Bivariate Normal Distribution for Indeterminacy: Characteristics and Data Generation Algorithm

The existing bivariate normal distribution and its related algorithms in classical statistics cannot account for the degree of indeterminacy when applied under uncertainty. To address this gap, the main objective of this manuscript is to introduce bivariate neutrosophic random variables and study their properties through expectation and variance. In this paper, we also propose the neutrosophic bivariate normal distribution along with some of its key properties. Furthermore, we develop an algorithm based on the proposed distribution to generate imprecise data. A detailed simulation is carried out to examine the effect of the degree of indeterminacy on the data. The comparative study reveals that the variates produced by the proposed algorithm differ from those generated by the existing algorithm. To demonstrate its practical use, we provide a numerical example applying the bivariate normal distribution. Based on the simulation, comparative study, and numerical example, we recommend incorporating the degree of indeterminacy when generating data from the bivariate normal distribution under uncertainty.