A simple modification of trinomial distribution

Statistical distributions play an important role in analyzing data and are fundamental to data science. They provide a framework for understanding and modeling various data phenomena, which enable accurate predictions, meaningful insights, and effective decision-making. Classical discrete probability distributions, such as binomial, trinomial, and multinomial distributions, require the possible outcomes for each trial to be mutually exclusive, where the outcomes cannot occur simultaneously. In normal situation, when involving a decision-making process, the answer should be “Yes” or “No” only. However, the uncertainty may arise leading the outcome of “Not Sure” and this is not a mutually exclusive outcome with “Yes” and “No”. Therefore, this study took the initiative to modify the classical trinomial distribution to accommodate a non-mutually exclusive outcome. The probability mass function (PMF) of the Modification of Trinomial Distribution (MoTD) is derived through trinomial expansion. The parameters of MoTD estimated using the maximum likelihood method and the method of moment to ensure those obtained estimators are unbiased, sufficient, efficient, and consistent. The MoTD was tested on work-life balance data, and its performance in terms of standard deviation was compared to the binomial and trinomial distributions. The findings indicate that the parameters of MoTD fulfil the properties of good estimators. A test on real data showed that MoTD performed better compared to the binomial and trinomial distributions, as it produced lower standard deviations, signifying smaller dispersion. In conclusion, the MoTD extends the classical trinomial distribution by allowing “Not Sure” to be non-mutually exclusive outcome. MoTD can help decision-makers dealing with uncertainty by minimizing the standard deviation in data analysis, leading to better decision-making.