The effect of imperfect rankings on Tsallis entropy in ranked set sampling scheme

Ranked set sampling scheme has an important role in different scientific areas. Comparison between the information contained in samples based on different sampling schemes has been widely discussed in the literature. It has been emphasized that the information contained in ranked set samples is more than that of simple random samples of the same size based on Fisher information, Shannon entropy, extropy, R & egrave;nyi and Kullback-Leibler information. According to this essay, the effect of imperfect rankings on uncertainty and information contained in samples is studied in terms of Tsallis entropy. Further, we inquire about monotonic properties under the imperfect and perfect rankings by means of stochastic orders. Tsallis entropy of simple random sampling is compared to the ranked set sampling and maximum ranked set sampling with unequal sample sizes schemes under both perfect and imperfect rankings. Finally, discrimination information of order alpha is studied between the mentioned data sets.