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SPSS® 12.0 Command Syntax Reference

SPSS® 12.0 Command Syntax Reference

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40 Universals<br />

Random Variable and Distribution Functions<br />

Random variable and distribution function keywords are all of form prefix.suffix, where the<br />

prefix specifies the function to be applied to the distribution and the suffix specifies the<br />

distribution.<br />

• Random variable and distribution functions take both constants and variables for arguments.<br />

• A function argument, if required, must come first and is denoted by q (quantile) for<br />

cumulative distribution and probability density functions and p (probability) for inverse<br />

distribution functions.<br />

• All random variable and distribution functions must specify distribution parameters,<br />

denoted by a, b, and/or c, according to the number required.<br />

• All arguments are real numbers.<br />

• Restrictions to distribution parameters a, b, and c apply to all functions for that distribution.<br />

Restrictions for the function parameter p or q apply to that particular distribution<br />

function. The program issues a warning and returns system-missing when it encounters<br />

an out-of-range value for an argument.<br />

The following are possible prefixes:<br />

CDF Cumulative distribution function. A cumulative distribution function<br />

CDF.d_spec(q,a,...) returns a probability p that a variate with the specified<br />

distribution (d_spec) falls below q for continuous functions and at or below<br />

q for discrete functions.<br />

IDF Inverse distribution function. Inverse distribution functions are not available<br />

for discrete distributions. An inverse distribution function IDF.d_spec(p,a,...)<br />

returns a value q such that CDF.d_spec(q,a,...)=p with the specified distribution<br />

(d_spec).<br />

PDF Probability density function. A probability density function PDF.d_spec(q,a,...)<br />

returns the density of the specified distribution (d_spec) at q for continuous<br />

functions and the probability that a random variable with the specified distribution<br />

equals q for discrete functions.<br />

RV Random number generation function. A random number generation function<br />

RV.d_spec(a,...) generates an independent observation with the specified<br />

distribution (d_spec).<br />

NCDF Noncentral cumulative distribution function. A noncentral distribution function<br />

NCDF.d_spec(q,a,b,...) returns a probability p that a variate with the<br />

specified noncentral distribution falls below q. It is available only for beta,<br />

chi-square, F, and Student’s t.<br />

NPDF Noncentral probability density function. A noncentral probability density<br />

function NCDF.d_spec(q,a,b,...) returns the density of the specified distribution<br />

(d_spec) at q. It is available only for beta, chi-square, F, and Student’s t.<br />

SIG Tail probability function. A tail probability function SIG.d_spec(q,a,...)<br />

returns a probability p that a variate with the specified distribution (d_spec) is<br />

larger than q.

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