STABILITY OF INFORMATION GRANULATION AND INFORMATION GRANULES

2002 ◽  
Vol 02 (02) ◽  
pp. 221-238
Author(s):  
WITOLD PEDRYCZ ◽  
GEORGE VUKOVICH
Keyword(s):  
Experimental Evidence ◽  
Statistical Inference ◽  
Real World ◽  
Goodness Of Fit ◽  
Broad Class ◽  
Experimental Studies ◽  
Goodness Of Fit Test ◽  
Information Granules ◽  
Information Granulation ◽  
Nonparametric Testing

In this study, we introduce a notion of stability of information granules. Granulation of information results in a series of chunks of information usually referred to as information granules. Information granules are basic building entities involved in the formation of a broad class of systems. Information granules are percepts — entities being perceived by humans as being essential when working with some real-world phenomena, especially describing and interacting with them. The percepts need to be comprehensible. They should also reflect the experimental evidence. All in all, they should be stable meaning that they are conceptual entities that reconcile experimental reality with the subjective and ultimately observer-based judgment about the environment. Once being stable, information granules could be viewed as architecture-independent. The proposed algorithmic environment supporting this concept dwells on the ideas of statistical inference that helps quantify stability through a nonparametric testing. The χ2 goodness-of-fit test is used here as a validation mechanism. First, the study elaborates on the formation of information granules and concentrates on the descriptive and prescriptive ways of their design. In the sequel, it is revealed how these two ways interact with the construction of stable information granules. A number of experimental studies are also included.

A test for fuzzy exponentiality based on Kullback-Leibler information

2021 ◽  
pp. 1-8
Author(s):  
Lingtao Kong
Keyword(s):  
Biological Sciences ◽  
Monte Carlo ◽  
Goodness Of Fit ◽  
Experimental Studies ◽  
Real Data ◽  
Test Statistics ◽  
Test Statistic ◽  
Goodness Of Fit Test ◽  
Higher Power ◽  
Leibler Information

The exponential distribution has been widely used in engineering, social and biological sciences. In this paper, we propose a new goodness-of-fit test for fuzzy exponentiality using α-pessimistic value. The test statistics is established based on Kullback-Leibler information. By using Monte Carlo method, we obtain the empirical critical points of the test statistic at four different significant levels. To evaluate the performance of the proposed test, we compare it with four commonly used tests through some simulations. Experimental studies show that the proposed test has higher power than other tests in most cases. In particular, for the uniform and linear failure rate alternatives, our method has the best performance. A real data example is investigated to show the application of our test.

Using a Five-Step Procedure for Inferential Statistical Analyses

2010 ◽  
Vol 72 (3) ◽  
pp. 186-188 ◽  
Author(s):  
Lawrence F. Kamin
Keyword(s):  
Statistical Inference ◽  
Experimental Analysis ◽  
Single Unit ◽  
Goodness Of Fit ◽  
Statistical Analyses ◽  
Introductory Biology ◽  
Goodness Of Fit Test ◽  
Chi Square ◽  
Inference Problems ◽  
Step Procedure

Many statistics texts pose inferential statistical problems in a disjointed way. By using a simple five-step procedure as a template for statistical inference problems, the student can solve problems in an organized fashion. The problem and its solution will thus be a stand-by-itself organic whole and a single unit of thought and effort. The described procedure can be used for both parametric and nonparametric inferential tests. The example given is a chi-square goodness-of-fit test of a genetics experiment involving a dihybrid cross in corn that follows a 9:3:3:1 ratio. This experimental analysis is commonly done in introductory biology labs.

The frequency goodness of fit test for probability chains

1951 ◽  
Vol 47 (1) ◽  
pp. 86-95 ◽  
Author(s):  
M. S. Bartlett
Keyword(s):  
Stochastic Processes ◽  
Statistical Inference ◽  
Goodness Of Fit ◽  
Goodness Of Fit Test ◽  
Recent Developments

1. Introduction. Following recent developments in the theory of stochastic processes, a beginning has been made by various authors with the associated problems of sampling and statistical inference as these are concerned with dependent and ordered observations, they are distinct from and usually more difficult than the corresponding problems for independent and unordered observations.

