[en] The purpose of this paper is to clarify the relation between the inclusive hadron distribution in positron-electron annihilation and the parton fragmentation function, and to examine whether or not the scaling is realized in the parton fragmentation function. The inclusive single particle distribution of positron-electron annihilation process can be written in the spin 1/2 parton model. In terms of scaling variables and structure functions, the desired relation between the parton fragmentation function and the inclusive hadron spectra in the spin 1/2 parton model is obtained. The hadron distribution function can be derived. For actual calculation, the rapidity of the hadron is used for the expression of the distribution function. The calculated inclusive pion spectra are plotted and shown in a figure. The nonscaling phenomenon can be qualitatively explained by simple distribution. Though the available center-of-mass energy of the presently existing colliding beam is not enough to grow sizably the central plateau in parton fragmentation function, the nonscaling phenomenon in the small x (one of the scaling variables) can be regarded as an evidence for the existence of pionization and the approximate Feynman scaling in the rapidity variable. (Kato, T.)