Statistical properties of negative binomial distribution under impressive observation

It is observed that some random variables are measured with uncertainty. In this paper, we intend to generate some properties of negative binomial distribution under imprecise measurement. These properties include fuzzy mean, fuzzy variance, fuzzy moment and fuzzy moment generating function. The uncertainty in the observations may not be addressed with the classical approach to probability distribution; therefore, fuzzy set theory helps to modify the classical approach.

Adepoju, A.A. (2018). Performance of Fuzzy Control Chart Over the Traditional Control Chart, Benin Journal of Statistics, 1(1), 101-112.

Buckley, J.J. (2006). Fuzzy Probability and Statistics, Springer, New York.

Kahraman, C. and Kabak, O. (2016). Fuzzy Statistical Decision-Making: Theory and Application, Springer, Switzerland.

Kareema, A.A. and Abdul, H.A. (2012). Fuzzy Geometric Distribution with Properties, Achieves Des Sciences, 65(2), 13-19.

Mendel, J.M., John, R.I. and Liu, F. (2006). Interval Type-2 Fuzzy Logic Systems made Simple, IEEE Transactions on Fuzzy Systems, 14(6), 808–821.

Poongodi, T. and Muthulakshmi, S. (2015). Fuzzy Control Chart for Number of Customers of E/M/1 Queuing Model, International Journal of Advanced Scientific and Technical Research, 3(5), 9–22.

Sheldon, R. (2010). A First Course in Probability (8th Ed.), Pearson Education Inc., Waterloo, Canada.

Wang, G., Xu, Y. and Qin, C. (2019). Basic Fuzzy Event Space and Probability Distribution of Probability Fuzzy Space, Mathematics, 7(542), 1-15.

Zadeh, L.A. (1971). Similarity Relations and Fuzzy Orderings, Information Sciences, 3(2), 177–200.

Zadeh, L.A. (1975). The concept of a Linguistic Variable and Its Application to Approximate Reasoning, Information Sciences, 8, 199–249.

Zadeh, L.A. (1965). Fuzzy Sets, Information and control, 8(3), 338–353