An Asymptotic Conditional Test of Independence in Bernoulli Sequences Using the Number of Runs Given the Number of Successes

Sungsu Kim () and Chong Jin Park
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Sungsu Kim: University of Louisiana at Lafayette
Chong Jin Park: San Diego State University

Sankhya A: The Indian Journal of Statistics, 2021, vol. 83, issue 1, No 6, 143-154

Abstract: Abstract In this paper, we prove the asymptotic normality of the conditional distribution of the number of runs given the number of successes for a sequence of independent Bernoulli random variables. In our proof, the Frobenius-Harper technique is used to represent the number of runs as the sum of independent and not necessarily identically distributed Bernoulli random variables. Then, an asymptotic conditional test for independence is provided. Our simulation results exhibit that the test based on conditional distribution performs better that one based on unconditional distribution, over the entire range of success probability and first order correlation. In addition, the UMVUEs of the factorial moments and the probabilities of the number of runs are presented in this paper.

Keywords: Binary data; Factorial moment; Frobenius-Harper technique; Number of runs; Probability distribution; Test of independence; Primary 62M07; Secondary 62E20 (search for similar items in EconPapers)
Date: 2021
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DOI: 10.1007/s13171-019-00176-1

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