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Abstract: The Receiver Operating Characteristic (ROC) chart is well known in medicine and machine learning. In particular the area under the ROC chart measures the probability of correct selection in a two alternative forced choice (2AFC) scenario. The gains chart is closely related to the ROC curve but carries extra information about the rate at which the classifier identifies response, information that is not carried by the ROC chart. In this note, we point out that the appropriate area under the gains chart is identical to the analogous area under the ROC chart and that the gains chart is therefor to be preferred as a summary of classifier success. Keywords: ROC curve, gains chart, 2AFC. |
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Abstract: For finding coherent and logical solution to various real life problems containing uncertainty, impreciseness and vagueness, fuzzy soft set theory is gaining importance. Later on a theoretical study of the intuitionistic fuzzy soft set was developed. The combination of intuitionistic fuzzy set and intuitionistic fuzzy soft set are more useful for application point of view in the field wherever uncertainty due to vagueness appear in more complex form. In the present communication the concepts of fuzzy soft set and Intuitionistic fuzzy soft Setare defined as hybridization of fuzzy set and soft set theory. A new method of application of intuitionistic fuzzy soft set is studied in Medical Diagnosis following Sanchez’s approach. A hypothetical case study is also discussed in brief using the proposed method. Keywords: Fuzzy set, Soft set, Fuzzy soft set, Intuitionistic fuzzy soft set, Medical documentation, Medic diagnosis. |
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Abstract: In this article, the normal distribution model (NDM) is extended. A introduction to a new Extended Normal Distribution (ENDM) and its derivate models used in many applications is proposed. The author proposes the new model (ENDM) which generalizes the normal distribution models. This class of ENDM approximates an unknown risk-neutral density. The paper discusses different properties of the ENDM. In particular, the applicability of the new model with three parameters in a way to justify the representation of combination of normal distributions is presented. The potential of the proposed distribution for modelling and analyzing statistical data with reference to extensive sets of observations. Statistical properties of the proposed distribution have also been studied. The findings of this work will be useful to practitioners in applied fields of health care. Keywords: Normal Distribution, Goodness-of-fit, Characteristics Function, Survival Function, Mixtures, Health Care. |
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Abstract: This paper considers some classical and bootstrap methods in constructing confidence intervals for the kurtosis parameter of a distribution. The bootstrap techniques used are: Bias-Corrected Standard Bootstrap, Efron’s Percentile Bootstrap, Hall’s Percentile Bootstrap and Bias-Corrected Percentile Bootstrap. The performance of these estimators is compared through confidence intervals by determining the average width and probabilities of capturing the kurtosis parameter of a distribution. We observed that the parametric method works well in terms of coverage probability when data come from a normal distribution, while the bootstrap intervals struggled in constantly reaching a 95% confidence level. When sample data are from a distribution with negative kurtosis, both parametric and bootstrap confidence intervals performed well, although we noticed that bootstrap methods tend to have shorter intervals. When it comes to positive kurtosis, bootstrap methods perform slightly better than classical methods in the sense of high coverage probability. For illustration purposes, two real life health related data are analyzed. Keywords: Beta Distribution, Bootstrap Techniques, Confidence Interval, Kurtosis Parameter, Simulation. |
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Abstract: In this article, we analyze renal failure data from patients with mesangioproliferative glomerulonephritis (MPGN) which was modeled by [1] non-parametrically using the Kaplan-Meier curve. In their work, they showed that the clinical variables, large increase serum creatinine (LISC) and systolic blood pressure >160 mmHg (SBP>160), and morphological variables, benign nephrosclerosis present (BNP) and interstitial score group 5-6 (IS5-6) were part of the variables which indicated progression to end-stage renal failure (ESRF). Though survival curves associated with these variables may be difficult to model by existing parametric distributions in literature. Therefore, we introduce a four-parameter Odd Weibull extension, the exponentiated Odd Weibull (EOW) distribution which is very versatile in modeling lifetime data that its hazard function exhibits ten different hazard shapes as well as various density shapes. Basic properties of the EOW distribution are presented. In the presence of random censoring, a small simulation study is conducted to assess the coverage probabilities of the estimated parameters of the EOW distribution using the maximum likelihood method. Our results show that the EOW distribution is very convenient and reliable to analyze the MPGN data since it provides an excellent fit for the variables LISC, SBP>160, BNP, and IS5-6. Furthermore, advantages of using the EOW distribution over the Kaplan-Meier curve are discussed. Comparisons of the EOW distribution with other Weibull-related distributions are also presented. Keywords: Coverage probability, hazard function, maximum likelihood, random censoring, survival function. |