Chi-square test under indeterminacy: an application using pulse count data

Background The data obtained from the counting process is known as the count data. In practice, the counting can be done at the same time or the time of the count is not the same. To test either the K counts are differed significantly or not, the Chi-square test for K counts is applied. Results The paper presents the Chi-square tests for K counts under neutrosophic statistics. The test statistic of the proposed test when K counts are recorded at the same time and different time are proposed. The testing procedure of the proposed test is explained with the help of pulse count data. Conclusions From the analysis of pulse count data, it can be concluded that the proposed test suggests the cardiologists use different treatment methods on patients. In addition, the proposed test gives more information than the traditional test under uncertainty.

Statistical Analysis for Food Quality in the Presence of Vague Information

The present study introduces the neutrosophic statistical test to see investigate the difference between variances of two populations when correlation exits in pair observations. The procedure and statistic of the proposed test under neutrosophic statistics are introduced in the paper. The application of the proposed test is given using the food industry data. The efficiency of the proposed test is compared with that of the existing test in terms of the measure of indeterminacy, flexibility, and information. From the real application and comparative studies, it is concluded that the proposed test is quite reasonable to apply in uncertainty.

Radar Circular Data Analysis Using a New Watson’s Goodness of Test under Complexity

Watson’s test is applied to test either the given angular data follows the specified distribution or not. The existing Watson’s test under classical statistics is applied when there is no uncertainty and indeterminacy in sample size or angular data. Under indeterminacy, the existing Watson’s test cannot be applied for testing purposes. Neutrosophic statistics is an alternative to classical statistics for this kind of situation. The Watson’s test under neutrosophic statistics is proposed in this paper. The test statistic of Watson’s test is introduced first. The operational procedure of the proposed Watson’s test is discussed with the help of radar data. From the data analysis and simulation study, it is concluded the proposed Watson’s test is efficient than the existing Watson’s test.

Testing Internal Quality Control of Clinical Laboratory Data Using Paired t -Test under Uncertainty

The existing paired t -test under classical statistics cannot be applied when the data is obtained from the complex process, having interval, uncertainty, indeterminacy, and incompleteness. In this paper, the modification of the paired t -test under neutrosophic statistics is proposed. The testing criterion of the proposed paired t -test is given. The application of the proposed paired t -test is given using the interval quality control of clinical laboratory data. From the analysis, it can be seen than the proposed test is quite effective and informative to apply for testing the measurement tools in the clinical laboratory.

Neutrosophic ratio-type estimators for estimating the population mean

All researches, under classical statistics, are based on determinate, crisp data to estimate the mean of the population when auxiliary information is available. Such estimates often are biased. The goal is to find the best estimates for the unknown value of the population mean with minimum mean square error (MSE). The neutrosophic statistics, generalization of classical statistics tackles vague, indeterminate, uncertain information. Thus, for the first time under neutrosophic statistics, to overcome the issues of estimation of the population mean of neutrosophic data, we have developed the neutrosophic ratio-type estimators for estimating the mean of the finite population utilizing auxiliary information. The neutrosophic observation is of the form $${Z}_{N}={Z}_{L}+{Z}_{U}{I}_{N}\, {\rm where}\, {I}_{N}\in \left[{I}_{L}, {I}_{U}\right], {Z}_{N}\in [{Z}_{l}, {Z}_{u}]$$ Z N = Z L + Z U I N where I N ∈ I L , I U , Z N ∈ [ Z l , Z u ] . The proposed estimators are very helpful to compute results when dealing with ambiguous, vague, and neutrosophic-type data. The results of these estimators are not single-valued but provide an interval form in which our population parameter may have more chance to lie. It increases the efficiency of the estimators, since we have an estimated interval that contains the unknown value of the population mean provided a minimum MSE. The efficiency of the proposed neutrosophic ratio-type estimators is also discussed using neutrosophic data of temperature and also by using simulation. A comparison is also conducted to illustrate the usefulness of Neutrosophic Ratio-type estimators over the classical estimators.

Testing the normality of heart associated variables having neutrosophic numbers

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.

A new sudden death chart for the Weibull distribution under complexity

This article presents a new control chart for monitoring reliability using sudden death testing under the neutrosophic statistics (NS). The average run lengths of the in-control and the out-of-control process have been determined for evaluating the quick detection ability for small and moderate shifts. For the industrial use, tables and figures have been presented for different parameters. The proposed control chart is efficient in comparison with the existing control chart under classical statistics and value addition in the toolkit of the quality control personnel.

Neutrosophic D’Agostino Test of Normality: An Application to Water Data

The D’Agostino test has been widely applied for testing the normality of the data. The existing D’Agostino test cannot be applied when the data have some indeterminate observations or observations which are obtained from the complex systems. In this paper, we present a D’Agostino test under neutrosophic statistics. We propose the D’Agostino test to test the normality of the data having indeterminate observations. The design of the proposed test is given and implemented with the help of real data. From the comparison, it is concluded that the proposed test is effective, adequate, and suitable to be applied in the presence of indeterminacy.

Process Monitoring for Gamma Distributed Product under Neutrosophic Statistics Using Resampling Scheme

In this article, a repetitive sampling control chart for the gamma distribution under the indeterminate environment has been presented. The control chart coefficients, probability of in-control, probability of out-of-control, and average run lengths have been determined under the assumption of the symmetrical property of the normal distribution using the neutrosophic interval method. The performance of the designed chart has been evaluated using the average run length measurements under different process settings for an indeterminate environment. In-control and out-of-control nature of the proposed chart under different levels of shifts have been described. The comparison of the proposed chart has been made with the existing chart. A real-world example from the healthcare department has been included for the practical application of the proposed chart. It has been observed from the simulation study and real example that the proposed control chart is efficient in quick monitoring of the out-of-control process. It can be concluded that the proposed control chart can be applied effectively in uncertainty.