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If we investigate $n$ patients for SARS. The indicator of sequence of the trails is $X_i$ ($X_i=1$ is for success and $0$ is not success). And the sequence indicator is available for all n independent SARS patients . Reciprocal probability is $R=1/p$. Reciprocal probability stands for number of trails needed to obtain an expected of a first success. I was wondering that based on the record $X_1 ,…, X_n$ what is the unbiased estimation of $R$?

user203039
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  • Please search our site for [unbiased binomial estimation](https://stats.stackexchange.com/search?q=unbiased+binomial+estimat*.) – whuber Jun 14 '20 at 17:10
  • whuber, should I consider the question as binomial distribution? – user203039 Jun 14 '20 at 17:35
  • If it's not, then please explain what characteristic of these trials would prevent that. The implicit assumptions in your question are that the trials are independent with identical chances of success. Note, though, that any departure from these assumptions requires an explicit quantitative model. For instance, if the trials are not assumed to have equal chances of success, then what are you assuming about those chances? – whuber Jun 14 '20 at 20:36
  • Thank you for your help,whuber. I am not againts what you said. I am just trying to learn. I was wondering why we did not use geometric distribution if we look to obtain an expected time of a first success? – user203039 Jun 15 '20 at 00:17
  • The distribution to use is the one that corresponds to your experiment. So far, the construction of your experiment is obscure and all we have to go on is your mention of independent patients and "sequence of trials." If you believe that requires some non-Binomial model, then please supply the information necessary to determine an appropriate model. – whuber Jun 15 '20 at 12:46

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