Biostat Lab Section ProbabilityQuantile Functions

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Biostat Lab Section Probability/Quantile
Functions

• Yu-Fen Li

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SAS Functions

• A SAS function performs a computation or system
  manipulation on arguments and returns a value.
• One can use SAS functions in
• DATA step programming statements,
• a WHERE expression,
• macro language statements,
• PROC REPORT, and
• Structured Query Language (SQL).

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SAS CALL Routines

• A CALL routine alters variable values or performs
  other system functions. CALL routines are similar
  to functions, but differ from functions in that
  you cannot use them in assignment statements.
• All SAS CALL routines are invoked with CALL
  statements that is, the name of the routine must
  appear after the keyword CALL on the CALL
  statement.

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Using SAS Functions Restrictions on Function
Arguments

• If the value of an argument is invalid, SAS
  prints an error message and sets the result to a
  missing value.
• Some functions require that their arguments be
  restricted within a certain range. For example,
  the argument of the LOG function must be greater
  than 0.

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Using SAS Functions Restrictions on Function
Arguments

• Most functions do not permit missing values as
  arguments. Exceptions include some of the
  descriptive statistics functions and financial
  functions.
• For some probability functions, combinations of
  extreme values can cause convergence problems.

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Syntax of Functions (1)

• function-name (argument-1lt. . .,argument-ngt)
• where
• function-name names the function.
• argument can be a variable name, constant, or
  any SAS expression, including another function.
  The number and kind of arguments allowed are
  described with individual functions. Multiple
  arguments are separated by a comma.
• xmax(cash,credit)

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Syntax of Functions (2)

• function-name (OF variable-list)
• where
• (OF variable-list) can be any form of a SAS
  variable list, including individual variable
  names. If more than one variable list appears,
  separate them with a space.
• asum(of x y z)

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Syntax of Functions (3)

• function-name (OF array-name)
• where
• (OF array-name)names a currently defined
  array. Specifying an array in this way causes SAS
  to treat the array as a list of the variables
  instead of processing only one element of the
  array at a time.
• array y10 y1-y10
• xsum(of y)

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Syntax of CALL Routines

• CALL routine-name (argument-1lt. . .,argument-ngt)
  
• where
• routine-name names a SAS CALL routine.
• argument can be a variable name, a constant, any
  SAS expression, an external module name, an array
  reference, or a function. Multiple arguments are
  separated by a comma.

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Probability (1)

• CDF Computes cumulative distribution functions
• CDF ('dist',quantile,parm-1, . . . ,parm-k)
• ycdf('BINOM',4,.5,10)
• PDF Computes probability density (mass)
  functions
• PDF ('dist',quantile,parm-1, . . . ,parm-k)
• zpdf('NORMAL',1.96)

P(Ylt4)0.37695, if YB(10,.5)
fz(1.96)0.058441, if ZN(0,1)
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Probability (2)

• POISSON Returns the probability from a Poisson
  distribution
• POISSON(lambda,k)
• xpoisson(1,2)
• PROBBNML Returns the probability from a binomial
  distribution
• PROBBNML(p,n,k)
• xprobbnml(0.5,10,4)

P(X2)0.9196986029, if XP(1)
P(X4)0.376953125, if XB(10,.5)
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Probability (3)

• PROBNORM Returns the probability from the
  standard normal distribution
• PROBNORM(x)
• xprobnorm(1.96)
• PROBCHI Returns the probability from a
  chi-squared distribution
• PROBF Returns the probability from an F
  distribution
• PROBT Returns the probability from a t
  distribution

P(Xlt1.96)0.9750021049, if XN(0,1)
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Quantile

• PROBIT Returns a quantile from the standard
  normal distribution
• PROBIT(p)
• xprobit(.025)
• CINV Returns a quantile from the chi-squared
  distribution
• FINV Returns a quantile from the F distribution
• TINV Returns a quantile from the t distribution

fx (-1.959963985 )0.025, if XN(0,1)
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Assignment

• Create a series of numbers (x) between 3 and 3
  (-3.0, -2.9, -2.8, .., 2.8,2.9,3.0) in EXCEL,
  and read in the file into SAS
• Compute the p.d.f. for the above xs by assuming
  XN(0,1)
• Generate a 2-way scatter plot p.d.f. of X vs X
• Find a z value that cut off the lower tail of 10
  of a standard normal distribution