The development from fractal geometry to fractal statistics was established in this paper. Interesting features such as self similarity, scale invariance, and the spacefilling property of objects (fractal dimension) of fractal geometry provided an enormous groundwork to build a link towards the statistical paradigm since most data sets are endowed with its non-normal and irregular characteristic. A new probability distribution called fractal distribution was modeled to accommodate this non-normal conforming characteristic of most data sets and sample investigations were presented at the end of the paper.