Sample from a distribution constructed by Dirac measures

Asked Apr 24 '19 at 09:56

Active Apr 25 '19 at 05:19

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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.

edited Apr 25 '19 at 05:19

asked Apr 24 '19 at 09:56

Fly_back

The link is not open to everyone, can you elaborate? – Cherny Apr 24 '19 at 10:41
@Cherny, the name of the paper is "new tests for jumps in semimartingale models". The exact problem actually is in the description. – Fly_back Apr 24 '19 at 11:38
Flip a fair coin whose faces are marked with the values $1-\tau$ and $1+\tau.$ – whuber Apr 25 '19 at 13:08
@whuber in other words, it is a bernoulli distribution? – Fly_back Apr 28 '19 at 08:50
It is an affine transform of a Bernoulli distribution. Bernoulli distributions are given by $p\delta_1 + (1-p)\delta_0.$ – whuber Apr 28 '19 at 15:44

Sample from a distribution constructed by Dirac measures

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