RANTBL Function

Returns a random variate from a tabled probability distribution.

Category:	Random Number
Tip:	If you want to change the seed value during execution, you must use the CALL RANTBL routine instead of the RANTBL function.

Syntax

RANTBL(seed,p1,... p_i... ,p_n)

Required Arguments

seed

is a numeric constant, variable, or expression with an integer value. If seed ≤ 0, the time of day is used to initialize the seed stream.

Range	seed < 2³¹−1
See	Seed Values for more information about seed values.

p_i

is a numeric constant, variable, or expression.

Range

0 ≤ p_i ≤ 1 for 0 <i ≤ n

Details

The RANTBL function returns a variate that is generated from the probability mass function defined by p₁ through p_n. An inverse transform method applied to a RANUNI uniform variate is used. RANTBL returns

\begin{matrix} \begin{matrix} 1 & w i t h p r o b a b i l i t y p_{1} \end{matrix} \\ \begin{matrix} 2 & w i t h p r o b a b i l i t y p_{2} \end{matrix} \\ . \\ . \\ . \\ \begin{matrix} n & w i t h p r o b a b i l i t y p_{n} \end{matrix} \\ \begin{matrix} n + 1 & w i t h p r o b a b i l i t y 1 - Σ_{i = 1}^{n} p_{i} i f Σ_{i = 1}^{n} p_{i} \leq 1 \end{matrix} \end{matrix}

If, for some index j<n,

Σ_{i = 1}^{j} p_{i} \geq 1

, RANTBL returns only the indices 1 through j with the probability of occurrence of the index j equal to

1 - Σ_{i = 1}^{j - 1} p_{i}

Let n=3 and P1, P2, and P3 be three probabilities with P1+P2+P3=1, and M1, M2, and M3 be three variables. The variable X in these statements

array m{3} m1-m3;
x=m{rantbl(seed,of p1-p3)};

will be assigned one of the values of M1, M2, or M3 with probabilities of occurrence P1, P2, and P3, respectively.

For a discussion and example of an effective use of the random number CALL routines, see Starting, Stopping, and Restarting a Stream.

Comparisons

The CALL RANTBL routine, an alternative to the RANTBL function, gives greater control of the seed and random number streams.