# Example 7.7: Tabulate binomial probabilities

July 25, 2009
By

(This article was first published on SAS and R, and kindly contributed to R-bloggers)

Suppose we wanted to assess the probability P(X=x) for a binomial random variate with n = 10 and with p = .81, .84, ..., .99. This could be helpful, for example, in various game settings.

In SAS, we ﬁnd the probability that X=x using differences in the CDF calculated via the cdf function (1.10.1). We loop through the various binomial probabilities and values of x using the do ... end structure (section 1.11.1). Finally, we store the probabilities in implicitly named variables via an array statement (section 1.11.5).

SAS
data table (drop=j);array probs [11] prob0 prob1 - prob10;do p = .81 to .99 by .03;  do j = 0 to 10;    if j eq 1 then probs[j+1] = cdf("BINOMIAL", 0, p, 10);    else probs[j+1] = cdf("BINOMIAL", j, p, 10)                          - cdf("BINOMIAL", j-1, p, 10);    end;  output;  end;run;

The results are printed with two decimal places using the format statement (section 1.2.4). The options statement (section A.4) uses the ls option to narrow the output width to be compatible with Blogger.

options ls=64;proc print data=table noobs;   var p prob0 prob1 - prob10;   format _numeric_ 3.2; run;

And the results are:
                                                         p       p    p    p    p    p    p    p    p    p    p    r       r    r    r    r    r    r    r    r    r    r    o       o    o    o    o    o    o    o    o    o    o    b       b    b    b    b    b    b    b    b    b    b    1  p    0    1    2    3    4    5    6    7    8    9    0.81  .00  .00  .00  .00  .00  .02  .08  .19  .30  .29  .12.84  .00  .00  .00  .00  .00  .01  .05  .15  .29  .33  .17.87  .00  .00  .00  .00  .00  .00  .03  .10  .25  .37  .25.90  .00  .00  .00  .00  .00  .00  .01  .06  .19  .39  .35.93  .00  .00  .00  .00  .00  .00  .00  .02  .12  .36  .48.96  .00  .00  .00  .00  .00  .00  .00  .01  .05  .28  .66.99  .00  .00  .00  .00  .00  .00  .00  .00  .00  .09  .90

R
In R we start by making a vector of the binomial probabilities, using the : operator (section 1.11.3) to generate a sequence of integers. After creating a matrix (section B.4.4) to hold the table results, we loop (section 1.11.1) through the binomial probabilities, calling the dbinom() function (section 1.1) to ﬁnd the probability that X=x. This calculation is nested within the round() function (section 1.2.5) to reduce the digits displayed. Finally, we glue the vector of binomial probabilities to the results.

p <- .78 + (3 * 1:7)/100allprobs <- matrix(nrow=length(p), ncol=11)for (i in 1:length(p)) {   allprobs[i,] <- round(dbinom(0:10, 10, p[i]),2)}table <- cbind(p, allprobs)table

With the result:
        p                                        [1,] 0.81 0 0 0 0 0 0.02 0.08 0.19 0.30 0.29 0.12[2,] 0.84 0 0 0 0 0 0.01 0.05 0.15 0.29 0.33 0.17[3,] 0.87 0 0 0 0 0 0.00 0.03 0.10 0.25 0.37 0.25[4,] 0.90 0 0 0 0 0 0.00 0.01 0.06 0.19 0.39 0.35[5,] 0.93 0 0 0 0 0 0.00 0.00 0.02 0.12 0.36 0.48[6,] 0.96 0 0 0 0 0 0.00 0.00 0.01 0.05 0.28 0.66[7,] 0.99 0 0 0 0 0 0.00 0.00 0.00 0.00 0.09 0.90

As with the example of jittered scatterplots for dichotomous y by continuous x, (Example 7.3, Example 7.4, and Example 7.5) we will revisit this example for improvement in later entries.

To leave a comment for the author, please follow the link and comment on his blog: SAS and R.

R-bloggers.com offers daily e-mail updates about R news and tutorials on topics such as: visualization (ggplot2, Boxplots, maps, animation), programming (RStudio, Sweave, LaTeX, SQL, Eclipse, git, hadoop, Web Scraping) statistics (regression, PCA, time series, trading) and more...

If you got this far, why not subscribe for updates from the site? Choose your flavor: e-mail, twitter, RSS, or facebook...

Tags: , , , , ,

Comments are closed.