Convolution of independent binomial variables: an approximation method and a comparative study

Abstract This paper has developed an approximation (the J approximation) to the convolution of independent binomial variables. The paper has also compared the performances of the J approximation with the only existing one — the Speevak and Yu's (SY) approximation. Many numerical examples are given with various values of proportions of success, sample sizes and sums of the number of successes. The results show that when the value of the measure of deviation (m.d.) of the proportions of success p i 's are not too large, the J approximation is strikingly close to actual values and much better than the SY approximation. Although their accuracy decreases with increases in the values of the sum of the proportions of success p D , the two approximations are still good when the value of p D is as large as 0.3.