The generalized modified Bessel distribution is considered one of the most suitable mixed distributions, as this distribution is more general than the two distributions (normal and T) as special cases, and it is considered that the generalized modified Bessel distribution as a special case of the symmetrical hyperbolic distributions, and this distribution has practical applications in a variety of areas which includes stock market data presentation, quality control data and filtering random-sign analysis. To conduct any study on data that follows this distribution, its parameters must be estimated to be able to predict and obtain accurate results to solve a particular problem. The characteristics of the community are determined by studying a sample drawn from it, provided that the sample bears the maximum degree of accuracy to represent the community, and this leads to reducing the costs of the field study due to the small size of the sample about the size of the community. There are several sampling methods to determine the sample size to be used in statistical inference, and one of these methods is using the Bayesian sampling method, which in its study depends on taking into account the loss functions with the cost function.[13] was the first to use the Bayesian method to estimate the linear regression model, assuming that the random error distribution is a generalized multivariate modified Bessel distribution when the prior distribution of parameters is a proper distribution, which is the result of mixing two continuous probability distributions. They are the normal distribution and the generalized inverse Gaussian distribution [14]. [11] Determine the Bayesian sample size to estimate the mean and the difference between the mean of the normal distribution when the variance is known and estimate the variance when the mean is known, as well as determine the Bayesian sample size to estimate the parameter of the Poisson and Exponential distribution using different loss functions. [11] The research provided a general introduction to the subject and a description of the generalized modified Bessel distribution, as well as the Bayesian sample size determination to estimate the mean parameter when the prior distribution is proper and using a quadratic loss function.