On Statistical Development of Neutrosophic Gamma Distribution with Applications to Complex Data Analysis

Abstract

In the absence of a correct distribution theory for complex data, neutrosophic algebra can be very useful in quantifying uncertainty. In applied data analysis, implementation of existing gamma distribution becomes inadequate for some applications when dealing with an imprecise, uncertain, or vague dataset. Most existing works have explored distributional properties of the gamma distribution under the assumption that data do not have any kind of indeterminacy. Yet, analytical properties of the gamma model for the more realistic setting when data involved uncertainties remain largely underdeveloped. This paper fills such a gap and develops the notion of neutrosophic gamma distribution (NGD). The proposed distribution represents a generalized structure of the existing gamma distribution. The basic distributional properties, including moments, shape coefficients, and moment generating function (MGF), are established. Several examples are considered to emphasize the relevance of the proposed NGD for dealing with circumstances with inadequate or ambiguous knowledge about the distributional characteristics. The estimation framework for treating vague parameters of the NGD is developed. The Monte Carlo simulation is implemented to examine the performance of the proposed model. The proposed model is applied to a real dataset for the purpose of dealing with inaccurate and vague statistical data. Results show that the NGD has better flexibility in handling real data over the conventional gamma distribution.

A new one-parameter discrete probability distribution with its neutrosophic extension: mathematical properties and applications

“…The concept of neutrosophic probability as a function was originally presented by [ 32 ], where U is a neutrosophic sample space and defined the probability mapping to take the form where and . Furthermore, many scholars have studied various neutrosophic probability models such as Poisson, binomial, exponential, uniform, normal, Weibull, Kumaraswamy, generalized Pareto, Maxwell, Lognormal, and Gamma, see [ 2 , 9 , 11 , 23 – 25 , 29 , 31 ]. In many cases, researchers investigate goodness-of-fit tests, neutrosophic time series prediction, and modeling, such as neutrosophic logarithmic models, neutrosophic moving averages, and neutrosophic linear models, as shown in [ 3 , 10 , 13 ].…”

Truncated variable algorithm using DUS-neutrosophic Weibull distribution

“…Recently, Nayana et al [20] introduced the DUS-neutrosophic Weibull distribution and compared the performance with the DUS-Weibull distribution under CS. More information on NS can be seen in [21][22][23]. The importance of neutrosophic theory and the difference between neutrosophic theory and fuzzy set theory can be seen in [24][25][26][27][28].…”