ON THE NUMBER OF l-OVERLAPPING SUCCESS RUNS OF LENGTH k UNDER q- SEQUENCE OF BINARY TRIALS

Abstract

probability. The probability mass function, first and second moments of the number of l-overlapping successruns of length k in X1, X2, . . . , Xnare obtained. The new distribution generalizes, Type I and Type IIq-binomial distributions which were recently studied in the literature

Keywords

• Discrete distributions, q-Distributions, Runs

References

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13. Table 1. Probability mass function of N12,3,2 q x q = 0.5, θ = 0.5 q = 0.5, θ = 0.8 q = 0.8, θ = 0.5 4526 1169 0888 0694 0550 0438 0350 0312 0215 0172 0687 0002 7668 1243 0570 0270 0130 0062 0030 0016 0004 0003 0002
14. Table 2. E Nn,k,l for different values of θ, q, n, k and l q n l k (θ, q) (0.2, 0.5) (0.5, 0.2) (0.5, 0.5) (0.5, 1) 05509 00948 00177 00034 00041 (0.8, 0.5) 64504 10233 85677 54280 97420 5 05860 05968 12499 0 2 05510 00948 00177 00034 00041 06153 06279 18749 21949 5 0 2 05510 00948 00177 00034 00041 06226 06357 24999 37657 5
15. Table 3. V ar Nn,k,l for different values of θ, q, n, k and l q n l k (θ, q) (0.2, 0.5) (0.5, 0.2) (0.5, 0.5) (0.5, 1) 07342 01035 00191 00037 00061 (0.8, 0.5) 26448 42630 32089 66825 39907 5 14111 14252 24268 0 2 08553 01090 00192 00037 00061 16908 17082 40429 25853 5 0 2 09760 01145 00195 00037 00061 17900 18093 59765 00807 5 2 4 6 8 10 2 4 6 8 10 (n=12, l=2, q=0.5, θ=0.5) q=0.5 2 4 6 8 10 2 4 6 8 10 (n=12,k=5,q=0.5,θ=0.5) θ=0.8 2 4 6 8 10 2 4 6 8 10 (n=12, k=3, l=2, θ=0.5) 2 4 6 8 10 2 4 6 8 1012 (n=12, k=3, l=2, q=0.5)
16. Figure 1. Probability mass function of N12,k,l for different settings 2 4 6 8 θ q=0.5, k=4 2 4 6 8 θ q=0.5, k=6 2 4 6 8 θ q=0.5, k=8 2 4 6 8 θ q=0.9, k=4 2 4 6 8 θ q=0.9, k=6 2 4 6 8 θ q=0.9, k=8 2 4 6 8 θ 2 4 6 8 θ 2 4 6 8 θ Figure 2. E N10,k,l for different values of θ, q, k and l q 2 4 6 8 θ q=0.5, k=8 2 4 6 8 θ q=0.9, k=4 2 4 6 8 θ q=0.9, k=6 2 4 6 8 θ q=0.9, k=8 2 4 6 8 θ 2 4 6 8 θ 2 4 6 8 θ Figure 3. V ar N10,k,l for different values of θ, q, k and l q