On a Multivariate Analog of the Zolotarev Problem

A generalized multivariate problem due to V. M. Zolotarev is considered. Some related results on geometric random sums and (multivariate) geometric stable distributions are extended to a more general case of “anisotropic” random summation where sums of independent random vectors with multivariate random index having a special multivariate geometric distribution are considered. Anisotropic-geometric stable distributions are introduced. It is demonstrated that these distributions are coordinate-wise scale mixtures of elliptically contoured stable distributions with the Marshall–Olkin mixing distributions. The corresponding “anisotropic” analogs of multivariate Laplace, Linnik and Mittag–Leffler distributions are introduced. Some relations between these distributions are presented.

Thresholding-based White Blood Cells Segmentation from Microscopic Blood Images

Digital image processing has a significant role in different research areas, including medical image processing, object detection, biometrics, information hiding, and image compression. Image segmentation, which is one of the most important steps in processing medical image, makes the objects inside images more meaningful. For example, from microscopic images, blood cancer can be identified which is known as leukemia; for this purpose at first, the white blood cells (WBCs) need to be segmented. This paper focuses on developing a segmentation technique for segmenting WBCs from microscopic blood images based on thresholding segmentation technique and it compares with the most commonly used segmentation technique which is known as color-k-means clustering. The comparison is done based on three well-known measurements, used for evaluating segmentation techniques which are probability random index, variance of information, and global consistency error. Experimental results demonstrate that the proposed thresholding-based segmentation technique provides better results compared to color-k-means clustering technique for segmenting WBCs as well as the time consumption of the proposed technique is less than the color-k-means which are 70.8144 ms and 204.7188 ms, respectively.

Comparison of Approaches to Select a Propensity Score Matched Control Group in the Absence of an Obvious Start of Follow Up for this Group: An Example Study on the Economic Impact of the DMP Bronchial Asthma

Background Claims data are a valuable data source to investigate the economic impact of new health care services. While the date of enrollment into the new service is an obvious start of follow-up for participants, the strategy to select potential controls is not straightforward due to a missing start of follow-up to ascertain possible confounders. The aim of this study was to compare different approaches to select controls via Propensity Score Matching (PSM) using the disease management program (DMP) bronchial asthma (BA) as an example. Methods We conducted a retrospective cohort study of BA patients between 2013 and 2016 to examine total one-year health care costs and all-cause mortality. We implemented different scenarios regarding the selection of potential controls: I) allotment of a random index date with subsequent PSM, II) calendar year-based PSM (landmark analysis) and III) calendar quarter-based PSM. In scenario I, we applied 2 approaches to assign a random index date: a) assign random index date among all quarters with a BA diagnosis and b) assign random index date and thereafter examine if a BA diagnosis was documented in that quarter. Results No significant differences in total one-year health care costs between DMP BA participants and non-participants were observed in any of the scenarios. This could to some extent be explained by the higher mortality in the control groups in all scenarios. Conclusion If the loss of potential controls can be compensated, scenario Ib is a pragmatic option to select a control group. If that is not the case, scenario III is the more sophisticated approach, with the limitation that baseline characteristics prior PSM cannot be depicted and computational time or memory size needed to conduct the analysis need to be sufficient.

PROBABILITY RANDOM INDEX BASED CLUSTERING FOR SEGMENTATION OF PET-CT IMAGES

Medical image segmentation is a vital process in medical diagnosis and evaluation of tumor response to therapy. Current segmentation methods works only on single modality image like positron emission tomography has low resolution and gives only functional information; Computed Tomography has low contrast and provides structural information. This paper focus on segmentation of multimodality PET-CT image. In recent days PET-CT is advanced multimodal imaging equipment, which gives both functional and anatomical information in a single image. Probability random index is a new methodology adopted to segment the portion of an image, which is most essential for determining the actual intricacies involved in the portion of a body. The clustering is another methodology used to group similar pixel locations into a single group based on unpredictable random values of an image. The probability based clustering has been incorporated to overcome the drawbacks of existing methods of segmentation like over segmentation and under segmentation. The over segmentation has been eliminated by incorporating random values generated from the features of dataset of images. Similarly under segmentation has been eliminated by removing barriers of lack of collecting similarly values from clustering. Thus, the proposed method eliminates both over segmentation and under segmentation drawbacks of the existing methods. The proposed probability random index based clustering has yielded good results in comparision with other contemporary methods, which shall be observed from the section, results and analysis. The proposed probability random indexed clustering has yielded a good result of 88.41% on benchmark dataset.

Passive versus Active Fund Performance: Do Index Funds Have Skill?

We apply methods designed to measure mutual fund skill to a cross section of funds that is unlikely to exhibit managerial portfolio selection skill: index funds. Surprisingly, these tests imply index fund skill exists, is persistent, and is in similar proportion as in active funds. We use the distribution of passive fund performance to gauge the incremental ability of active managers. Outperformance by top active funds is lower when benchmarked to the index fund distribution and disappears when we account for residual risk. Stochastic dominance tests suggest no risk-averse investor should choose a random active fund over a random index fund.