Disclaimer: By using this algorithm you acknowledge that it is done so at your own risk. UNICEF, LSTM and Spectra Analytics Limited and associated groups or individuals take no responsibility for errors in the model, its implementation or the outcomes resulting from using the model. Please notify Professor JJ Valadez of any errors you encounter so the calculator can be improved (firstname.lastname@example.org).
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The algorithm for finding optimal values of the sample size n and decision rule d for the Hypergeometric model for a population size N proceeds as follows:
Start with n=1, d=0
Calculate the rounded upper threshold number, H = round(p_up*N)
Calculate the rounded lower threshold number, L = round(p_low*N)
Calculate alpha, which is the CDF of the hypergeometric distribution: alpha=CDF(d, N, H, n)
Calculate beta, which is 1 – CDF(d, N, L, n)
If alpha <= alpha_threshold and beta <= beta_threshold then the solution is (n, d), otherwise continue
If d=n then increase n by 1 and set d=0. Otherwise increase d by 1
Return to step 2
The procedure for the Binomial model is similar, with the Binomial CDF used in place of the Hypergeometric. The Binomial CDF takes three parameters: CDF(d, N, p), where p is either the upper threshold probability p_up (in step 2) or the lower threshold p_low (in step 3)
Both of these models assume a random sample from the supervision area, and the Binomial model assumes that the probability of sampling the same person twice is very small.