Yun Soo Kim

Heterogeneous Cutoffs in Stopped Bernoulli Trials: Sharp Thresholds and Finite-Sample Bias

We consider m independent components in which Bernoulli trials have success probability p. In component i, trials stop at the first success or upon reaching the prescribed cutoff ni, whichever occurs first. We study how the expected proportion of successes among all trials perfor...

Aggregate Success Rate in Stopped Bernoulli Trials: Expectation, Monotonicity, and Convergence

We consider m independent sequences of Bernoulli trials with success probability p, each terminated at its first success or after n trials, whichever occurs first. Let Xm,n,p denote the proportion of successes among all trials performed across the m components. We derive a unifie...

Aggregate Success Rate in Stopped Bernoulli Trials: Expectation, Monotonicity, and Convergence

We consider m independent sequences of Bernoulli trials with success probability p, each terminated at its first success or after n trials, whichever occurs first. Let Xm,n,p denote the proportion of successes among all trials performed across the m components. We derive a unifie...

Aggregate Stability in Repeated Restricted Geometric Experiments with Heterogeneous Cutoffs

Consider m independent Bernoulli sequences with a common success probability 0 < p < 1, each stopped at the first success or at a prescribed cutoff. We allow the cutoffs to form an arbitrary deterministic sequence, with finite and unrestricted cutoffs permitted. We prove that the...

Aggregate Stability in Repeated Restricted Geometric Experiments with Heterogeneous Cutoffs

Consider m independent Bernoulli sequences with a common success probability 0 < p < 1, each stopped at the first success or at a prescribed cutoff. We allow the cutoffs to form an arbitrary deterministic sequence, with finite and unrestricted cutoffs permitted. We prove that the...

The Aggregate Success Rate in Repeated Restricted Geometric Experiments: Expectation, Monotonicity, and Convergence

We consider m independent sequences of Bernoulli trials with success probability p, each terminated at its first success or after n trials, whichever occurs first. Let Xm,n,p denote the proportion of successes among all trials performed across the m components. We derive a unifie...