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

Abstract

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.

KEYWORDS:

• Sample size determination
• binomial dynamic linear model
• beta-distribution method
• F-distribution method
• maximized probability method (MPM)

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Funding

The author(s) reported there is no funding associated with the work featured in this article.

Notes on contributors

Massoud Nakhkoob

Massoud Nakhkoob is a research statistician scholar and data scientist with the Civil Aviation Organization of Iran. He received his PhD in Statistics from Bircham International University, Spain. He has also been a lecturer in the Civil Aviation Technology College for about 10 years. He has extensive studies and experience in statistical modelling, time series analysis, bayesian forecasting, and reliability engineering, and is also a professional and experienced software designer and developer with .Net technology. He is currently studying and working on the applications of statistical and data sciences in medicine and pharmacology. He was also granted a US patent by the United States of America (USPTO) in the year 2020 for his important innovative invention. He is also inventor of Binomial DLM (BDLM) time series model and has published research papers in the area of statistical science. He has also published books in the fields including reliability engineering, computer science, etc.