[R] Generate random Bernoulli draws

[Berry, Charles]

A liitle math goes along way. See below.

> On Jul 5, 2018, at 10:35 PM, Marino David <davidmarino838 using gmail.com> wrote:
> 
> Dear Bert,
> 
> I know it is a simple question. But for me, at current, I fail to implement
> it. So, I ask for help here.
> 
> It is not homework.
> 
> Best,
> 
> David
> 
> 2018-07-06 13:32 GMT+08:00 Bert Gunter <bgunter.4567 using gmail.com>:
> 
>> Is this homework?
>> 
>> (There is an informal no-homework policy on this list).
>> 
>> Cheers,
>> Bert
>> 
>> 
>> 
>> Bert Gunter
>> 
>> "The trouble with having an open mind is that people keep coming along and
>> sticking things into it."
>> -- Opus (aka Berkeley Breathed in his "Bloom County" comic strip )
>> 
>> On Thu, Jul 5, 2018 at 10:23 PM, Marino David <davidmarino838 using gmail.com>
>> wrote:
>> 
>>> Dear All,
>>> 
>>> I would like to generate N random Bernoulli draws given a probability
>>> function F(x)=1-exp(-2.5*x) in which x follows  uniform distribution, say
>>> x~U(0,2).

If each Bernoulli draw is based on its own draw of x, then

	rbinom( N, 1, 0.8013476 )

is what you want.

It is left as an exercise for the reader to verify that the constant 0.8013476 is correct up to approximation error, and to prove that such a Bernoulli mixture is also Bernoulli. Perhaps, 

	?integrate

will help.

But if the x's are shared you need to use runif, expm1, and (possibly) rep to produce a vector to be used in place of  the prob argument.

HTH,

Chuck


>>> 
>>> Can some one leave me some code lines for implementing this?
>>> 
>>> Thanks in advance.
>>> 
>>> David
>>> 
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>>> 
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>> 
>> 
> 
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