A New Growth Rate Measure in Identifying Extended Gompertz Growth Curve and Development of Goodness-of-fit Test

2021 ◽  
pp. 000806832110372
Author(s):  
Farhana Yeasmin ◽  
Ranadeep Daw ◽  
Bratati Chakraborty ◽  
Arindam Gupta ◽  
Sabyasachi Bhattacharya ◽  
...  
Keyword(s):  
Growth Rate ◽  
Growth Curve ◽  
Goodness Of Fit ◽  
Growth Models ◽  
Broad Class ◽  
Growth Dynamics ◽  
Living Organism ◽  
Fundamental Aspect ◽  
Mathematical Form ◽  
Goodness Of Fit Test

Growth is a fundamental aspect of a living organism. Growth curves play an important role in explaining the complex dynamics of growth trajectories. The development of a large class of growth models provides more choices to explain complex growth dynamics. However, identifying a suitable growth curve from a broad class of growth models becomes a challenging task. Relative Growth Rate (RGR) is the most popular measure in the growth-related study. It serves many purposes in growth curve literature, including constructing any goodness-of-fit index of some growth dynamics. However, the goodness-of-fit test based on RGR is restricted to only simple growth models. This study aims to develop a new growth rate function, instantaneous maturity rate (IMR), which can play an important role in identifying growth models. We have explored that the measure has synergy in mathematical form with IMR. However, unlike the hazard rate, IMR is a random variable when the size/RGR variable is stochastic. We have derived the exact and asymptotic distribution of this measure under the Gaussian setup of both the size and RGR variables. We have constructed a goodness-of-fit test for the extended Gompertz growth model based on the instantaneous maturity rate. We have checked the performance of the test through simulation studies as well as real data. AMS 2010 subject classifications: 62Mxx, 92Bxx, 62P10

Validation of the CASUS score in Tunisian patients: a quality management tool in intensive care units

2020 ◽  
Vol 30 (Supplement_5) ◽  
Author(s):  
T Besbes ◽  
S Mleyhi ◽  
J Sahli ◽  
M Messai ◽  
J Ziadi ◽  
...  
Keyword(s):  
Cardiac Surgery ◽  
Roc Curve ◽  
Goodness Of Fit ◽  
Cardiovascular Surgery ◽  
Management Tool ◽  
Medical Decision ◽  
Tunisian Population ◽  
Correct Classification ◽  
Goodness Of Fit Test ◽  
A Value

Abstract Background Early prediction of patients at highest risk of a poor outcome after cardiovascular surgery, including death can aid medical decision making, and adapt health care management in order to improve prognosis. In this context, we conducted this study to validate the CASUS severity score after cardiac surgery in the Tunisian population. Methods This is a retrospective cohort study conducted among patients who underwent cardiac surgery under extracorporeal circulation during the year 2018 at the Cardiovascular Surgery Department of La Rabta University Hospital in Tunisia. Data were collected from the patients hospitalization records. The discrimination of the score was assessed using the ROC curve and the calibration using the Hosmer-Lemeshow goodness of fit test and then by constructing the calibration curve. Overall correct classification was also obtained. Results In our study, the observed mortality rate was 10.52% among the 95 included patients. The discriminating power of the CASUS score was estimated by the area under the ROC curve (AUC), this scoring system had a good discrimination with AUC greater than 0.9 from postoperative Day 0 to Day 5.From postoperative day 0 to day 5, the Hosmer-Lemeshow's test gave a value of chi square test statistic ranging from 1.474 to 8.42 and a value of level of significance ranging from 0.39 to 0.99 indicating a good calibration. The overall correct classification rate from postoperative day 0 to day 5 ranged from 84.4% to 92.4%. Conclusions Despite the differences in the profile of the risk factors between the Tunisian population and the population constituting the database used to develop the CASUS score, we can say that this risk model presents acceptable performances in our population, attested by adequate discrimination and calibration. Prospective and especially multicentre studies on larger samples are needed before definitively conclude on the performance of this model in our country. Key messages The casus score seems to be valid to predict mortality among patients undergoing cardiac surgery. Multicenter study on larger sample is needed to derive and validate models able to predict in-hospitals mortality.

Goodness-of-fit test with a robustness feature

Test ◽  
2021 ◽  
Author(s):  
Jiming Jiang ◽  
Mahmoud Torabi
Keyword(s):  
Goodness Of Fit ◽  
Goodness Of Fit Test
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