the numeric left location parameter.

r

is the right location parameter.
The CDF function for the beta
distribution returns the
probability that an observation from a beta distribution, with shape parameters a and b, is less than or equal to v. The
following equation describes the CDF function of the beta distribution:
where
and
where

m

is an integer random variable that counts
the number of successes.

p

is a numeric probability of success.
Range: 
0 p
1 

n

is an integer parameter that counts the
number of independent Bernoulli trials.
The CDF function for the binomial distribution returns
the probability that an observation from a binomial distribution, with parameters p and n, is less than or equal to m. The
equation follows:
Note: There are no location or scale parameters for the binomial distribution.
CDF('CAUCHY',x<,,>)

where

x

is a numeric random variable.


is a numeric location parameter.


is a numeric scale parameter.
Default: 
1 
Range: 
> 0 
The CDF function for the Cauchy distribution returns
the probability that an observation from a Cauchy distribution, with the location
parameter and the scale parameter , is less than or equal
to x. The equation follows:
CDF('CHISQUARE',x,df
<,nc>)

where

x

is a numeric random variable.

df

is a numeric degrees of freedom parameter.

nc

is an optional numeric noncentrality parameter.
Range: 
nc 0 
The CDF function for the chisquare
distribution returns
the probability that an observation from a chisquare distribution, with df degrees of freedom and noncentrality parameter nc,
is less than or equal to x. This function accepts noninteger
degrees of freedom. If nc is omitted or equal to zero, the value
returned is from the central chisquare distribution. In the following equation,
let $\nu$ = df and let $\lambda$ = nc. The following
equation describes the CDF function of the chisquare distribution:
where
P_{c}(.,.) denotes
the probability from the central chisquare distribution:
and where
P_{g}(
y,
b) is the probability from the gamma distribution given
by
CDF('EXPONENTIAL',x
<,>)

where

x

is a numeric random variable.


is a scale parameter.
Default: 
1 
Range: 
> 0 
The CDF function for the exponential distribution
returns
the probability that an observation from an exponential distribution, with
the scale parameter , is less than or equal to x. The
equation follows:
where

x

is a numeric random variable.

ndf

is a numeric numerator degrees of freedom
parameter.

ddf

is a numeric denominator degrees of freedom
parameter.

nc

is a numeric noncentrality parameter.
Range: 
nc 0 
The CDF function for the F
distribution
returns the probability that an observation from an F distribution,
with ndf numerator degrees of freedom, ddf denominator
degrees of freedom, and noncentrality parameter nc, is less
than or equal to x. This function accepts noninteger degrees
of freedom for ndf and ddf. If nc is
omitted or equal to zero, the value returned is from a central F
distribution. In the following equation, let $\nu_1$ = ndf, let
$\nu_2$ = ddf, and let $\lambda$ = nc. The following
equation describes the CDF function of the F distribution:
where
P_{f}(
f,
u_{1},
u_{2}) is
the probability from the central
F distribution with
and
P_{B}(
x,
a,
b) is the probability from the standard beta distribution.
Note: There are no
location or scale parameters for the F distribution.
CDF('GAMMA',x,a<,>)

where

x

is a numeric random variable.

a

is a numeric shape parameter.


is a numeric scale parameter.
Default: 
1 
Range: 
> 0 
The CDF function for the gamma distribution returns
the probability that an observation from a gamma distribution, with shape
parameter a and scale parameter , is less than or equal
to x. The equation follows:
where

m

is a numeric random variable that denotes
the number of failures.

p

is a numeric probability of success.
Range: 
0 p
1 
The CDF function for the geometric distribution returns
the probability that an observation from a geometric distribution, with parameter p, is less than or equal to m. The equation
follows:
Note: There are no location or scale parameters for this distribution.
where

x

is an integer random variable.

N

is an integer population size parameter.

R

is an integer number of items in the category
of interest.

n

is an integer sample size parameter.

o

is an optional numeric odds ratio parameter.
The CDF function for the hypergeometric
distribution
returns the probability that an observation from an extended hypergeometric
distribution, with population size N, number of items R, sample size n, and odds ratio o, is less
than or equal to x. If o is omitted or equal to
1, the value returned is from the usual hypergeometric distribution. The
equation follows:
CDF('LAPLACE',x<,,>)

where

x

is a numeric random variable.


is a numeric location parameter.


is a numeric scale parameter.
Default: 
1 
Range: 
> 0 
The CDF function for the Laplace distribution returns
the probability that an observation from the Laplace distribution, with the
location parameter and the scale parameter , is less than or
equal to x. The equation follows:
CDF('LOGISTIC',x<,,>)

where

x

is a numeric random variable.


is a numeric location parameter


is a numeric scale parameter.
Default: 
1 
Range: 
> 0 
The CDF function for the logistic distribution
returns
the probability that an observation from a logistic distribution, with a location
parameter and a scale parameter , is less than or equal
to x. The equation follows:
CDF('LOGNORMAL',x<,,>)

where

x

is a numeric random variable.


