Akademik Veri Yönetim Sistemi
12th International Congress on Fundamental and Applied Sciences, İstanbul, Türkiye, 2 - 04 Eylül 2025, ss.74, (Özet Bildiri)
An understanding of the probability distribution ascribed to a given dataset enables commentary on the characteristics of the underlying population and the formulation of prospective inferences. In the event that the dataset is sufficiently large, the law of large numbers or the central limit theorem may be employed to ascertain the probability distribution of the data set. However, in instances where the sample size is relatively limited, it becomes difficult to estimation of the probability density function (PDF) of the population. Furthermore, the determination of the PDF that best describes the available data introduces an additional level of complexity to the analysis. Failure to consider this complexity can have significant consequences. This paper will address this challenge by exploring the use of maximum entropy and Bayesian logical inference. In this paper, the likelihood function is obtained with Maximum entropy and a priori distributions of means and standard deviations are assigned. Bayesian logical inference is used to construct posterior distribution functions. The distributions, which were derived theoretically, were then applied to milk yields for seven dairy cows. Simulation results obtained with Mathematica programming language show the effectiveness, flexibility and robustness of the method in obtaining the mean and variance distributions of the data when the number of data is small.