Several statistical aspects of the APTGP distribution are dissected in this article. These aspects include moments, the arithmetic mean, the moment generating function, the quantile function, reliability, and the hazard function. In addition, the primary objective of this section will be to compare and contrast the suggested distribution with a number of distinct iterations of the Pareto distribution. These variants of the Pareto distribution include the Pareto distribution, the alpha-power Pareto distribution, and the generalized Pareto distribution. One actual dataset has been taken into consideration so that the effectiveness of the suggested distribution may be evaluated. In addition, the utility of the recommended distribution has been assessed and compared to other iterations of the Pareto distribution in order to determine which version is most advantageous. The comparison was made, and as a direct result of doing so, it is now plainly clear that the distribution that is currently being offered is more adaptable than the distributions that were previously provided.