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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: The Poisson and the Negative Binomial distributions are commonly used as analytic tools to model count data. The Poisson is characterized by the equality of mean and variance whereas the Negative Binomial has a variance larger than the mean and therefore is appropriate to model over-dispersed count data. The Generalized Poisson Distribution is becoming a popular alternative to the Negative Binomial. We have considered inference procedures on a modified form of this distribution when two samples are available from two independent populations and the target effect size of interest is the ratio of the two population means. The statistical objective is to construct confidence limits on the ratio. We first test the presence of over dispersion and derive several estimators in the single sample situation. When two samples are available, our interest is focused on the estimation of an effect size measured by the ratio of the respective population means. We have compared two methods; namely the Fieller’s and the delta methods in terms of coverage probabilities. We have illustrated the methodologies on published genomic datasets. Keywords: Overdispersion, Parameter orthogonality, Fieller’s theorem, Mixed estimator, Delta method, Coverage probabilities. |
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Abstract: Keywords: RAPT, cross-cultural adaptation, predictive validity, logistic regression, repeated leave-one-out bootstrap. |
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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: The present study is concerned with the estimation of shape and scale parameter of Lomax distribution using Bayesian approximation techniques (Lindley’s Approximation). Different priors viz gamma, exponential and Levy priors are used to obtain the Bayes estimates of parameters of Lomax distributions under Lindley approximation technique. For comparing the efficiency of the obtained results a simulation study is carried out using R-software. Keywords: Lomax distribution, Bayesian Estimation, Prior, Loss functions, Lindley’s Approximation. /td> |