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#Python code shown below#This code is issued under the Creative Commons CC0 "License"from__future__importdivisionimportnumpyasnpimportmatplotlib.pyplotasplt#Set domain of the graphMaxTrials=10000MinTrials=1UCB=np.zeros(MaxTrials)#Get points that are evenly spaced in log-spacetrials=np.exp(np.linspace(np.log(MinTrials),np.log(MaxTrials),100))#One-sided exact binomial upper confidence bound, equivalent to Clopper-Pearson#The choice of confidence interval does matter, but this is reasonable and#is typically the one from which Rule of 3 is derived#See Agresti and Coull 1998 for alternative binomial confidence intervalsUCB=[1-0.05**(1/i)foriintrials]Rule_of_3=[3/iforiintrials]plt.figure(figsize=(4,3.2))plt.axes([0.17,0.13,0.79,0.8])plt.hold(True)A=[]a,=plt.plot(trials,UCB,'-',color='orange',lw=2.5)b,=plt.plot(trials,Rule_of_3,'-',color='purple',lw=2.5)#FormattingA.append(a)A.append(b)ax=plt.gca()ax.set_yscale('log')ax.set_xscale('log')ax.grid()plt.xlabel("Sample Size")plt.ylabel(r"95% Upper Confidence Bound")leg_str=[]leg_str.append(" Exact Binomial")leg_str.append(" Rule of Three")bx=plt.legend(A,leg_str,numpoints=1,handletextpad=0,loc="upper right")plt.savefig("rule_of_three.svg")
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