Questions tagged [stopping-time]

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How to explain these jump-discontinuities in the expected stopping time of a SPRT?

Suppose a sequential probability ratio test (SPRT) with $$\alpha=P(\text{Type I error})=P(\text{Type II error})=\beta = 10\%$$ is used to decide between $$\ H_0: p=1/2\quad\text{vs.}\quad H_1: p=b\,$$ ...
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1answer
33 views

Stopping Time for a sequence of Random Variables

If $M$ and $N$ are stopping times of sequence $\{X_n\}$ where $n \geq 1$. Then are $min (M, N)$ and $max(M,N)$ also stopping times of the sequence $\{X_n\}$ ? Is there any rigorous way to prove ...
4
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2answers
372 views

Is peeking in A/B tests bad even if you don't stop your experiment?

I have been asked a test about A/B testing that I'm unsure how to answer. Say you're running a conversion rate experiment, and my A variation has a conversion rate of 2% and my B variation has a 2.2% ...
2
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0answers
57 views

(Generalised) Negative Multinomial Distribution

Fix some probability vector $( p_1, \ldots, p_N)$, and let $X$ be a categorical random variable with these probabilities, i.e. $$P ( X = x ) = p_x \quad \text{for } x \in \{ 1, \ldots, N \}.$$ ...
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52 views

generating process of acceptance-rejection algorithm

The acceptance-rejection algorithm is described as follows: suppose you have RVs $X$ and $Y$ with densities $f_X$ and $f_Y$, respectively, and there exists a constant $c$ such that $\frac{f_X(t)}{f_Y(...