Talk:Zero-truncated Poisson distribution

Not just OR but lacks veracity
In the example given it is false that a patient cannot stay for less than one day. Fiddle  Faddle  19:07, 7 August 2013 (UTC)
 * This article is not OR; a Google search turns up many results for this term. It appears to be a logical extension of a Poisson distribution for processes that cannot take a 0 value.  And the example of the hospital stay refers to the statistics of insurance carriers: a patient is not declared to be "admitted" to a hospital until xyr stay is at least one day; i.e. admissions of 0 days are not possible under such rules.  WikiDan61 ChatMe!ReadMe!! 19:26, 7 August 2013 (UTC)


 * On the contrary. Hospital patients are considered 'admitted' for many different reasons for durations less than a single day. Insurance is not the sole arbiter here. I accept your removal of the PROD, but I contest the assertion that the example is not OR. Fiddle   Faddle  19:29, 7 August 2013 (UTC)
 * In that case, I present you with this link which specifically uses the hospital stay example. WikiDan61 ChatMe!ReadMe!! 19:59, 7 August 2013 (UTC)
 * I see your link, and simply state that this is not always the case. For example a hospital in my UK area deems you to be admitted if you remain in a clinic under treatment in excess of four hours. They go through the admissions process, even if you leave them several minutes later. The log your admission in hours because they cannot log it as a day until a day has elapsed. Examples do not have to be based upon reality, but, where reality and examples diverge, that divergence must be noted and stated clearly. This leaves us with the interesting paradox that it is then OR to make that statement. Far better, then, to use an indisputable example. Fiddle   Faddle  20:28, 7 August 2013 (UTC)
 * How about we change the example to something like the number of items in a customer's basket at a checkout line. Presumably, the customer won't wait on line with 0 items, so we can safely call this a ZTP, no?  WikiDan61 ChatMe!ReadMe!! 12:13, 8 August 2013 (UTC)
 * To me that makes perfect sense. An example must not be capable of misinterpretation or it is a poor example. Of course I may have managed to achieve this already with subtle wording changes. This I leave to you since you appear to have genuine expertise in this area. Fiddle   Faddle  13:29, 8 August 2013 (UTC)

Solution to method of moments estimator equation
The article states that there is no closed form for the equation


 * $$ \frac{\widehat{\lambda}}{1-e^{-\widehat{\lambda}}} = \bar{x} $$

Correct me if I'm wrong, but I believe the solution can be written as


 * $$ \widehat{\lambda} = \bar{x} + W_0\left(\frac{-\bar{x}}{\exp{\bar{x}}}\right),$$

where $$W_0$$ is the principal branch of the Lambert W function. Not elementary, but it is a closed form. Harrydiv321 (talk) 19:31, 25 March 2024 (UTC)


 * Also, is it just me, or does some of the prose in this article read like the output of ChatGPT? Harrydiv321 (talk) 20:07, 25 March 2024 (UTC)
 * After taking a closer look it seems a certain user has added a number of ChatGPT-generated paragraphs related to the zero-truncated Poisson distribution and provided references that link to ResearchGate articles about distributions which are NOT the subject of this article, here are the refs copy-pasted
 * The last one IS about ZTP but is only tangentially related. I will remove the refs along with the seemingly GPT-generated content if no objections are raised Harrydiv321 (talk) 20:34, 25 March 2024 (UTC)