Abstract: In the recent era, the introduction of a new family of distributions has gotten great attention due to the curbs of the classical univariate distributions. This study introduces a novel family of distributions called a new type 1 alpha power family of distributions. Based on the novel family, a special model called a new type 1 alpha power Weibull model is studied in depth. The new model has very interesting patterns and it is very flexible. Thus, it can model the real data with the failure rate patterns of increasing, decreasing, parabola-down, and bathtub. Its applicability is studied by applying it to the health sector data, and time-to-recovery of breast cancer patients, and its performance is compared to seven well-known models. Based on the model comparison, it is the best model to fit the health-related data with no exceptional features. Furthermore, the popular models for the data with exceptional features such as correlation, overdispersion, and zero-inflation in aggregate are explored with applications to epileptic seizer data. Sometimes, these features are beyond the probability distribution models. Hence, this study has implemented eight possible models separately to these data and they are compared based on the standard techniques. Accordingly, the zero-inflated Poisson-normal-gamma model which includes the random effects in the linear predictor to handle the three features simultaneously has shown its supremacy over the others and is the best model to fit the health-related data with these features. PubDate: Thu, 31 Aug 2023 15:05:01 +000
Abstract: The linear combination of Student’s random variables (RVs) appears in many statistical applications. Unfortunately, the Student’s distribution is not closed under convolution, thus, deriving an exact and general distribution for the linear combination of Student’s RVs is infeasible, which motivates a fitting/approximation approach. Here, we focus on the scenario where the only constraint is that the number of degrees of freedom of each RV is greater than two. Notice that since the odd moments/cumulants of the Student’s distribution are zero and the even moments/cumulants do not exist when their order is greater than the number of degrees of freedom, it becomes impossible to use conventional approaches based on moments/cumulants of order one or higher than two. To circumvent this issue, herein we propose fitting such a distribution to that of a scaled Student’s RV by exploiting the second moment together with either the first absolute moment or the characteristic function (CF). For the fitting based on the absolute moment, we depart from the case of the linear combination of Student’s RVs and then generalize to through a simple iterative procedure. Meanwhile, the CF-based fitting is direct, but its accuracy (measured in terms of the Bhattacharyya distance metric) depends on the CF parameter configuration, for which we propose a simple but accurate approach. We numerically show that the CF-based fitting usually outperforms the absolute moment-based fitting and that both the scale and number of degrees of freedom of the fitting distribution increase almost linearly with . PubDate: Fri, 09 Jun 2023 06:20:01 +000
Abstract: Spatial data analysis provides valuable information to the government as well as companies. The rapid improvement of modern technology with a geographic information system (GIS) can lead to the collection and storage of more spatial data. We developed algorithms to choose optimal locations from those permanently in a space for an efficient spatial data analysis. Distances between neighboring permanent locations are not necessary to be equispaced distances. Robust and sequential methods were used to develop algorithms for design construction. The constructed designs are robust against misspecified regression responses and variance/covariance structures of responses. The proposed method can be extended for future works of image analysis which includes 3 dimensional image analysis. PubDate: Wed, 10 May 2023 02:05:01 +000
Abstract: Empirical evidence suggests that the traditional GARCH-type models are unable to accurately estimate the volatility of financial markets. To improve on the accuracy of the traditional GARCH-type models, a hybrid model (BSGARCH (1, 1)) that combines the flexibility of B-splines with the GARCH (1, 1) model has been proposed in the study. The lagged residuals from the GARCH (1, 1) model are fitted with a B-spline estimator and added to the results produced from the GARCH (1, 1) model. The proposed BSGARCH (1, 1) model was applied to simulated data and two real financial time series data (NASDAQ 100 and S&P 500). The outcome was then compared to the outcomes of the GARCH (1, 1), EGARCH (1, 1), GJR-GARCH (1, 1), and APARCH (1, 1) with different error distributions (ED) using the mean absolute percentage error (MAPE), the root mean square error (RMSE), Theil’s inequality coefficient (TIC) and QLIKE. It was concluded that the proposed BSGARCH (1, 1) model outperforms the traditional GARCH-type models that were considered in the study based on the performance metrics, and thus, it can be used for estimating volatility of stock markets. PubDate: Tue, 25 Apr 2023 05:50:01 +000
Abstract: Prostate cancer occurs when cells in the prostate gland grow out of control. Almost all prostate cancers are adenocarcinomas. The survival rate for prostate cancer patients depends on the screening outcome, which can be either no prostate cancer, early detection, and late detection or advanced stage detection. The main objective of this study was to estimate the risk factors affecting the screening outcome of prostate cancer. With ordinal outcomes, a generalized Bayesian ordinal logistic model was considered in the analysis. The generalized Bayesian ordinal logistic model helped in estimation of coefficient parameters of the risk factors affecting each level of prostate cancer-screening outcomes. In the study, positive coefficients, that is, , indicated that the higher values on the explanatory variable increased the chances of the respondent being in a higher category of the dependent variable than the current one, while the negative coefficients, that is, , signified that the higher values on the explanatory variable increased the likelihood of being in the current or lower category of prostate cancer. For instance, from the analysis, positive or negative outcomes of prostate cancer showed that an increase in weight lowered the chances of an individual having the disease. PubDate: Mon, 06 Mar 2023 08:05:02 +000
Abstract: Background. Survival analysis attracted the attention of different scientists from various domains such as engineering, health, and social sciences. It has been widely exploited in clinical trials when comparing different treatments looking at their survival probabilities. Kaplan–Meier curves plotted from the Kaplan–Meier estimates of survival probabilities are used to depict the general image for such situations. Methods. The weighted log-rank test has been dealt with by suggesting different weight functions which give specific strength in specific situations. In this work, we proposed a new weight function comprising all numbers at risk, i.e., the overall number at risk and the separate numbers at risk in the groups under study, to detect late differences between survival curves. Results. The new test has been found to be a good alternative after the FH (0, 1) test in detecting late differences, and it outperformed all tests in case of small samples and heavy censoring rates according to the simulation studies. The new test kept the same strength when applied to real data where it showed itself to be among the powerful ones or even outperforms all other tests under consideration. Conclusion. As the new test stays stronger in the case of small samples and heavy censoring rates, it may be a better choice whenever targeting the detection of late differences between the survival curves. PubDate: Wed, 01 Mar 2023 07:20:01 +000
Abstract: In the context of a sample survey, the collection of information on a sensitive variable is difficult, which may cause nonresponse and measurement errors. Due to this, the estimates can be biased and the variation may increase. To overcome this difficulty, we propose an estimator for the estimation of a sensitive variable by using auxiliary information in the presence of nonresponse and measurement errors simultaneously. The properties of the proposed estimators have been studied, and the results have been compared with those of the usual complete response estimator. Theoretical results have been verified through a simulation study using an artificial population and two real-life applications. With the outcomes of the proposed estimator, a suitable recommendation has been made to the survey statisticians for their real-life application. PubDate: Thu, 16 Feb 2023 07:05:02 +000
Open Access journal
