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I am reading the paper in the following link

https://link.springer.com/article/10.1007/s11203-009-9037-8

In the page 19, the author suggests to sample $\eta_i$ from the following distribution

$P^{\eta} = \frac{1}{2}(\delta_{1-\tau}+\delta_{1+\tau})$,

where $\delta$ stands for the Dirac measure. $\tau$ is a constant that relatively small, e.g.,$\tau=0.1$ or 0.05.

My question is that how can we sample from that distribution. In addition, what are the properties of the distribution, e.g., expectation, variance, pdf and cdf.

Thanks in advance.

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  • $\begingroup$ The link is not open to everyone, can you elaborate? $\endgroup$
    – Cherny
    Commented Apr 24, 2019 at 10:41
  • $\begingroup$ @Cherny, the name of the paper is "new tests for jumps in semimartingale models". The exact problem actually is in the description. $\endgroup$
    – Fly_back
    Commented Apr 24, 2019 at 11:38
  • $\begingroup$ Flip a fair coin whose faces are marked with the values $1-\tau$ and $1+\tau.$ $\endgroup$
    – whuber ♦
    Commented Apr 25, 2019 at 13:08
  • $\begingroup$ @whuber in other words, it is a bernoulli distribution? $\endgroup$
    – Fly_back
    Commented Apr 28, 2019 at 8:50
  • $\begingroup$ It is an affine transform of a Bernoulli distribution. Bernoulli distributions are given by $p\delta_1 + (1-p)\delta_0.$ $\endgroup$
    – whuber ♦
    Commented Apr 28, 2019 at 15:44

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