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| HISTOGRAM Statement |
The following entries provide detailed descriptions of options for the HISTOGRAM statement.
for fitted curves
requested with the BETA and GAMMA options.
Enclose the ALPHA= option in parentheses
after the BETA or GAMMA options.
If you do not specify a value for ,the procedure calculates a maximum likelihood estimate.
See Example 4.1.
You can specify A= as an alias for ALPHA= if you use it as a
beta-option.
You can specify SHAPE= as an alias for ALPHA= if you use it
as a gamma-option.
at which iteration terminates in
the Newton-Raphson approximation of the maximum likelihood estimate
of for curves requested by the GAMMA option.
Enclose the ALPHADELTA= option in parentheses after the GAMMA option.
Iteration continues until the change in is less than the value specified or until the number of
iterations exceeds the value of the
MAXITER= option.
The default value is 0.00001.
in the Newton-Raphson
approximation of the maximum likelihood
estimate of for fitted gamma distributions
requested with the GAMMA option. Enclose the
ALPHAINITIAL= option in parentheses after the GAMMA option.
The default value is Thom's approximation of the estimate of .Refer to Johnson et al. (1994).
whereand
lower threshold parameter (lower endpoint parameter)
scale parameter
shape parameter
shape parameter
h = width of histogram interval
and above by the value 
.You can specify and 
using the THETA=
and SIGMA= beta-options.
The following statements
fit a beta distribution bounded between 50 and 75,
using maximum likelihood estimates for and
:
proc capability;
histogram length / beta(theta=50 sigma=25);
run;
and
. and . If these parameters
are known, you can specify their values with the ALPHA=
and BETA= beta-options. If you do not specify
values, the procedure calculates
maximum likelihood estimates for and . for beta
density curves requested with the BETA option. Enclose
the BETA= option in parentheses after the BETA option. If you do
not specify a value for , the procedure calculates
a maximum likelihood estimate.
See Example 4.1.
proc capability;
histogram length / kernel(c=0.5 1.0 mise);
run;
proc capability;
histogram length / kernel(c=1 2 3 k=normal quadratic);
run;
in the Newton-Raphson
approximation of the maximum likelihood estimate of
c for Weibull curves requested with the WEIBULL option.
Enclose the CINITIAL= option in parentheses after the WEIBULL option.
The default value is 1.8 (refer to Johnson et al. 1994).
for
Johnson SB and Johnson SU
density curves requested with the SB and SU options. Enclose
the DELTA= option in parentheses after the SB or SU option. If you do
not specify a value for , the procedure calculates
an estimate.
where
must be less than or equal to
the minimum data value. You can specify with
the THETA= exponential-option. The default value
for is zero.
If you specify THETA=EST, a maximum likelihood estimate
is computed for .You can specify with the
SIGMA= exponential-option. By default, a maximum
likelihood estimate is computed for . For example,
the following statements fit an exponential curve with
and with a maximum likelihood estimate for :
proc capability;
histogram / exponential(theta=10 l=2 color=red);
run;
proc capability;
histogram length / normal(fill) cfill=green pfill=solid;
run;
Depending on the area to be filled
(outside or between the specification limits),
you can specify the color and pattern with
options in the SPEC statement and HISTOGRAM statement,
as summarized in the following table:
| Area Under Curve | Statement | Option |
| between specification | HISTOGRAM | CFILL=color |
| limits | HISTOGRAM | PFILL=pattern |
| left of lower | SPEC | CLEFT=color |
| specification limit | SPEC | PLEFT=pattern |
| right of upper | SPEC | CRIGHT=color |
| specification limit | SPEC | PRIGHT=pattern |
whereThe parameter
for the gamma distribution
must be less than the minimum data value. You can
specify with the THETA= gamma-option.
The default value for is 0.
If you specify THETA=EST, a maximum likelihood estimate
is computed for .In addition,
the gamma distribution has a shape parameter and a scale parameter . You can specify these
parameters with the ALPHA= and SIGMA= gamma-options.
By default, maximum likelihood estimates are computed
for and . For example, the following
statements fit a gamma curve with 
and with maximum
likelihood estimates for and :
proc capability;
histogram length / gamma(theta=4);
run;
Note that the maximum likelihood estimate of is calculated iteratively using the Newton-Raphson
approximation. The ALPHADELTA=,
ALPHAINITIAL=, and MAXITER= gamma-options control the
approximation.
for
Johnson SB and Johnson SU
density curves requested with the SB and SU options. Enclose
the GAMMA= option in parentheses after the SB or SU option. If you do
not specify a value for , the procedure calculates
an estimate.
|
proc capability;
histogram length / kernel(k=quadratic);
run;
proc capability;
histogram length / kernel(c=0.5 1.0 1.5 k=normal quadratic);
run;
| FILL | specifies that the area under the curve is to be filled |
| COLOR= | specifies the color of the curve |
| L= | specifies the line style for the curve |
| W= | specifies the width of the curve |
| K= | specifies the type of kernel function |
| C= | specifies the smoothing parameter |
| SYMBOL= | specifies the character used to plot the kernel density curve if the histogram is produced on a line printer |
whereNote that the lognormal distribution is also referred to as the SL distribution in the Johnson system of distributions.
scale parameter
for the lognormal distribution
must be less than the minimum data value. You can
specify with the THETA= lognormal-option.
The default value for is zero.
If you specify THETA=EST, a maximum likelihood estimate
is computed for .You can specify the
parameters and 
with the SIGMA= and ZETA=
lognormal-options.
