In this paper, tests of skewness and kurtosis are introduced under neutrosophic statistics. The necessary measures and neutrosophic forms of these estimators are introduced. The application of the proposed tests is given using the data associated with heart diseases. From the real example analysis, the proposed tests are quite flexible and informative than the existing tests under classical statistics. In addition, it is concluded from the analysis that the proposed tests give information about the measure of indeterminacy in the presence of uncertainty.
MicceriT., The unicorn, the normal curve, and other improbable creatures, Psychological Bulletin105 (1989), 156.
2.
BlancaM.J., ArnauJ., López-MontielD., BonoR. and BendayanR., Skewness and kurtosis in real data samples, Methodology, (2013).
3.
HoggR.V. and ProceduresA.R., A partial review and some suggestions for future applications and theory, J Amer Statist Assoc69 (1967), 909–923.
4.
KimT.-H. and WhiteH., On more robust estimation of skewness and kurtosis, Finance Research Letters1 (2004), 56–73.
5.
BonatoM., Robust estimation of skewness and kurtosis in distributions with infinite higher moments, Finance Research Letters8 (2011), 77–87.
6.
KeselmanH., WilcoxR.R., LixL.M., AlginaJ. and FradetteK., Adaptive robust estimation and testing, British Journal of Mathematical and Statistical Psychology60 (2007), 267–293.
7.
KacprzykJ., SzmidtE., ZadrożnyS., AtanassovK.T. and KrawczakM., Advances in Fuzzy Logic and Technology 2017: Proceedings of: EUSFLAT-2017–The 10th Conference of the European Society for Fuzzy Logic and Technology, September 11–15, 2017, Warsaw, Poland IWIFSGN’2017–The Sixteenth International Workshop on Intuitionistic Fuzzy Sets and Generalized Nets, September 13–15, 2017, Warsaw, Poland: Springer, (2017).
8.
TaheriS.M. and HesamianG., Non-parametric statistical tests for fuzzy observations: fuzzy test statistic approach, International Journal of Fuzzy Logic and Intelligent Systems17 (2017), 145–153.
9.
GrzegorzewskiP., Testing statistical hypotheses with vague data, Fuzzy Sets and Systems112 (2000), 501–510.
10.
LallaM., FacchinettiG. and MastroleoG., Vagueness evaluation of the crisp output in a fuzzy inference system, Fuzzy Sets and Systems159 (2008), 3297–3312.
11.
GrzegorzewskiP., k-sample median test for vague data, International Journal of Intelligent Systems24 (2009), 529–539.
12.
GrzegorzewskiP. and ŚpiewakM., The sign test and the signed-rank test for interval-valued data, International Journal of Intelligent Systems34 (2019), 2122–2150.
13.
SmarandacheF., Neutrosophy, Neutrosophic Probability, Set, and Logic, ProQuest Information & Learning, Ann Arbor, Michigan, USA105 (1998), 118–123.
14.
HanafyI., SalamaA. and MahfouzM., Correlation coefficients of neutrosophic sets by centroid method: Infinite Study, (2013).
15.
AiwuZ., JianguoD. and HongjunG., Interval valued neutrosophic sets and multi-attribute decision-making based on generalized weighted aggregation operator, Journal of Intelligent & Fuzzy Systems29 (2015), 2697–2706.
GuoY., ŞengürA. and TianJ.-W., A novel breast ultrasound image segmentation algorithm based on neutrosophic similarity score and level set, Computer Methods and Programs in Biomedicine123 (2016), 43–53.
18.
PatroS. and SmarandacheF., The Neutrosophic Statistical Distribution, More Problems, More Solutions: Infinite Study, (2016).
19.
Abdel-BassetM., MohamedM., ZhouY. and HezamI., Multi-criteria group decision making based on neutrosophic analytic hierarchy process, Journal of Intelligent & Fuzzy Systems33 (2017), 4055–4066.
Abdel-BassetM., ZhouY., MohamedM. and ChangV., A group decision making framework based on neutrosophic VIKOR approach for e-government website evaluation, Journal of Intelligent & Fuzzy Systems34 (2018), 4213–4224.
22.
PengX. and DaiJ., Approaches to single-valued neutrosophic MADM based on MABAC, TOPSIS and new similarity measure with score function, Neural Computing and Applications29 (2018), 939–954.
23.
Abdel-BassetM., MohamedM., ElhosenyM., ChiclanaF. and ZaiedA.E.-N.H., Cosine similarity measures of bipolar neutrosophic set for diagnosis of bipolar disorder diseases, Artificial Intelligence in Medicine101 (2019), 101735.
24.
Abdel-BassetM., NabeehN.A., El-GhareebH.A. and AboelfetouhA., Utilising neutrosophic theory to solve transition difficulties of IoT-based enterprises, Enterprise Information Systems, (2019), 1–21.
25.
NabeehN.A., SmarandacheF., Abdel-BassetM., El-GhareebH.A. and AboelfetouhA., An integrated neutrosophic-topsis approach and its application to personnel selection: A new trend in brain processing and analysis, IEEE Access7 (2019), 29734–29744.
26.
HabibS., ButtM.A., AkramM. and SmarandacheF., A neutrosophic clinical decision-making system for cardiovascular diseases risk analysis, Journal of Intelligent & Fuzzy Systems (2020), 1–23.
27.
SmarandacheF., Introduction to neutrosophic statistics: Infinite Study, (2014).
28.
ChenJ., YeJ. and DuS., Scale effect and anisotropy analyzed for neutrosophic numbers of rock joint roughness coefficient based on neutrosophic statistics, Symmetry9 (2017), 208.
29.
ChenJ., YeJ., DuS. and YongR., Expressions of rock joint roughness coefficient using neutrosophic interval statistical numbers, Symmetry9 (2017), 123.
30.
AslamM. and SattamM., Analyzing Alloy Melting Points Data Using a New Mann-Whitney Test under Indeterminacy, Journal of King Saud University-Science, (2020).
31.
AslamM., Design of the Bartlett and Hartley tests for homogeneity of variances under indeterminacy environment, Journal of Taibah University for Science14 (2020), 6–10.
32.
AslamM., On detecting outliers in complex data using Dixon’s test under neutrosophic statistics, Journal of King Saud University-Science, (2020).
33.
HoggR.V., On adaptive statistical inferences, Communications in Statistics-Theory and Methods11 (1982), 2531–2542.
34.
BonoR., ArnauJ., AlarcónR. and BlancaM.J., Bias, Precision, and Accuracy of Skewness and Kurtosis Estimators for Frequently Used Continuous Distributions, Symmetry12 (2020), 19.
35.
ReedJ.III and StarkD., Hinge estimators of location: Robust to asymmetry, Computer Methods and Programs in Biomedicine49 (1996), 11–17.
36.
D’AgostinoR.B. and CuretonE.E., A class of simple linear estimators of the standard deviation of the normal distribution, Journal of the American Statistical Association68 (1973), 207–210.
37.
HoggR.V., FisherD.M. and RandlesR.H., A two-sample adaptive distribution-free test, Journal of the American Statistical Association70 (1975), 656–661.
38.
OthmanA.R., KeselmanH., WilcoxR.R., FradetteK. and PadmanabhanA., A test of symmetry, Journal of Modern Applied Statistical Methods1 (2002), 39.
39.
GioiaF. and LauroC.N., Basic statistical methods for interval data, Statistica Applicata17 (2005), 75–104.
