Functions and CALL Routines |
Returns a value from a probability density (mass) distribution.
Category: |
Probability
|
Alias: |
PMF
|
PDF (dist,quantile<,parm-1, ...
,parm-k>)
|
-
dist
-
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
|
Chi-Square |
CHISQUARE
|
Exponential |
EXPONENTIAL
|
F |
F
|
Gamma |
GAMMA
|
Geometric |
GEOMETRIC
|
Hypergeometric |
HYPERGEOMETRIC
|
Laplace |
LAPLACE
|
Logistic |
LOGISTIC
|
Lognormal |
LOGNORMAL
|
Negative binomial |
NEGBINOMIAL
|
Normal |
NORMAL|GAUSS
|
Normal mixture |
NORMALMIX
|
Pareto |
PARETO
|
Poisson |
POISSON
|
T |
T
|
Uniform |
UNIFORM
|
Wald (inverse Gaussian) |
WALD|IGAUSS
|
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.
-
parm-1,...,parm-k
-
are optional numeric constants, variables,
or expressions that specify the values of shape, location, or scale parameters that are appropriate for the specific
distribution.
See: |
Details for complete information about these
parameters |
where
-
x
-
is a numeric random variable.
-
p
-
is a numeric probability of success.
Range: |
0 p
1 |
The PDF function for the Bernoulli distribution returns
the probability density function of a Bernoulli distribution, with probability
of success equal to p. The PDF function is evaluated at the value 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 PDF function for the beta
distribution returns the
probability density function of a beta distribution, with shape parameters a and b. The PDF function is evaluated at the value x. The equation follows:
Note: The quantity
is forced to be
.
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 PDF function for the binomial distribution returns
the probability density function of a binomial distribution, with parameters p and n, which is evaluated at the value m.
The equation follows:
Note: There are no location or scale parameters for the binomial distribution.
PDF('CAUCHY',x<,,>)
|
where
-
x
-
is a numeric random variable.
-
-
is a numeric location parameter.
-
-
is a numeric scale parameter.
Default: |
1 |
Range: |
> 0 |
The PDF function for the Cauchy distribution returns
the probability density function of a Cauchy distribution, with the location
parameter and the scale parameter . The PDF function is evaluated
at the value x. The equation follows:
PDF('CHISQUARE',x,df
<,nc>)
|
where
-
x
-
is a numeric random variable.
-
df
-
is a numeric degrees of freedom parameter.
-
nc
-
is an optional numeric non-centrality parameter.
Range: |
nc 0 |
The PDF function for the chi-square
distribution returns
the probability density function of a chi-square distribution, with df degrees of freedom and non-centrality parameter nc.
The PDF function is evaluated at the value x. This function accepts
non-integer degrees of freedom. If nc is omitted or equal to
zero, the value returned is from the central chi-square distribution. The
following equation describes the PDF function of the chi-square distribution,
where
pc(.,.) denotes
the density from the central chi-square distribution:
and where
pg(
y,
b) is the density from the gamma distribution, which
is given by
PDF('EXPONENTIAL',x
<,>)
|
where
-
x
-
is a numeric random variable.
-
-
is a scale parameter.
Default: |
1 |
Range: |
> 0 |
The PDF function for the exponential distribution
returns
the probability density function of an exponential distribution, with the
scale parameter . The PDF function is evaluated at the value 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 non-centrality parameter.
Range: |
nc 0 |
The PDF function for the F
distribution
returns the probability density function of an F distribution,
with ndf numerator degrees of freedom, ddf denominator
degrees of freedom, and non-centrality parameter nc. The PDF
function is evaluated at the value x. This PDF function accepts
non-integer 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 PDF function of the F
distribution.
where
pf(
f,
u1,
u2) is
the density from the central
F distribution with
and where
pB(
x,
a,
b) is the density from the standard beta
distribution.
Note: There are no location or scale parameters for the F distribution.
PDF('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 PDF function for the gamma distribution returns
the probability density function of a gamma distribution, with the shape
parameter a and the scale parameter . The PDF function
is evaluated at the value x. The equation follows:
where
-
m
-
is a numeric random variable that denotes
the number of failures before the first success.
Range: |
m 0 |
-
p
-
is a numeric probability of success.
Range: |
0 p
1 |
The PDF function for the geometric distribution returns
the probability density function of a geometric distribution, with parameter p. The PDF function is evaluated at the value 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 PDF function for the hypergeometric
distribution
returns the probability density function of an extended hypergeometric distribution,
with population size N, number of items R, sample
size n, and odds ratio o. The PDF function is evaluated
at the value x. If o is omitted or equal to 1, the
value returned is from the usual hypergeometric distribution. The equation
follows:
PDF('LAPLACE',x<,,>)
|
where
-
x
-
is a numeric random variable.