By default, maximum likelihood estimates are computed for
and . For example, the following statements
fit a lognormal distribution function with a default value
of 
and with maximum likelihood estimates for and :
proc capability;
histogram length / lognormal;
run;
The LOGNORMAL option can appear only once in a HISTOGRAM
statement. Table 4.2 and
Table 4.6 list options that
you can specify with the LOGNORMAL option.
See Example 4.2
and "Formulas for Fitted Curves".
for fitted gamma curves requested
with the GAMMA option and c for fitted Weibull curves
requested with the WEIBULL option. Enclose the MAXITER= option in
parentheses after the GAMMA or WEIBULL option.
The default is 20.
proc capability;
histogram length / gamma(theta=3 midpercents)
run;
midpoints=2 to 10 by 0.5then all of the observations and specification limits must fall between 1.75 and 10.25 (otherwise, a default list of midpoints is used).
proc capability;
histogram length / midpoints=20 to 80 by 10
haxis=axis1;
axis1 length=6 in order=10 20 30 40 50 60 70 80 90;
run;
for normal density
curves requested with the NORMAL option. Enclose
the MU= option in parentheses after the NORMAL option. The
default value is the sample mean.
whereNote that the normal distribution is also referred to as the SN distribution in the Johnson system of distributions.mean
and with the MU= and SIGMA= normal-options, as shown
in the following statements:
proc capability;
histogram length / normal(mu=14 sigma=0.05);
run;
and . The NORMAL option can
appear only once in a HISTOGRAM statement. Table 4.2
and Table 4.7
list options that you can specify with the NORMAL option.
See Figure 4.4 and
"Formulas for Fitted Curves".
proc capability;
histogram length / lognormal(percents=1 3 5 95 97 99);
run;
| ||||||||||||||||||||||||||||
whereThe SB distribution is bounded below by the parameter
shape parameter
shape parameter
h = width of histogram interval
and above by the value .The parameter
must be less than the minimum data value. You can
specify with the THETA= SB-option,
or you can request that be estimated
with the THETA = EST SB-option.
The default value for is zero.
The sum must be greater than the maximum
data value.
The default value for is one.
You can specify with the SIGMA= SB-option,
or you can request that be estimated
with the SIGMA = EST SB-option.
You can
specify with the DELTA= SB-option,
and you can
specify with the GAMMA= SB-option.
Note that the SB-options are given in
parentheses after the SB option.
proc capability;
histogram length / sb;
histogram length / sb( theta=est sigma=est );
histogram length / sb( theta=0.5 sigma=8.4
delta=0.8 gamma=-0.6 );
run;
The first HISTOGRAM statement fits an SB distribution
with default values of and 
and with percentile-based estimates for
and .The second HISTOGRAM statement estimates
all four parameters with the method of percentiles.
The third HISTOGRAM statement displays
an SB curve with specified values for all four
parameters.
for curves requested
with the BETA, EXPONENTIAL, GAMMA, LOGNORMAL, NORMAL, SB, SU,
and WEIBULL options. Enclose the SIGMA= option in parentheses after
the distribution option. The following table summarizes
the use of the SIGMA= option:
| Distribution Keyword | SIGMA= Specifies | Default Value | Alias |
| BETA | scale parameter | 1 | SCALE= |
| EXPONENTIAL | scale parameter | maximum likelihood estimate | SCALE= |
| GAMMA | scale parameter | maximum likelihood estimate | SCALE= |
| LOGNORMAL | shape parameter | maximum likelihood estimate | SHAPE= |
| NORMAL | scale parameter | standard deviation | |
| SB | scale parameter | 1 | SCALE= |
| SU | scale parameter | percentile-based estimate | |
| WEIBULL | scale parameter | maximum likelihood estimate | SCALE= |
.For syntax examples, see the entries for the BETA and NORMAL
options.
![p(x) = \{ \frac{ \delta h x 100\%}{\sigma \sqrt{2\pi} }
\frac{ 1 }
{ \sqrt{ 1 ...
...}{\sigma} )
)^2
]
& {for x \gt \theta } \ 0 & {for x \leq \theta\space }
.](images/hsteq41.gif)
whereYou can specify the parameters with the THETA=, SIGMA=, DELTA=, and GAMMA= SU-options, which are enclosed in parentheses after the SU option. If you do not specify these parameters, they are estimated.
proc capability;
histogram length / su;
histogram length / su( theta=0.5 sigma=8.4
delta=0.8 gamma=-0.6 );
run;
The first HISTOGRAM statement estimates
all four parameters with the method of percentiles.
The second HISTOGRAM statement displays
an SU curve with specified values for all four
parameters.
for curves
requested with the BETA, EXPONENTIAL, GAMMA, LOGNORMAL, SB, and
WEIBULL options, and the location parameter for curves
requested with the SU option. Enclose the THETA= option in parentheses
after the curve option. See Example 4.1.
The default value is zero.
If you specify THETA=EST, an estimate
is computed for .
proc capability;
histogram length / normal(w=3);
run;
The default is 1.
whereThe parameter
must be less than the minimum
data value. You can specify with the THETA=
Weibull-option.
The default value for is zero.
If you specify THETA=EST, a maximum likelihood estimate
is computed for .You can specify and c
with the SIGMA= and C= Weibull-options.
By default, maximum likelihood estimates are computed for
c and . For example, the following statements
fit a Weibull distribution with 
and with
maximum likelihood estimates for and c:
proc capability;
histogram length / weibull(theta=15);
run;
for
lognormal density curves requested with the LOGNORMAL
option. Enclose the ZETA= option in parentheses after the LOGNORMAL
option. By default, the procedure calculates a maximum
likelihood estimate for . You can specify the
SCALE= option as an alias for the ZETA= option.
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Copyright © 1999 by SAS Institute Inc., Cary, NC, USA. All rights reserved.