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The criteria used for sample size determination are generally developed based on applying averaging techniques to the possible values a variable can take on. This paper presented new methods for estimation of sample size, in particular for binomial distribution, when an observation on number of successes is available. In this paper, first, the general criteria for the determination of sample size were reviewed. Next, the BDLM process was concisely introduced and fit to the first real-world dataset. Then, based on the model, four new methods for the estimation of the missing total number of trials in binomial time series were developed with the illustrated small dataset, where number of successes at any specific time point was known. In addition, the worst outcome criterion was evaluated based on the highest probability density (HPD) confidence set by using the illustrated data and the results were compared with those of the new methods developed in the present paper. Later, an illustration of COVID-19 trinomial data was presented in which BDLM was fit to the time series of cured cases infected due to COVID-19 disease. Finally, the new methods of estimation of missing total confirmed cases evaluated by the relatively large dataset.

Estimation of missing total number of trials in binomial time series analysis by a BDLM process with an illustration of the COVID-19 pandemic data