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The paper deals with three generalized dependent setups arising from asequence of Bernoulli trials. Various distributional properties, such asprobability generating function, probability mass function and moments arediscussed for these setups and their waiting time. Also, explicit forms ofprobability generating function and probability mass function are obtained.Finally, two applications to demonstrate the relevance of the results aregiven.

Generalizations of Distributions Related to ($k_1,k_2$)-runs