**PROBBETA: probability values from a beta
distribution **

PROBBETA(x,a,b)

where 0<-x<= 1 and 0<a,b.

This function returns probability values from
a beta distribution. The a and b values are the shape parameters
of the beta distribution, and x is the value at which the distribution
is to be evaluated. The density is:

The incomplete beta function may be obtained from this function by multiplying the beta probability by values of the complete beta function, which may be computed from the GAMMA function.

This function is related to many of the.common distributions of statistics and also has applications in analyzing order statistics (see Michael and Schucany, 1979).

**PROBBNML: probability values from a binomial
distribution **PROBBNML(p,n,m)

where 0<-p<- 1, l<-n, 0<~m<=n.

This function returns the probability that an observation from a binomial distribution with parameters p and n is less than or equal to m. The binomial probability parameter is p, and n is the degree of the binomial distribution. A single term in the binomial distribution can be obtained as the difference of two values of the cumulative binomial distribution.

If X = PROBBNML(p,n,m), then:

Example:

PROBBNML(.5, 10, 4) = .37695

**PROBCHI: computes probability values for
the chi-square distributions **

** **PROBCH
I(x, df)

The PROBCHI function computes the probability
that a random variable with a central chi-square distribution,
with *df *degrees of freedom, falls below the x value given.

**PROBF: the probability for the F distribution
**

** **PRO
BF(x, ndf,ddf)

The PROBF function computes the probability
that a random variable with an F distribution, with *ndf *numerator
degrees of freedom and *ddf *denominator degrees of freedom,
falls below the x value given. To find the significance level,
use:

1 - PROBF(x, ndf, ddf).

This function accepts noninteger degrees
of freedom.

**PROBGAM: probability values for the gamma
distribution **

PROBGAM(x, eta)

The PROBGAM function computes the probability that a random variable with a gamma distribution with shape parameter r/falls below the x value given. The GAMINV function is the function inverse of PROBGAM.

The density is:

where is the shape
parameter.

**PROBHYPR: probabilities from a hypergeometric
distribution**

PROBHYPR(n n,k,n,x, or)

where:

l<=nn

l<=k<=nn

l<=n<=nn

MAX(O,k +n-nn) *<= x *<= MIN(k,n)

This function return~ the probability
that an observation from a hypergeometric distribution with total
sample *nn, *margins n and k, and odds ratio or is less than
or equal to x. The or argument can be omitted; if it is, the or
parameter is assumed to be 1.

Example:

PROBHYPR(10,5,3,2) = .9167

PROBHYPR(10,5,3,2, 1.5) = .8541

**PROBNEGB: probability values for the negative
binomial distribution **

** **PROBNEGB(p,n,m)

where 0<= p<- 1, 1 <- n, and 0<= m.

This function returns the probability that an observation from a negative binomial distribution with parameters p and n is less than or equal to m. The binomial probability parameter is p and n is the degree of the negative binomial distribution. The value of a single term in the negative binomial distribution can be obtained by a difference of two values of the cumulative distribution.

If X= PROBNEGB(p,n,m) then:

Example:

PROBNEGB(.5,2,1)= .5

**PROBNORM: computes probabilities for normal
distributions **PROBNORM(x)

The PROBNORM function computes the probability that a random variable with a normal (0,1) distribution falls below the x value given. This function is equivalent to:

The PROBIT function is the function inverse of PROBNORM.

Examples:

PROBNORM(O) = .5

PROBNORM(1.96) = .975

**PROBT: the probability for the t distribution
function **

PROBT(x, df)

The PROBT function computes the probability that a random variable with a Student's t distribution with dfdegrees of freedom falls below the x value given. For a two-tailed test, compute the significance level by:

(1 - PROBT(ABS(x),DF))*2

This function accepts noninteger degrees of freedom.

Example:

PROBT(.9,5) = 0.795

**Statistical Computing
**

1) Use the TPROB and/or TINV commands in SAS
to generate and plot data creating the bell shaped student-t distribution
curve.

Example: YES.DATA

Data;

do i=1 to 20;

t=1.5+i/10;

p=probt(t,9);

output;

end;

proc print;

proc plot;

plot p*t;

run;

2) Create a table of t-statistic values with
their degrees of freedom and probabilities displayed.

Example: creating a beautiful T-table in SAS
(output on green paper at computing center)

Data;

do t=0 to 4.2 by .001;

ndf=1;

array df df1-df30;

do over df;

df=1-probt(t,ndf);

ndf=ndf+1;

end;

output;

end;

proc print; id t; var df1-df10;

proc print; id t; var df11-df20;

proc print;id t; var df21-df30;

run;

**Inverting a Matrix in SAS
**

ready

SAS

proc iml;

xTx={5 3 2, 8 4 5, 7 9 1};

print xTx;

IxTx=INV(xTx);

print IxTx;

quit;

**Inverting a Matrix
in SPEAKEZ**

Ready

SPEAKEZ

XTX=MATRIX(3,3: 5,3,2,8,4,5,7,9,1);

INVERSE(XTX);

quit;

ready

help math;

help statistics;

help inverse;

help probt;

help users;

NDPRINT and POLIST are both READY mode commands.

NDPRINT FUN.DATA will cause the printer in
the computing center to print the contests of the physical sequential
(PS) data set FUN.DATA.

NDPRINT PDS.DATA(HTWT) will cause the printer
in the computing center to print the contents of the single member.
HTWT of a partitioned organization data set.

POLIST prints all members contents of a partitioned organization (PO) data set like PDS.DATA:

READY;

POLIST PDS.DATA

You must logon with your social security number to use this command:

LOGON GABCDE ID

** **

Alternatively use POLIST to print all member contents at terminal:

POLIST PDS.DATA