-
-
is a numeric location parameter.
-
-
is a numeric scale parameter.
Default: |
1 |
Range: |
> 0 |
The PDF function for the Laplace distribution returns
the probability density function of the Laplace distribution, with the location
parameter and the scale parameter . The PDF function is evaluated
at the value x. The equation follows:
PDF('LOGISTIC',x<,,>)
|
where
-
x
-
is a numeric random variable.
-
-
is a numeric location parameter.
-
-
is a numeric scale parameter.
Default: |
1 |
Range: |
> 0 |
The PDF function for the logistic distribution
returns
the probability density function of a logistic distribution, with the location
parameter and the scale parameter . The PDF function is evaluated
at the value x. The equation follows:
PDF('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 PDF function for the lognormal distribution returns the probability
density function of a lognormal distribution, with the log scale parameter
and the shape parameter . The PDF function is evaluated
at the value 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 PDF function for the negative binomial
distribution
returns the probability density function of a negative binomial distribution,
with probability of success p and number of successes n. The PDF function is evaluated at the value m. The equation
follows:
Note: There are no location or scale parameters for the negative binomial distribution.
PDF('NORMAL',x<,,>)
|
where
-
x
-
is a numeric random variable.
-
-
is a numeric location parameter.
-
-
is a numeric scale parameter.
Default: |
1 |
Range: |
> 0 |
The PDF function for the normal distribution returns
the probability density function of a normal distribution, with the location
parameter and the scale parameter . The PDF function is
evaluated at the value x. The equation follows:
PDF('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 PDF 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 PDF function for the Pareto distribution
returns
the probability density function of a Pareto distribution, with the shape
parameter a and the scale parameter k. The PDF function
is evaluated at the value x. The equation follows:
where
-
n
-
is an integer random variable.
-
m
-
is a numeric mean parameter.
The PDF function for the Poisson distribution
returns
the probability density function of a Poisson distribution, with mean m. The PDF function is evaluated at the value 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 non-centrality parameter.
The PDF function for the T distribution
returns the probability density function of a T distribution,
with degrees of freedom df and non-centrality parameter nc. The PDF function is evaluated at the value x. This
PDF function accepts non-integer 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.
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 PDF function for the uniform
distribution returns
the probability density function of a uniform distribution, with the left
location parameter l and the right location parameter r. The PDF function is evaluated at the value x. The equation
follows:
where
-
x
-
is a numeric random variable.
-
d
-
is a numeric shape parameter.
The PDF function for the Wald distribution
returns the
probability density function of a Wald distribution, with shape parameter d, which is evaluated at the value x. The equation follows:
Note: There are no location or scale parameters for the Wald distribution.
PDF('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 PDF function for the Weibull distribution returns
the probability density function of a Weibull distribution, with the shape
parameter a and the scale parameter . The PDF function
is evaluated at the value x. The equation follows:
SAS Statements |
Results |
y=pdf('BERN',0,.25);
|
0.75
|
y=pdf('BERN',1,.25);
|
0.25
|
y=pdf('BETA',0.2,3,4);
|
1.2288
|
y=pdf('BINOM',4,.5,10);
|
0.20508
|
y=pdf('CAUCHY',2);
|
0.063662
|
y=pdf('CHISQ',11.264,11);
|
0.081686
|
y=pdf('EXPO',1);
|
0.36788
|
y=pdf('F',3.32,2,3);
|
0.054027
|
y=pdf('GAMMA',1,3);
|
0.18394
|
y=pdf('HYPER',2,200,50,10);
|
0.28685
|
y=pdf('LAPLACE',1);
|
0.18394
|
y=pdf('LOGISTIC',1);
|
0.19661
|
y=pdf('LOGNORMAL',1);
|
0.39894
|
y=pdf('NEGB',1,.5,2);
|
0.25
|
y=pdf('NORMAL',1.96);
|
0.058441
|
y=pdf('NORMALMIX',2.3,3,.33,.33,.34,
.5,1.5,2.5,.79,1.6,4.3);
|
0.1166
|
y=pdf('PARETO',1,1);
|
1
|
y=pdf('POISSON',2,1);
|
0.18394
|
y=pdf('T',.9,5);
|
0.24194
|
y=pdf('UNIFORM',0.25);
|
1
|
y=pdf('WALD',1,2);
|
0.56419
|
y=pdf('WEIBULL',1,2);
|
0.73576
|
Copyright © 2011 by SAS Institute Inc., Cary, NC, USA. All rights reserved.