specifies a numeric log scale parameter.
(exp() is a scale parameter.)


specifies a numeric shape parameter.
Default: 
1 
Range: 
> 0 
The CDF function for the lognormal distribution returns the probability
that an observation from a lognormal distribution, with the log scale parameter
and the shape parameter , is less than or equal to x.
The equation follows:
where

m

is a positive integer random variable that
counts the number of failures.

p

is a numeric probability of success.
Range: 
0 p
1 

n

is a numeric value that counts the number
of successes.
The CDF function for the negative binomial
distribution
returns the probability that an observation from a negative binomial distribution,
with probability of success p and number of successes n, is less than or equal to m. The equation follows:
Note: There are no location or scale parameters for the negative binomial distribution.
CDF('NORMAL',x<,,>)

where

x

is a numeric random variable.


is a numeric location parameter.


is a numeric scale parameter.
Default: 
1 
Range: 
> 0 
The CDF function for the normal distribution returns
the probability that an observation from the normal distribution, with the
location parameter and the scale parameter , is less than
or equal to x. The equation follows:
CDF('NORMALMIX',x,n,p,m,s)

where

x

is a numeric random variable.

n

is the integer number of mixtures.

p

is the n proportions,
, where
.

m

is the n means
.

s

is the n standard deviations
.
The CDF function for the normal mixture
distribution
returns the probability that an observation from a mixture of normal distribution
is less than or equal to x. The equation follows:
Note: There are no location or scale parameters for the normal mixture distribution.
where

x

is a numeric random variable.

a

is a numeric shape parameter.

k

is a numeric scale parameter.
The CDF function for the Pareto distribution
returns
the probability that an observation from a Pareto distribution, with the shape
parameter a and the scale parameter k, is less than
or equal to x. The equation follows:
where

n

is an integer random variable.

m

is a numeric mean parameter.
The CDF function for the Poisson distribution
returns
the probability that an observation from a Poisson distribution, with mean
m, is less than or equal to n. The equation follows:
Note: There are no location or scale parameters for the Poisson distribution.
where

t

is a numeric random variable.

df

is a numeric degrees of freedom parameter.

nc

is an optional numeric noncentrality parameter.
The CDF function for the T distribution
returns the probability that an observation from a T distribution,
with degrees of freedom df and noncentrality parameter nc, is less than or equal to x. This function accepts
noninteger degrees of freedom. If nc is omitted or equal to
zero, the value returned is from the central T distribution.
In the following equation, let $\nu$ = df and let $\delta$ = nc. The equation follows:
Note: There are no location or scale parameters for the T distribution.
where

x

is a numeric random variable.

l

is the numeric left location parameter.

r

is the numeric right location parameter.
The CDF function for the uniform
distribution returns
the probability that an observation from a uniform distribution, with the
left location parameter l and the right location parameter r, is less than or equal to x. The equation follows:
Note: The default values for l and r are 0 and 1, respectively.
where

x

is a numeric random variable.

d

is a numeric shape parameter.
The CDF function for the Wald distribution
returns the
probability that an observation from a Wald distribution, with shape parameter d, is less than or equal to x. The equation follows:
where (.) denotes the probability from the standard
normal distribution.
Note: There are no location or scale parameters for the Wald distribution.
CDF('WEIBULL',x,a<,>)

where

x

is a numeric random variable.

a

is a numeric shape parameter.


is a numeric scale parameter.
Default: 
1 
Range: 
> 0 
The CDF function for the Weibull distribution returns
the probability that an observation from a Weibull distribution, with the
shape parameter a and the scale parameter is less than
or equal to x. The equation follows:
SAS Statements 
Results 
y=cdf('BERN',0,.25);

0.75

y=cdf('BETA',0.2,3,4);

0.09888

y=cdf('BINOM',4,.5,10);

0.37695

y=cdf('CAUCHY',2);

0.85242

y=cdf('CHISQ',11.264,11);

0.57858

y=cdf('EXPO',1);

0.63212

y=cdf('F',3.32,2,3);

0.82639

y=cdf('GAMMA',1,3);

0.080301

y=cdf('HYPER',2,200,50,10);

0.52367

y=cdf('LAPLACE',1);

0.81606

y=cdf('LOGISTIC',1);

0.73106

y=cdf('LOGNORMAL',1);

0.5

y=cdf('NEGB',1,.5,2);

0.5

y=cdf('NORMAL',1.96);

0.97500

y=cdf('NORMALMIX',2.3,3,.33,.33,.34,
.5,1.5,2.5,.79,1.6,4.3);

0.7181

y=cdf('PARETO',1,1);

0

y=cdf('POISSON',2,1);

0.91970

y=cdf('T',.9,5);

0.79531

y=cdf('UNIFORM',0.25);

0.25

y=cdf('WALD',1,2);

0.62770

y=cdf('WEIBULL',1,2);

0.63212

Copyright © 2011 by SAS Institute Inc., Cary, NC, USA. All rights reserved.