Some goodness-of-fit tests for the Poisson distribution with applications in Biodosimetry

Optimal Stein-type goodness-of-fit tests for count data

Common count distributions, such as the Poisson (binomial) distribution for unbounded (bounded) counts considered here, can be characterized by appropriate Stein identities. These identities, in turn, might be utilized to define a corresponding goodness-of-fit (GoF) test, the test statistic of which involves the computation of weighted means for a user-selected weight function f. Here, the choice of f should be done with respect to the relevant alternative scenario, as it will have great impact on the GoF-test's performance. We derive the asymptotics of both the Poisson and binomial Stein-type GoF-statistic for general count distributions (we also briefly consider the negative-binomial case), such that the asymptotic power is easily computed for arbitrary alternatives. This allows for an efficient implementation of optimal Stein tests, that is, which are most powerful within a given class  F $\mathcal {F}$ of weight functions. The performance and application of the optimal Stein-type GoF-tests is investigated by simulations and several medical data examples.

Neutrosophic F-Test for Two Counts of Data from the Poisson Distribution with Application in Climatology

This paper addresses the modification of the F-test for count data following the Poisson distribution. The F-test when the count data are expressed in intervals is considered in this paper. The proposed F-test is evaluated using real data from climatology. The comparative study showed the efficiency of the F-test for count data under neutrosophic statistics over the F-test for count data under classical statistics.

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.

Neutrosophic statistical test for counts in climatology

The existing F-test for two counts data from the Poisson distribution under classical statistics can be applied only when the counts in the data are exact or not intervals. The existing test cannot be applied when the count data is indeterminate, in the interval, and uncertain. In this paper, the F-test for two counts data from the Poisson distribution under classical statistics is designed. The test for two counts recording at the same time or different times is presented. The daily and the monthly number of records broken data in the U.S from the weather department is selected for the application of the proposed test. The application and comparison studies show the efficiency of the proposed test. The proposed test was found to be informative, flexible, and appropriate to be applied in an uncertain environment.