Thanks for the pointer, Francesco.

I am in the process of setting up my environment. 
Hope to start soon.

With Regards,
Shilpa.

On Wednesday, January 24, 2018 at 2:24:48 PM UTC+5:30, Francesco Bonazzi 
wrote:
>
> Some ideas for the probability module:
>
>
>    - hyperparameters
>    - random matrices
>    - stochastic processes (through indexed random variables)
>    
>
> On Tuesday, 23 January 2018 12:03:33 UTC+1, Leonid Kovalev wrote:
>>
>> There is a discussion at https://github.com/sympy/sympy/pull/13943 but 
>> no separate issue (yet). 
>>
>> On Jan 23, 2018 5:27 AM, "Shilpa Sangappa" <shilpa....@gmail.com> wrote:
>>
>>> Thanks Leonid, for pointing me to this issue. I will start looking into 
>>> it.
>>> What is the issue id? 
>>>
>>> With Regards,
>>> Shilpa.
>>>
>>> P.S.: I didn't get a notification of your reply to my e-mail. Is there 
>>> any settings that I need to do?
>>>
>>> On Tuesday, January 23, 2018 at 12:04:50 AM UTC+5:30, Leonid Kovalev 
>>> wrote:
>>>>
>>>> Thanks for your interest. An issue that recently came up in the 
>>>> Probability module is sampling from a Poisson distribution 
>>>> <https://en.wikipedia.org/wiki/Poisson_distribution>. It used to not 
>>>> work at all, and now it does but the algorithm is not efficient when the 
>>>> parameter lamda is large. For example:
>>>>
>>>> from sympy.stats import *
>>>> sample(Poisson('x', 1000))
>>>>
>>>> can take a while to return. 
>>>>
>>>> Usually one can sample by generating a Uniform(0, 1) random number u, 
>>>> and then apply the inverse of the cumulative distribution function (CDF) 
>>>> to 
>>>> u. But there isn't a formula for the inverse of the of a Poisson random 
>>>> variable. The current algorithm 
>>>> <https://github.com/sympy/sympy/blob/master/sympy/stats/drv_types.py#L31> 
>>>> simply 
>>>> goes over all integers looking for the first one where CDF(n) >= u. There 
>>>> ought to be a better way of doing this. 
>>>>
>>>> The first idea that comes to mind is to make giant steps (in power of 
>>>> 2) until CDF(n) >= u is reached, and then refine by bisection. But perhaps 
>>>> it's better to do research first, there is probably an algorithm out there 
>>>> that we can use. Maybe R has it? https://www.r-project.org/ 
>>>>
>>>>
>>>>  
>>>>
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