Questions tagged [stopping-time]
The stopping-time tag has no usage guidance.
5
questions
1
vote
1
answer
49
views
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 $$\ H_0: p=1/2\quad\text{vs.}\quad H_1: p=b\,$$ ...
- 281
0
votes
1
answer
45
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 ...
- 127
4
votes
2
answers
399
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% ...
- 89
2
votes
0
answers
72
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.
$$P ( X = x ) = p_x \quad \text{for } x \in \{ 1, \ldots, N \}.$$
...
- 1,286
0
votes
1
answer
71
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(...
- 885